diff --git a/CREDITS.md b/CREDITS.md new file mode 100644 index 00000000..4ad43a83 --- /dev/null +++ b/CREDITS.md @@ -0,0 +1,6 @@ +# Credits + +List of people who contributed to this project: + +- [Fabio Fatelli](https://github.com/ffatelli) - Simplexn +- [Emanuele Loprevite](https://github.com/EmaLoprevite) - Simplexn diff --git a/examples/psimplexn_examples.jl b/examples/psimplexn_examples.jl new file mode 100644 index 00000000..57b42497 --- /dev/null +++ b/examples/psimplexn_examples.jl @@ -0,0 +1,75 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - parallel examples --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +include("../src/psimplexn.jl") + +using Test + +VOID = [Int64[]],[[0]] # the empty simplicial model + +@time begin + +@testset "Global Examples" begin + @testset "Simplexn Examples" begin + @testset "Example 1" begin + @test plarExtrude1(([[0,0],[1,0],[2,0],[0,1],[1,1],[2,1],[0,2],[1,2],[2,2]],[[0,1,3],[1,2,4],[2,4,5],[3,4,6],[4,6,7],[5,7,8]]), repeat([1,2,-3],4)) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 0, 3], [1, 0, 3], [2, 0, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [0, 0, 6], [1, 0, 6], [2, 0, 6], [0, 1, 6], [1, 1, 6], [2, 1, 6], [0, 2, 6], [1, 2, 6], [2, 2, 6], [0, 0, 7], [1, 0, 7], [2, 0, 7], [0, 1, 7], [1, 1, 7], [2, 1, 7], [0, 2, 7], [1, 2, 7], [2, 2, 7], [0, 0, 9], [1, 0, 9], [2, 0, 9], [0, 1, 9], [1, 1, 9], [2, 1, 9], [0, 2, 9], [1, 2, 9], [2, 2, 9], [0, 0, 12], [1, 0, 12], [2, 0, 12], [0, 1, 12], [1, 1, 12], [2, 1, 12], [0, 2, 12], [1, 2, 12], [2, 2, 12], [0, 0, 13], [1, 0, 13], [2, 0, 13], [0, 1, 13], [1, 1, 13], [2, 1, 13], [0, 2, 13], [1, 2, 13], [2, 2, 13], [0, 0, 15], [1, 0, 15], [2, 0, 15], [0, 1, 15], [1, 1, 15], [2, 1, 15], [0, 2, 15], [1, 2, 15], [2, 2, 15], [0, 0, 18], [1, 0, 18], [2, 0, 18], [0, 1, 18], [1, 1, 18], [2, 1, 18], [0, 2, 18], [1, 2, 18], [2, 2, 18], [0, 0, 19], [1, 0, 19], [2, 0, 19], [0, 1, 19], [1, 1, 19], [2, 1, 19], [0, 2, 19], [1, 2, 19], [2, 2, 19], [0, 0, 21], [1, 0, 21], [2, 0, 21], [0, 1, 21], [1, 1, 21], [2, 1, 21], [0, 2, 21], [1, 2, 21], [2, 2, 21], [0, 0, 24], [1, 0, 24], [2, 0, 24], [0, 1, 24], [1, 1, 24], [2, 1, 24], [0, 2, 24], [1, 2, 24], [2, 2, 24]], [[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11], [4, 5, 11, 13], [5, 11, 13, 14], [3, 4, 6, 12], [4, 6, 12, 13], [6, 12, 13, 15], [4, 6, 7, 13], [6, 7, 13, 15], [7, 13, 15, 16], [5, 7, 8, 14], [7, 8, 14, 16], [8, 14, 16, 17], [9, 10, 12, 18], [10, 12, 18, 19], [12, 18, 19, 21], [10, 11, 13, 19], [11, 13, 19, 20], [13, 19, 20, 22], [11, 13, 14, 20], [13, 14, 20, 22], [14, 20, 22, 23], [12, 13, 15, 21], [13, 15, 21, 22], [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26], [27, 28, 30, 36], [28, 30, 36, 37], [30, 36, 37, 39], [28, 29, 31, 37], [29, 31, 37, 38], [31, 37, 38, 40], [29, 31, 32, 38], [31, 32, 38, 40], [32, 38, 40, 41], [30, 31, 33, 39], [31, 33, 39, 40], [33, 39, 40, 42], [31, 33, 34, 40], [33, 34, 40, 42], [34, 40, 42, 43], [32, 34, 35, 41], [34, 35, 41, 43], [35, 41, 43, 44], [36, 37, 39, 45], [37, 39, 45, 46], [39, 45, 46, 48], [37, 38, 40, 46], [38, 40, 46, 47], [40, 46, 47, 49], [38, 40, 41, 47], [40, 41, 47, 49], [41, 47, 49, 50], [39, 40, 42, 48], [40, 42, 48, 49], [42, 48, 49, 51], [40, 42, 43, 49], [42, 43, 49, 51], [43, 49, 51, 52], [41, 43, 44, 50], [43, 44, 50, 52], [44, 50, 52, 53], [54, 55, 57, 63], [55, 57, 63, 64], [57, 63, 64, 66], [55, 56, 58, 64], [56, 58, 64, 65], [58, 64, 65, 67], [56, 58, 59, 65], [58, 59, 65, 67], [59, 65, 67, 68], [57, 58, 60, 66], [58, 60, 66, 67], [60, 66, 67, 69], [58, 60, 61, 67], [60, 61, 67, 69], [61, 67, 69, 70], [59, 61, 62, 68], [61, 62, 68, 70], [62, 68, 70, 71], [63, 64, 66, 72], [64, 66, 72, 73], [66, 72, 73, 75], [64, 65, 67, 73], [65, 67, 73, 74], [67, 73, 74, 76], [65, 67, 68, 74], [67, 68, 74, 76], [68, 74, 76, 77], [66, 67, 69, 75], [67, 69, 75, 76], [69, 75, 76, 78], [67, 69, 70, 76], [69, 70, 76, 78], [70, 76, 78, 79], [68, 70, 71, 77], [70, 71, 77, 79], [71, 77, 79, 80], [81, 82, 84, 90], [82, 84, 90, 91], [84, 90, 91, 93], [82, 83, 85, 91], [83, 85, 91, 92], [85, 91, 92, 94], [83, 85, 86, 92], [85, 86, 92, 94], [86, 92, 94, 95], [84, 85, 87, 93], [85, 87, 93, 94], [87, 93, 94, 96], [85, 87, 88, 94], [87, 88, 94, 96], [88, 94, 96, 97], [86, 88, 89, 95], [88, 89, 95, 97], [89, 95, 97, 98], [90, 91, 93, 99], [91, 93, 99, 100], [93, 99, 100, 102], [91, 92, 94, 100], [92, 94, 100, 101], [94, 100, 101, 103], [92, 94, 95, 101], [94, 95, 101, 103], [95, 101, 103, 104], [93, 94, 96, 102], [94, 96, 102, 103], [96, 102, 103, 105], [94, 96, 97, 103], [96, 97, 103, 105], [97, 103, 105, 106], [95, 97, 98, 104], [97, 98, 104, 106], [98, 104, 106, 107]]) + end + @testset "Example 2" begin + model = plarExtrude1(VOID, repeat([1],10)) + @test model == ([[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) + + model = plarExtrude1(model, repeat([1],10)) + @test model == ([[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4], [0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [9, 6], [10, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 7], [9, 7], [10, 7], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [9, 8], [10, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10], [10, 10]], [[0, 1, 11], [1, 11, 12], [1, 2, 12], [2, 12, 13], [2, 3, 13], [3, 13, 14], [3, 4, 14], [4, 14, 15], [4, 5, 15], [5, 15, 16], [5, 6, 16], [6, 16, 17], [6, 7, 17], [7, 17, 18], [7, 8, 18], [8, 18, 19], [8, 9, 19], [9, 19, 20], [9, 10, 20], [10, 20, 21], [11, 12, 22], [12, 22, 23], [12, 13, 23], [13, 23, 24], [13, 14, 24], [14, 24, 25], [14, 15, 25], [15, 25, 26], [15, 16, 26], [16, 26, 27], [16, 17, 27], [17, 27, 28], [17, 18, 28], [18, 28, 29], [18, 19, 29], [19, 29, 30], [19, 20, 30], [20, 30, 31], [20, 21, 31], [21, 31, 32], [22, 23, 33], [23, 33, 34], [23, 24, 34], [24, 34, 35], [24, 25, 35], [25, 35, 36], [25, 26, 36], [26, 36, 37], [26, 27, 37], [27, 37, 38], [27, 28, 38], [28, 38, 39], [28, 29, 39], [29, 39, 40], [29, 30, 40], [30, 40, 41], [30, 31, 41], [31, 41, 42], [31, 32, 42], [32, 42, 43], [33, 34, 44], [34, 44, 45], [34, 35, 45], [35, 45, 46], [35, 36, 46], [36, 46, 47], [36, 37, 47], [37, 47, 48], [37, 38, 48], [38, 48, 49], [38, 39, 49], [39, 49, 50], [39, 40, 50], [40, 50, 51], [40, 41, 51], [41, 51, 52], [41, 42, 52], [42, 52, 53], [42, 43, 53], [43, 53, 54], [44, 45, 55], [45, 55, 56], [45, 46, 56], [46, 56, 57], [46, 47, 57], [47, 57, 58], [47, 48, 58], [48, 58, 59], [48, 49, 59], [49, 59, 60], [49, 50, 60], [50, 60, 61], [50, 51, 61], [51, 61, 62], [51, 52, 62], [52, 62, 63], [52, 53, 63], [53, 63, 64], [53, 54, 64], [54, 64, 65], [55, 56, 66], [56, 66, 67], [56, 57, 67], [57, 67, 68], [57, 58, 68], [58, 68, 69], [58, 59, 69], [59, 69, 70], [59, 60, 70], [60, 70, 71], [60, 61, 71], [61, 71, 72], [61, 62, 72], [62, 72, 73], [62, 63, 73], [63, 73, 74], [63, 64, 74], [64, 74, 75], [64, 65, 75], [65, 75, 76], [66, 67, 77], [67, 77, 78], [67, 68, 78], [68, 78, 79], [68, 69, 79], [69, 79, 80], [69, 70, 80], [70, 80, 81], [70, 71, 81], [71, 81, 82], [71, 72, 82], [72, 82, 83], [72, 73, 83], [73, 83, 84], [73, 74, 84], [74, 84, 85], [74, 75, 85], [75, 85, 86], [75, 76, 86], [76, 86, 87], [77, 78, 88], [78, 88, 89], [78, 79, 89], [79, 89, 90], [79, 80, 90], [80, 90, 91], [80, 81, 91], [81, 91, 92], [81, 82, 92], [82, 92, 93], [82, 83, 93], [83, 93, 94], [83, 84, 94], [84, 94, 95], [84, 85, 95], [85, 95, 96], [85, 86, 96], [86, 96, 97], [86, 87, 97], [87, 97, 98], [88, 89, 99], [89, 99, 100], [89, 90, 100], [90, 100, 101], [90, 91, 101], [91, 101, 102], [91, 92, 102], [92, 102, 103], [92, 93, 103], [93, 103, 104], [93, 94, 104], [94, 104, 105], [94, 95, 105], [95, 105, 106], [95, 96, 106], [96, 106, 107], [96, 97, 107], [97, 107, 108], [97, 98, 108], [98, 108, 109], [99, 100, 110], [100, 110, 111], [100, 101, 111], [101, 111, 112], [101, 102, 112], [102, 112, 113], [102, 103, 113], [103, 113, 114], [103, 104, 114], [104, 114, 115], [104, 105, 115], [105, 115, 116], [105, 106, 116], [106, 116, 117], [106, 107, 117], [107, 117, 118], [107, 108, 118], [108, 118, 119], [108, 109, 119], [109, 119, 120]]) + + @test plarExtrude1(model, repeat([1],10)) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [4, 0, 0], [5, 0, 0], [6, 0, 0], [7, 0, 0], [8, 0, 0], [9, 0, 0], [10, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [4, 1, 0], [5, 1, 0], [6, 1, 0], [7, 1, 0], [8, 1, 0], [9, 1, 0], [10, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [4, 2, 0], [5, 2, 0], [6, 2, 0], [7, 2, 0], [8, 2, 0], [9, 2, 0], [10, 2, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [4, 3, 0], [5, 3, 0], [6, 3, 0], [7, 3, 0], [8, 3, 0], [9, 3, 0], [10, 3, 0], [0, 4, 0], [1, 4, 0], [2, 4, 0], [3, 4, 0], [4, 4, 0], [5, 4, 0], [6, 4, 0], [7, 4, 0], [8, 4, 0], [9, 4, 0], [10, 4, 0], [0, 5, 0], [1, 5, 0], [2, 5, 0], [3, 5, 0], [4, 5, 0], [5, 5, 0], [6, 5, 0], [7, 5, 0], [8, 5, 0], [9, 5, 0], [10, 5, 0], [0, 6, 0], [1, 6, 0], [2, 6, 0], [3, 6, 0], [4, 6, 0], [5, 6, 0], [6, 6, 0], [7, 6, 0], [8, 6, 0], [9, 6, 0], [10, 6, 0], [0, 7, 0], [1, 7, 0], [2, 7, 0], [3, 7, 0], [4, 7, 0], [5, 7, 0], [6, 7, 0], [7, 7, 0], [8, 7, 0], [9, 7, 0], [10, 7, 0], [0, 8, 0], [1, 8, 0], [2, 8, 0], [3, 8, 0], [4, 8, 0], [5, 8, 0], [6, 8, 0], [7, 8, 0], [8, 8, 0], [9, 8, 0], [10, 8, 0], [0, 9, 0], [1, 9, 0], [2, 9, 0], [3, 9, 0], [4, 9, 0], [5, 9, 0], [6, 9, 0], [7, 9, 0], [8, 9, 0], [9, 9, 0], [10, 9, 0], [0, 10, 0], [1, 10, 0], [2, 10, 0], [3, 10, 0], [4, 10, 0], [5, 10, 0], [6, 10, 0], [7, 10, 0], [8, 10, 0], [9, 10, 0], [10, 10, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [4, 0, 1], [5, 0, 1], [6, 0, 1], [7, 0, 1], [8, 0, 1], [9, 0, 1], [10, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [4, 1, 1], [5, 1, 1], [6, 1, 1], [7, 1, 1], [8, 1, 1], [9, 1, 1], [10, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [4, 2, 1], [5, 2, 1], [6, 2, 1], [7, 2, 1], [8, 2, 1], [9, 2, 1], [10, 2, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [4, 3, 1], [5, 3, 1], [6, 3, 1], [7, 3, 1], [8, 3, 1], [9, 3, 1], [10, 3, 1], [0, 4, 1], [1, 4, 1], [2, 4, 1], [3, 4, 1], [4, 4, 1], [5, 4, 1], [6, 4, 1], [7, 4, 1], [8, 4, 1], [9, 4, 1], [10, 4, 1], [0, 5, 1], [1, 5, 1], [2, 5, 1], [3, 5, 1], [4, 5, 1], [5, 5, 1], [6, 5, 1], [7, 5, 1], [8, 5, 1], [9, 5, 1], [10, 5, 1], [0, 6, 1], [1, 6, 1], [2, 6, 1], [3, 6, 1], [4, 6, 1], [5, 6, 1], [6, 6, 1], [7, 6, 1], [8, 6, 1], [9, 6, 1], [10, 6, 1], [0, 7, 1], [1, 7, 1], [2, 7, 1], [3, 7, 1], [4, 7, 1], [5, 7, 1], [6, 7, 1], [7, 7, 1], [8, 7, 1], [9, 7, 1], [10, 7, 1], [0, 8, 1], [1, 8, 1], [2, 8, 1], [3, 8, 1], [4, 8, 1], [5, 8, 1], [6, 8, 1], [7, 8, 1], [8, 8, 1], [9, 8, 1], [10, 8, 1], [0, 9, 1], [1, 9, 1], [2, 9, 1], [3, 9, 1], [4, 9, 1], [5, 9, 1], [6, 9, 1], [7, 9, 1], [8, 9, 1], [9, 9, 1], [10, 9, 1], [0, 10, 1], [1, 10, 1], [2, 10, 1], [3, 10, 1], [4, 10, 1], [5, 10, 1], [6, 10, 1], [7, 10, 1], [8, 10, 1], [9, 10, 1], 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[1170, 1280, 1290, 1291], [1159, 1160, 1170, 1280], [1160, 1170, 1280, 1281], [1170, 1280, 1281, 1291], [1160, 1170, 1171, 1281], [1170, 1171, 1281, 1291], [1171, 1281, 1291, 1292], [1160, 1161, 1171, 1281], [1161, 1171, 1281, 1282], [1171, 1281, 1282, 1292], [1161, 1171, 1172, 1282], [1171, 1172, 1282, 1292], [1172, 1282, 1292, 1293], [1161, 1162, 1172, 1282], [1162, 1172, 1282, 1283], [1172, 1282, 1283, 1293], [1162, 1172, 1173, 1283], [1172, 1173, 1283, 1293], [1173, 1283, 1293, 1294], [1162, 1163, 1173, 1283], [1163, 1173, 1283, 1284], [1173, 1283, 1284, 1294], [1163, 1173, 1174, 1284], [1173, 1174, 1284, 1294], [1174, 1284, 1294, 1295], [1163, 1164, 1174, 1284], [1164, 1174, 1284, 1285], [1174, 1284, 1285, 1295], [1164, 1174, 1175, 1285], [1174, 1175, 1285, 1295], [1175, 1285, 1295, 1296], [1164, 1165, 1175, 1285], [1165, 1175, 1285, 1286], [1175, 1285, 1286, 1296], [1165, 1175, 1176, 1286], [1175, 1176, 1286, 1296], [1176, 1286, 1296, 1297], [1166, 1167, 1177, 1287], [1167, 1177, 1287, 1288], [1177, 1287, 1288, 1298], [1167, 1177, 1178, 1288], [1177, 1178, 1288, 1298], [1178, 1288, 1298, 1299], [1167, 1168, 1178, 1288], [1168, 1178, 1288, 1289], [1178, 1288, 1289, 1299], [1168, 1178, 1179, 1289], [1178, 1179, 1289, 1299], [1179, 1289, 1299, 1300], [1168, 1169, 1179, 1289], [1169, 1179, 1289, 1290], [1179, 1289, 1290, 1300], [1169, 1179, 1180, 1290], [1179, 1180, 1290, 1300], [1180, 1290, 1300, 1301], [1169, 1170, 1180, 1290], [1170, 1180, 1290, 1291], [1180, 1290, 1291, 1301], [1170, 1180, 1181, 1291], [1180, 1181, 1291, 1301], [1181, 1291, 1301, 1302], [1170, 1171, 1181, 1291], [1171, 1181, 1291, 1292], [1181, 1291, 1292, 1302], [1171, 1181, 1182, 1292], [1181, 1182, 1292, 1302], [1182, 1292, 1302, 1303], [1171, 1172, 1182, 1292], [1172, 1182, 1292, 1293], [1182, 1292, 1293, 1303], [1172, 1182, 1183, 1293], [1182, 1183, 1293, 1303], [1183, 1293, 1303, 1304], [1172, 1173, 1183, 1293], [1173, 1183, 1293, 1294], [1183, 1293, 1294, 1304], [1173, 1183, 1184, 1294], [1183, 1184, 1294, 1304], [1184, 1294, 1304, 1305], [1173, 1174, 1184, 1294], [1174, 1184, 1294, 1295], [1184, 1294, 1295, 1305], [1174, 1184, 1185, 1295], [1184, 1185, 1295, 1305], [1185, 1295, 1305, 1306], [1174, 1175, 1185, 1295], [1175, 1185, 1295, 1296], [1185, 1295, 1296, 1306], [1175, 1185, 1186, 1296], [1185, 1186, 1296, 1306], [1186, 1296, 1306, 1307], [1175, 1176, 1186, 1296], [1176, 1186, 1296, 1297], [1186, 1296, 1297, 1307], [1176, 1186, 1187, 1297], [1186, 1187, 1297, 1307], [1187, 1297, 1307, 1308], [1177, 1178, 1188, 1298], [1178, 1188, 1298, 1299], [1188, 1298, 1299, 1309], [1178, 1188, 1189, 1299], [1188, 1189, 1299, 1309], [1189, 1299, 1309, 1310], [1178, 1179, 1189, 1299], [1179, 1189, 1299, 1300], [1189, 1299, 1300, 1310], [1179, 1189, 1190, 1300], [1189, 1190, 1300, 1310], [1190, 1300, 1310, 1311], [1179, 1180, 1190, 1300], [1180, 1190, 1300, 1301], [1190, 1300, 1301, 1311], [1180, 1190, 1191, 1301], [1190, 1191, 1301, 1311], [1191, 1301, 1311, 1312], [1180, 1181, 1191, 1301], [1181, 1191, 1301, 1302], [1191, 1301, 1302, 1312], [1181, 1191, 1192, 1302], [1191, 1192, 1302, 1312], [1192, 1302, 1312, 1313], [1181, 1182, 1192, 1302], [1182, 1192, 1302, 1303], [1192, 1302, 1303, 1313], [1182, 1192, 1193, 1303], [1192, 1193, 1303, 1313], [1193, 1303, 1313, 1314], [1182, 1183, 1193, 1303], [1183, 1193, 1303, 1304], [1193, 1303, 1304, 1314], [1183, 1193, 1194, 1304], [1193, 1194, 1304, 1314], [1194, 1304, 1314, 1315], [1183, 1184, 1194, 1304], [1184, 1194, 1304, 1305], [1194, 1304, 1305, 1315], [1184, 1194, 1195, 1305], [1194, 1195, 1305, 1315], [1195, 1305, 1315, 1316], [1184, 1185, 1195, 1305], [1185, 1195, 1305, 1306], [1195, 1305, 1306, 1316], [1185, 1195, 1196, 1306], [1195, 1196, 1306, 1316], [1196, 1306, 1316, 1317], [1185, 1186, 1196, 1306], [1186, 1196, 1306, 1307], [1196, 1306, 1307, 1317], [1186, 1196, 1197, 1307], [1196, 1197, 1307, 1317], [1197, 1307, 1317, 1318], [1186, 1187, 1197, 1307], [1187, 1197, 1307, 1308], [1197, 1307, 1308, 1318], [1187, 1197, 1198, 1308], [1197, 1198, 1308, 1318], [1198, 1308, 1318, 1319], [1188, 1189, 1199, 1309], [1189, 1199, 1309, 1310], [1199, 1309, 1310, 1320], [1189, 1199, 1200, 1310], [1199, 1200, 1310, 1320], [1200, 1310, 1320, 1321], [1189, 1190, 1200, 1310], [1190, 1200, 1310, 1311], [1200, 1310, 1311, 1321], [1190, 1200, 1201, 1311], [1200, 1201, 1311, 1321], [1201, 1311, 1321, 1322], [1190, 1191, 1201, 1311], [1191, 1201, 1311, 1312], [1201, 1311, 1312, 1322], [1191, 1201, 1202, 1312], [1201, 1202, 1312, 1322], [1202, 1312, 1322, 1323], [1191, 1192, 1202, 1312], [1192, 1202, 1312, 1313], [1202, 1312, 1313, 1323], [1192, 1202, 1203, 1313], [1202, 1203, 1313, 1323], [1203, 1313, 1323, 1324], [1192, 1193, 1203, 1313], [1193, 1203, 1313, 1314], [1203, 1313, 1314, 1324], [1193, 1203, 1204, 1314], [1203, 1204, 1314, 1324], [1204, 1314, 1324, 1325], [1193, 1194, 1204, 1314], [1194, 1204, 1314, 1315], [1204, 1314, 1315, 1325], [1194, 1204, 1205, 1315], [1204, 1205, 1315, 1325], [1205, 1315, 1325, 1326], [1194, 1195, 1205, 1315], [1195, 1205, 1315, 1316], [1205, 1315, 1316, 1326], [1195, 1205, 1206, 1316], [1205, 1206, 1316, 1326], [1206, 1316, 1326, 1327], [1195, 1196, 1206, 1316], [1196, 1206, 1316, 1317], [1206, 1316, 1317, 1327], [1196, 1206, 1207, 1317], [1206, 1207, 1317, 1327], [1207, 1317, 1327, 1328], [1196, 1197, 1207, 1317], [1197, 1207, 1317, 1318], [1207, 1317, 1318, 1328], [1197, 1207, 1208, 1318], [1207, 1208, 1318, 1328], [1208, 1318, 1328, 1329], [1197, 1198, 1208, 1318], [1198, 1208, 1318, 1319], [1208, 1318, 1319, 1329], [1198, 1208, 1209, 1319], [1208, 1209, 1319, 1329], [1209, 1319, 1329, 1330]]) + end + @testset "Example 3" begin + model = plarExtrude1(VOID, repeat([1,-1],10)) + @test model == ([[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]], [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19]]) + + @test plarExtrude1(model, repeat([1],10)) == ([[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0], [20, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2], [16, 2], [17, 2], [18, 2], [19, 2], [20, 2], [0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [11, 3], [12, 3], [13, 3], [14, 3], [15, 3], [16, 3], [17, 3], [18, 3], [19, 3], [20, 3], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4], [11, 4], [12, 4], [13, 4], [14, 4], [15, 4], [16, 4], [17, 4], [18, 4], [19, 4], [20, 4], [0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5], [12, 5], [13, 5], [14, 5], [15, 5], [16, 5], [17, 5], [18, 5], [19, 5], [20, 5], [0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [9, 6], [10, 6], [11, 6], [12, 6], [13, 6], [14, 6], [15, 6], [16, 6], [17, 6], [18, 6], [19, 6], [20, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 7], [9, 7], [10, 7], [11, 7], [12, 7], [13, 7], [14, 7], [15, 7], [16, 7], [17, 7], [18, 7], [19, 7], [20, 7], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [9, 8], [10, 8], [11, 8], [12, 8], [13, 8], [14, 8], [15, 8], [16, 8], [17, 8], [18, 8], [19, 8], [20, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [16, 9], [17, 9], [18, 9], [19, 9], [20, 9], [0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10], [10, 10], [11, 10], [12, 10], [13, 10], [14, 10], [15, 10], [16, 10], [17, 10], [18, 10], [19, 10], [20, 10]], [[0, 1, 21], [1, 21, 22], [2, 3, 23], [3, 23, 24], [4, 5, 25], [5, 25, 26], [6, 7, 27], [7, 27, 28], [8, 9, 29], [9, 29, 30], [10, 11, 31], [11, 31, 32], [12, 13, 33], [13, 33, 34], [14, 15, 35], [15, 35, 36], [16, 17, 37], [17, 37, 38], [18, 19, 39], [19, 39, 40], [21, 22, 42], [22, 42, 43], [23, 24, 44], [24, 44, 45], [25, 26, 46], [26, 46, 47], [27, 28, 48], [28, 48, 49], [29, 30, 50], [30, 50, 51], [31, 32, 52], [32, 52, 53], [33, 34, 54], [34, 54, 55], [35, 36, 56], [36, 56, 57], [37, 38, 58], [38, 58, 59], [39, 40, 60], [40, 60, 61], [42, 43, 63], [43, 63, 64], [44, 45, 65], [45, 65, 66], [46, 47, 67], [47, 67, 68], [48, 49, 69], [49, 69, 70], [50, 51, 71], [51, 71, 72], [52, 53, 73], [53, 73, 74], [54, 55, 75], [55, 75, 76], [56, 57, 77], [57, 77, 78], [58, 59, 79], [59, 79, 80], [60, 61, 81], [61, 81, 82], [63, 64, 84], [64, 84, 85], [65, 66, 86], [66, 86, 87], [67, 68, 88], [68, 88, 89], [69, 70, 90], [70, 90, 91], [71, 72, 92], [72, 92, 93], [73, 74, 94], [74, 94, 95], [75, 76, 96], [76, 96, 97], [77, 78, 98], [78, 98, 99], [79, 80, 100], [80, 100, 101], [81, 82, 102], [82, 102, 103], [84, 85, 105], [85, 105, 106], [86, 87, 107], [87, 107, 108], [88, 89, 109], [89, 109, 110], [90, 91, 111], [91, 111, 112], [92, 93, 113], [93, 113, 114], [94, 95, 115], [95, 115, 116], [96, 97, 117], [97, 117, 118], [98, 99, 119], [99, 119, 120], [100, 101, 121], [101, 121, 122], [102, 103, 123], [103, 123, 124], [105, 106, 126], [106, 126, 127], [107, 108, 128], [108, 128, 129], [109, 110, 130], [110, 130, 131], [111, 112, 132], [112, 132, 133], [113, 114, 134], [114, 134, 135], [115, 116, 136], [116, 136, 137], [117, 118, 138], [118, 138, 139], [119, 120, 140], [120, 140, 141], [121, 122, 142], [122, 142, 143], [123, 124, 144], [124, 144, 145], [126, 127, 147], [127, 147, 148], [128, 129, 149], [129, 149, 150], [130, 131, 151], [131, 151, 152], [132, 133, 153], [133, 153, 154], [134, 135, 155], [135, 155, 156], [136, 137, 157], [137, 157, 158], [138, 139, 159], [139, 159, 160], [140, 141, 161], [141, 161, 162], [142, 143, 163], [143, 163, 164], [144, 145, 165], [145, 165, 166], [147, 148, 168], [148, 168, 169], [149, 150, 170], [150, 170, 171], [151, 152, 172], [152, 172, 173], [153, 154, 174], [154, 174, 175], [155, 156, 176], [156, 176, 177], [157, 158, 178], [158, 178, 179], [159, 160, 180], [160, 180, 181], [161, 162, 182], [162, 182, 183], [163, 164, 184], [164, 184, 185], [165, 166, 186], [166, 186, 187], [168, 169, 189], [169, 189, 190], [170, 171, 191], [171, 191, 192], [172, 173, 193], [173, 193, 194], [174, 175, 195], [175, 195, 196], [176, 177, 197], [177, 197, 198], [178, 179, 199], [179, 199, 200], [180, 181, 201], [181, 201, 202], [182, 183, 203], [183, 203, 204], [184, 185, 205], [185, 205, 206], [186, 187, 207], [187, 207, 208], [189, 190, 210], [190, 210, 211], [191, 192, 212], [192, 212, 213], [193, 194, 214], [194, 214, 215], [195, 196, 216], [196, 216, 217], [197, 198, 218], [198, 218, 219], [199, 200, 220], [200, 220, 221], [201, 202, 222], [202, 222, 223], [203, 204, 224], [204, 224, 225], [205, 206, 226], [206, 226, 227], [207, 208, 228], [208, 228, 229]]) + + @test plarSimplexGrid1([3,3]) == ([[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2], [0, 3], [1, 3], [2, 3], [3, 3]], [[0, 1, 4], [1, 4, 5], [1, 2, 5], [2, 5, 6], [2, 3, 6], [3, 6, 7], [4, 5, 8], [5, 8, 9], [5, 6, 9], [6, 9, 10], [6, 7, 10], [7, 10, 11], [8, 9, 12], [9, 12, 13], [9, 10, 13], [10, 13, 14], [10, 11, 14], [11, 14, 15]]) + + @test plarSimplexGrid1([2,3,4]) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [0, 0, 3], [1, 0, 3], [2, 0, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [0, 0, 4], [1, 0, 4], [2, 0, 4], [0, 1, 4], [1, 1, 4], [2, 1, 4], [0, 2, 4], [1, 2, 4], [2, 2, 4], [0, 3, 4], [1, 3, 4], [2, 3, 4]], [[0, 1, 3, 12], [1, 3, 12, 13], [3, 12, 13, 15], [1, 3, 4, 13], [3, 4, 13, 15], [4, 13, 15, 16], [1, 2, 4, 13], [2, 4, 13, 14], [4, 13, 14, 16], [2, 4, 5, 14], [4, 5, 14, 16], [5, 14, 16, 17], [3, 4, 6, 15], [4, 6, 15, 16], [6, 15, 16, 18], [4, 6, 7, 16], [6, 7, 16, 18], [7, 16, 18, 19], [4, 5, 7, 16], [5, 7, 16, 17], [7, 16, 17, 19], [5, 7, 8, 17], [7, 8, 17, 19], [8, 17, 19, 20], [6, 7, 9, 18], [7, 9, 18, 19], [9, 18, 19, 21], [7, 9, 10, 19], [9, 10, 19, 21], [10, 19, 21, 22], [7, 8, 10, 19], [8, 10, 19, 20], [10, 19, 20, 22], [8, 10, 11, 20], [10, 11, 20, 22], [11, 20, 22, 23], [12, 13, 15, 24], [13, 15, 24, 25], [15, 24, 25, 27], [13, 15, 16, 25], [15, 16, 25, 27], [16, 25, 27, 28], [13, 14, 16, 25], [14, 16, 25, 26], [16, 25, 26, 28], [14, 16, 17, 26], [16, 17, 26, 28], [17, 26, 28, 29], [15, 16, 18, 27], [16, 18, 27, 28], [18, 27, 28, 30], [16, 18, 19, 28], [18, 19, 28, 30], [19, 28, 30, 31], [16, 17, 19, 28], [17, 19, 28, 29], [19, 28, 29, 31], [17, 19, 20, 29], [19, 20, 29, 31], [20, 29, 31, 32], [18, 19, 21, 30], [19, 21, 30, 31], [21, 30, 31, 33], [19, 21, 22, 31], [21, 22, 31, 33], [22, 31, 33, 34], [19, 20, 22, 31], [20, 22, 31, 32], [22, 31, 32, 34], [20, 22, 23, 32], [22, 23, 32, 34], [23, 32, 34, 35], [24, 25, 27, 36], [25, 27, 36, 37], [27, 36, 37, 39], [25, 27, 28, 37], [27, 28, 37, 39], [28, 37, 39, 40], [25, 26, 28, 37], [26, 28, 37, 38], [28, 37, 38, 40], [26, 28, 29, 38], [28, 29, 38, 40], [29, 38, 40, 41], [27, 28, 30, 39], [28, 30, 39, 40], [30, 39, 40, 42], [28, 30, 31, 40], [30, 31, 40, 42], [31, 40, 42, 43], [28, 29, 31, 40], [29, 31, 40, 41], [31, 40, 41, 43], [29, 31, 32, 41], [31, 32, 41, 43], [32, 41, 43, 44], [30, 31, 33, 42], [31, 33, 42, 43], [33, 42, 43, 45], [31, 33, 34, 43], [33, 34, 43, 45], [34, 43, 45, 46], [31, 32, 34, 43], [32, 34, 43, 44], [34, 43, 44, 46], [32, 34, 35, 44], [34, 35, 44, 46], [35, 44, 46, 47], [36, 37, 39, 48], [37, 39, 48, 49], [39, 48, 49, 51], [37, 39, 40, 49], [39, 40, 49, 51], [40, 49, 51, 52], [37, 38, 40, 49], [38, 40, 49, 50], [40, 49, 50, 52], [38, 40, 41, 50], [40, 41, 50, 52], [41, 50, 52, 53], [39, 40, 42, 51], [40, 42, 51, 52], [42, 51, 52, 54], [40, 42, 43, 52], [42, 43, 52, 54], [43, 52, 54, 55], [40, 41, 43, 52], [41, 43, 52, 53], [43, 52, 53, 55], [41, 43, 44, 53], [43, 44, 53, 55], [44, 53, 55, 56], [42, 43, 45, 54], [43, 45, 54, 55], [45, 54, 55, 57], [43, 45, 46, 55], [45, 46, 55, 57], [46, 55, 57, 58], [43, 44, 46, 55], [44, 46, 55, 56], [46, 55, 56, 58], [44, 46, 47, 56], [46, 47, 56, 58], [47, 56, 58, 59]]) + + V, CV = plarSimplexGrid1([1,1,1]) + @test (V, CV) == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1, 2, 4], [1, 2, 4, 5], [2, 4, 5, 6], [1, 2, 3, 5], [2, 3, 5, 6], [3, 5, 6, 7]]) + + SK2 = (V,plarSimplexFacets(CV)) + @test SK2 == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1, 2], [0, 1, 4], [0, 2, 4], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 5], [1, 4, 5], [2, 3, 5], [2, 3, 6], [2, 4, 5], [2, 4, 6], [2, 5, 6], [3, 5, 6], [3, 5, 7], [3, 6, 7], [4, 5, 6], [5, 6, 7]]) + + @test (V,plarSimplexFacets(SK2[2])) == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [2, 6], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [5, 6], [5, 7], [6, 7]]) + end + end + @testset "Simplexn Tests" begin + @testset "2D example" begin + V, FV = plarSimplexGrid1([3,3]) + @test V == [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2], [0, 3], [1, 3], [2, 3], [3, 3]] + @test FV == [[0, 1, 4], [1, 4, 5], [1, 2, 5], [2, 5, 6], [2, 3, 6], [3, 6, 7], [4, 5, 8], [5, 8, 9], [5, 6, 9], [6, 9, 10], [6, 7, 10], [7, 10, 11], [8, 9, 12], [9, 12, 13], [9, 10, 13], [10, 13, 14], [10, 11, 14], [11, 14, 15]] + + @test plarSimplexFacets(FV) == [[0, 1], [0, 4], [1, 2], [1, 4], [1, 5], [2, 3], [2, 5], [2, 6], [3, 6], [3, 7], [4, 5], [4, 8], [5, 6], [5, 8], [5, 9], [6, 7], [6, 9], [6, 10], [7, 10], [7, 11], [8, 9], [8, 12], [9, 10], [9, 12], [9, 13], [10, 11], [10, 13], [10, 14], [11, 14], [11, 15], [12, 13], [13, 14], [14, 15]] + end + @testset "3D example" begin + V, CV = plarSimplexGrid1([2,2,2]) + @test V == [[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + @test CV == [[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 3, 4, 10], [3, 4, 10, 12], [4, 10, 12, 13], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11], [4, 5, 11, 13], [5, 11, 13, 14], [3, 4, 6, 12], [4, 6, 12, 13], [6, 12, 13, 15], [4, 6, 7, 13], [6, 7, 13, 15], [7, 13, 15, 16], [4, 5, 7, 13], [5, 7, 13, 14], [7, 13, 14, 16], [5, 7, 8, 14], [7, 8, 14, 16], [8, 14, 16, 17], [9, 10, 12, 18], [10, 12, 18, 19], [12, 18, 19, 21], [10, 12, 13, 19], [12, 13, 19, 21], [13, 19, 21, 22], [10, 11, 13, 19], [11, 13, 19, 20], [13, 19, 20, 22], [11, 13, 14, 20], [13, 14, 20, 22], [14, 20, 22, 23], [12, 13, 15, 21], [13, 15, 21, 22], [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [13, 14, 16, 22], [14, 16, 22, 23], [16, 22, 23, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26]] + + FV = plarSimplexFacets(CV) + @test FV == [[0, 1, 3], [0, 1, 9], [0, 3, 9], [1, 2, 4], [1, 2, 10], [1, 3, 4], [1, 3, 9], [1, 3, 10], [1, 4, 10], [1, 9, 10], [2, 4, 5], [2, 4, 10], [2, 4, 11], [2, 5, 11], [2, 10, 11], [3, 4, 6], [3, 4, 10], [3, 4, 12], [3, 6, 12], [3, 9, 10], [3, 9, 12], [3, 10, 12], [4, 5, 7], [4, 5, 11], [4, 5, 13], [4, 6, 7], [4, 6, 12], [4, 6, 13], [4, 7, 13], [4, 10, 11], [4, 10, 12], [4, 10, 13], [4, 11, 13], [4, 12, 13], [5, 7, 8], [5, 7, 13], [5, 7, 14], [5, 8, 14], [5, 11, 13], [5, 11, 14], [5, 13, 14], [6, 7, 13], [6, 7, 15], [6, 12, 13], [6, 12, 15], [6, 13, 15], [7, 8, 14], [7, 8, 16], [7, 13, 14], [7, 13, 15], [7, 13, 16], [7, 14, 16], [7, 15, 16], [8, 14, 16], [8, 14, 17], [8, 16, 17], [9, 10, 12], [9, 10, 18], [9, 12, 18], [10, 11, 13], [10, 11, 19], [10, 12, 13], [10, 12, 18], [10, 12, 19], [10, 13, 19], [10, 18, 19], [11, 13, 14], [11, 13, 19], [11, 13, 20], [11, 14, 20], [11, 19, 20], [12, 13, 15], [12, 13, 19], [12, 13, 21], [12, 15, 21], [12, 18, 19], [12, 18, 21], [12, 19, 21], [13, 14, 16], [13, 14, 20], [13, 14, 22], [13, 15, 16], [13, 15, 21], [13, 15, 22], [13, 16, 22], [13, 19, 20], [13, 19, 21], [13, 19, 22], [13, 20, 22], [13, 21, 22], [14, 16, 17], [14, 16, 22], [14, 16, 23], [14, 17, 23], [14, 20, 22], [14, 20, 23], [14, 22, 23], [15, 16, 22], [15, 16, 24], [15, 21, 22], [15, 21, 24], [15, 22, 24], [16, 17, 23], [16, 17, 25], [16, 22, 23], [16, 22, 24], [16, 22, 25], [16, 23, 25], [16, 24, 25], [17, 23, 25], [17, 23, 26], [17, 25, 26], [18, 19, 21], [19, 20, 22], [19, 21, 22], [20, 22, 23], [21, 22, 24], [22, 23, 25], [22, 24, 25], [23, 25, 26]] + + @test plarSimplexFacets(FV) == [[0, 1], [0, 3], [0, 9], [1, 2], [1, 3], [1, 4], [1, 9], [1, 10], [2, 4], [2, 5], [2, 10], [2, 11], [3, 4], [3, 6], [3, 9], [3, 10], [3, 12], [4, 5], [4, 6], [4, 7], [4, 10], [4, 11], [4, 12], [4, 13], [5, 7], [5, 8], [5, 11], [5, 13], [5, 14], [6, 7], [6, 12], [6, 13], [6, 15], [7, 8], [7, 13], [7, 14], [7, 15], [7, 16], [8, 14], [8, 16], [8, 17], [9, 10], [9, 12], [9, 18], [10, 11], [10, 12], [10, 13], [10, 18], [10, 19], [11, 13], [11, 14], [11, 19], [11, 20], [12, 13], [12, 15], [12, 18], [12, 19], [12, 21], [13, 14], [13, 15], [13, 16], [13, 19], [13, 20], [13, 21], [13, 22], [14, 16], [14, 17], [14, 20], [14, 22], [14, 23], [15, 16], [15, 21], [15, 22], [15, 24], [16, 17], [16, 22], [16, 23], [16, 24], [16, 25], [17, 23], [17, 25], [17, 26], [18, 19], [18, 21], [19, 20], [19, 21], [19, 22], [20, 22], [20, 23], [21, 22], [21, 24], [22, 23], [22, 24], [22, 25], [23, 25], [23, 26], [24, 25], [25, 26]] + end + end + @testset "quads2tria Test" begin + verts, triangles = pquads2tria(([[8.6, 7.3, 3.0], [0.0, 0.0, 3.0], [3.6, 4.3, 0.0], [8.6, 7.6, 3.0], [3.6, 4.4, 0.3], [3.5, 0.3, 3.0], [0.3, 0.3, 0.3], [0.0, 0.3, 3.0], [0.0, 7.3, 0.3], [3.6, 7.3, 2.7], [8.6, 4.4, 0.0], [6.2, 7.6, 3.0], [6.0, 7.6, 2.7], [8.9, 7.6, 3.0], [5.1, 7.6, 3.0], [3.5, 7.3, 3.0], [8.9, 0.3, 0.3], [8.6, 4.4, 3.0], [6.0, 7.6, 3.0], [0.3, 4.3, 0.3], [0.3, 0.3, 0.0], [0.0, 7.3, 3.0], [6.0, 7.3, 1.3], [6.0, 7.6, 1.3], [6.0, 7.3, 0.3], [0.0, 0.0, 0.3], [7.1, 7.6, 3.0], [7.1, 7.3, 2.7], [0.3, 7.6, 0.3], [0.0, 4.3, 3.0], [8.6, 0.3, 0.0], [8.6, 7.3, 0.0], [5.1, 7.3, 2.7], [8.9, 7.3, 3.0], [3.5, 0.3, 0.0], [8.9, 0.3, 0.0], [8.9, 4.3, 0.0], [8.9, 7.6, 0.0], [3.6, 7.3, 0.0], [5.1, 7.3, 1.3], [8.6, 4.3, 3.0], [8.9, 0.0, 3.0], [8.6, 7.3, 1.3], [3.5, 0.0, 0.3], [5.1, 7.3, 3.0], [0.0, 7.6, 0.3], [0.3, 4.4, 0.0], [6.0, 7.3, 2.7], [8.6, 4.3, 0.0], [3.6, 0.0, 0.0], [3.5, 4.4, 3.0], [3.6, 7.3, 0.3], [0.3, 7.3, 0.3], [3.5, 0.3, 0.3], [0.3, 7.6, 0.0], [3.5, 4.3, 0.3], [8.6, 4.4, 0.3], [3.6, 7.3, 1.3], [3.6, 7.6, 3.0], [5.1, 7.6, 1.3], [0.3, 4.3, 3.0], [3.5, 0.0, 0.0], [3.6, 4.4, 0.0], [7.1, 7.6, 1.3], [3.5, 7.6, 0.0], [8.6, 0.0, 0.0], [0.0, 4.4, 3.0], [0.3, 4.4, 0.3], [3.5, 4.3, 3.0], [6.2, 7.3, 1.3], [8.9, 4.4, 0.0], [8.6, 7.3, 2.7], [8.9, 0.3, 3.0], [3.5, 7.3, 0.0], [3.6, 0.3, 0.0], [6.2, 7.3, 0.3], [8.6, 7.6, 2.7], [3.6, 7.6, 0.0], [0.0, 0.3, 0.0], [8.6, 7.3, 0.3], [3.5, 7.6, 0.3], [0.0, 7.3, 0.0], [0.3, 0.0, 0.0], [7.1, 7.6, 0.3], [0.0, 4.4, 0.3], [3.6, 7.6, 1.3], [0.0, 0.0, 0.0], [8.9, 4.4, 0.3], [8.9, 7.6, 0.3], [6.2, 7.3, 3.0], [6.2, 7.3, 2.7], [7.1, 7.3, 3.0], [0.0, 7.6, 0.0], [3.5, 7.6, 3.0], [0.0, 0.3, 0.3], [7.1, 7.6, 2.7], [3.6, 7.3, 3.0], [5.1, 7.3, 0.3], [0.3, 7.3, 3.0], [6.2, 7.6, 2.7], [0.3, 7.3, 0.0], [8.9, 0.0, 0.0], [0.3, 4.3, 0.0], [0.0, 4.3, 0.0], [5.1, 7.6, 0.3], [6.2, 7.6, 1.3], [3.5, 4.3, 0.0], [8.9, 7.3, 0.0], [6.0, 7.6, 0.3], [8.9, 4.3, 0.3], [8.6, 4.3, 0.3], [8.6, 7.6, 0.0], [0.3, 4.4, 3.0], [7.1, 7.3, 0.3], [0.3, 0.0, 0.3], [0.0, 4.4, 0.0], [3.5, 4.4, 0.3], [8.6, 7.6, 1.3], [3.5, 4.4, 0.0], [3.6, 4.3, 0.3], [6.0, 7.3, 3.0], [5.1, 7.6, 2.7], [3.6, 7.6, 2.7], [6.2, 7.6, 0.3], [8.9, 0.0, 0.3], [3.5, 0.0, 3.0], [0.0, 4.3, 0.3], [0.0, 7.6, 3.0], [8.9, 7.3, 0.3], [7.1, 7.3, 1.3], [8.9, 4.3, 3.0], [3.5, 7.3, 0.3], [8.6, 7.6, 0.3], [3.6, 7.6, 0.3], [3.6, 4.4, 3.0], [0.3, 0.0, 3.0], [0.3, 0.3, 3.0], [0.3, 7.6, 3.0], [8.9, 4.4, 3.0], [3.6, 4.3, 3.0], [3.6, 0.0, 0.3], [8.6, 0.0, 3.0], [3.6, 0.3, 3.0], [8.6, 0.3, 0.3], [3.6, 0.0, 3.0], [3.6, 0.3, 0.3], [8.6, 0.3, 3.0], [8.6, 0.0, 0.3], [5.6, 0.0, 3.0], [6.6, 0.3, 3.0], [5.6, 0.3, 3.0], [5.6, 0.3, 0.3], [6.6, 0.3, 2.5], [5.6, 0.0, 2.5], [6.6, 0.0, 2.5], [5.6, 0.0, 0.3], [3.6, 0.3, 2.5], [6.6, 0.0, 0.3], [8.6, 0.3, 2.5], [8.6, 0.0, 2.5], [5.6, 0.3, 2.5], [3.6, 0.0, 2.5], [6.6, 0.3, 0.3], [6.6, 0.0, 3.0]], [[0, 3, 13, 33], [0, 3, 26, 91], [0, 17, 33, 138], [0, 17, 42, 56, 71, 79], [0, 27, 71, 91], [1, 7, 25, 94], [1, 7, 135, 136], [1, 25, 114, 135], [2, 10, 48, 62], [2, 30, 48, 74], [2, 34, 74, 106], [2, 62, 106, 118], [3, 13, 76, 88, 117, 132], [3, 26, 76, 95], [4, 9, 51, 57, 96, 134], [4, 17, 56, 134], [4, 24, 51, 56, 75, 79, 97, 113], [5, 6, 53, 136], [5, 53, 55, 68], [5, 68, 139, 142], [5, 125, 135, 136], [5, 125, 142, 144], [6, 19, 53, 55], [6, 19, 60, 136], [7, 29, 60, 136], [7, 29, 94, 126], [8, 21, 45, 127], [8, 21, 66, 84], [8, 45, 81, 92], [8, 81, 84, 115], [9, 32, 39, 57], [9, 32, 44, 96], [10, 31, 38, 62], [10, 31, 70, 107], [10, 36, 48, 70], [11, 12, 18, 99], [11, 18, 89, 120], [11, 26, 89, 91], [11, 26, 95, 99], [12, 14, 18, 121], [12, 22, 23, 47], [12, 23, 99, 105], [12, 32, 47, 121], [13, 33, 88, 128], [14, 18, 44, 120], [14, 44, 58, 96], [14, 58, 121, 122], [15, 50, 96, 134], [15, 50, 116, 131], [15, 52, 98, 131], [15, 58, 93, 96], [15, 93, 98, 137], [16, 35, 36, 109], [16, 35, 101, 124], [16, 41, 72, 124], [16, 72, 109, 130], [17, 40, 130, 138], [17, 40, 134, 139], [19, 55, 60, 68], [20, 34, 61, 82], [20, 34, 102, 106], [20, 78, 82, 86], [20, 78, 102, 103], [21, 66, 98, 112], [21, 98, 127, 137], [22, 23, 39, 59], [22, 24, 39, 97], [22, 24, 69, 75], [22, 47, 69, 90], [23, 59, 104, 108], [23, 105, 108, 123], [25, 78, 86, 94], [25, 82, 86, 114], [27, 42, 71, 129], [27, 63, 95, 129], [27, 89, 90, 91], [27, 90, 95, 99], [28, 45, 54, 92], [28, 45, 127, 137], [28, 54, 64, 80], [28, 80, 93, 137], [29, 60, 66, 112], [29, 66, 84, 126], [30, 35, 36, 48], [30, 35, 65, 101], [30, 49, 65, 74], [31, 37, 107, 111], [31, 38, 77, 111], [32, 39, 59, 121], [32, 44, 47, 120], [33, 87, 128, 138], [34, 49, 61, 74], [36, 70, 87, 109], [37, 88, 107, 128], [37, 88, 111, 132], [38, 62, 73, 118], [38, 64, 73, 77], [39, 51, 57, 97], [40, 72, 130, 146], [40, 110, 119, 139], [40, 110, 143, 146, 158], [41, 72, 141, 146], [41, 124, 141, 147, 159], [42, 79, 113, 129], [43, 49, 61, 140], [43, 61, 82, 114], [43, 114, 125, 135], [43, 125, 140, 144, 161], [46, 73, 100, 118], [46, 81, 100, 115], [46, 102, 103, 115], [46, 102, 106, 118], [47, 89, 90, 120], [49, 65, 140, 147, 155, 157], [50, 60, 68, 112], [50, 67, 112, 116], [50, 68, 134, 139], [52, 67, 98, 112], [52, 67, 116, 131], [54, 64, 73, 100], [54, 81, 92, 100], [58, 80, 85, 93, 122, 133], [59, 85, 104, 133], [59, 85, 121, 122], [63, 69, 105, 129], [63, 76, 95, 117], [63, 83, 105, 123], [63, 83, 117, 132], [64, 77, 80, 133], [65, 101, 124, 147], [69, 75, 113, 129], [69, 90, 99, 105], [70, 87, 107, 128], [77, 83, 104, 108, 111, 123, 132, 133], [78, 94, 103, 126], [84, 103, 115, 126], [87, 109, 130, 138], [110, 119, 143, 145, 151, 162], [119, 139, 142, 145, 156], [140, 153, 155, 161], [141, 146, 149, 163], [141, 154, 159, 163], [142, 144, 148, 150], [142, 150, 156, 160], [143, 152, 158, 162], [144, 148, 153, 161], [145, 151, 156, 160], [146, 149, 152, 158], [147, 154, 157, 159], [148, 149, 150, 163], [148, 153, 154, 163], [149, 150, 152, 160], [151, 153, 155, 160], [151, 155, 157, 162], [152, 153, 154, 160], [152, 154, 157, 162]])) + @test verts == [[8.6, 7.3, 3.0], [0.0, 0.0, 3.0], [3.6, 4.3, 0.0], [8.6, 7.6, 3.0], [3.6, 4.4, 0.3], [3.5, 0.3, 3.0], [0.3, 0.3, 0.3], [0.0, 0.3, 3.0], [0.0, 7.3, 0.3], [3.6, 7.3, 2.7], [8.6, 4.4, 0.0], [6.2, 7.6, 3.0], [6.0, 7.6, 2.7], [8.9, 7.6, 3.0], [5.1, 7.6, 3.0], [3.5, 7.3, 3.0], [8.9, 0.3, 0.3], [8.6, 4.4, 3.0], [6.0, 7.6, 3.0], [0.3, 4.3, 0.3], [0.3, 0.3, 0.0], [0.0, 7.3, 3.0], [6.0, 7.3, 1.3], [6.0, 7.6, 1.3], [6.0, 7.3, 0.3], [0.0, 0.0, 0.3], [7.1, 7.6, 3.0], [7.1, 7.3, 2.7], [0.3, 7.6, 0.3], [0.0, 4.3, 3.0], [8.6, 0.3, 0.0], [8.6, 7.3, 0.0], [5.1, 7.3, 2.7], [8.9, 7.3, 3.0], [3.5, 0.3, 0.0], [8.9, 0.3, 0.0], [8.9, 4.3, 0.0], [8.9, 7.6, 0.0], [3.6, 7.3, 0.0], [5.1, 7.3, 1.3], [8.6, 4.3, 3.0], [8.9, 0.0, 3.0], [8.6, 7.3, 1.3], [3.5, 0.0, 0.3], [5.1, 7.3, 3.0], 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69, 22], [232, 22, 47], [232, 47, 90], [232, 90, 69], [233, 108, 23], [233, 23, 59], [233, 59, 104], [233, 104, 108], [234, 108, 23], [234, 23, 105], [234, 105, 123], [234, 123, 108], [235, 94, 25], [235, 25, 86], [235, 86, 78], [235, 78, 94], [236, 114, 25], [236, 25, 86], [236, 86, 82], [236, 82, 114], [237, 129, 27], [237, 27, 71], [237, 71, 42], [237, 42, 129], [238, 63, 129], [238, 129, 27], [238, 27, 95], [238, 95, 63], [239, 91, 27], [239, 27, 90], [239, 90, 89], [239, 89, 91], [240, 95, 27], [240, 27, 90], [240, 90, 99], [240, 99, 95], [241, 54, 28], [241, 28, 45], [241, 45, 92], [241, 92, 54], [242, 137, 28], [242, 28, 45], [242, 45, 127], [242, 127, 137], [243, 64, 80], [243, 80, 28], [243, 28, 54], [243, 54, 64], [244, 137, 28], [244, 28, 80], [244, 80, 93], [244, 93, 137], [245, 112, 66], [245, 66, 29], [245, 29, 60], [245, 60, 112], [246, 126, 29], [246, 29, 66], [246, 66, 84], [246, 84, 126], [247, 36, 48], [247, 48, 30], [247, 30, 35], [247, 35, 36], [248, 65, 30], [248, 30, 35], [248, 35, 101], [248, 101, 65], [249, 49, 74], [249, 74, 30], [249, 30, 65], [249, 65, 49], [250, 111, 31], [250, 31, 107], [250, 107, 37], [250, 37, 111], [251, 111, 31], [251, 31, 38], [251, 38, 77], [251, 77, 111], [252, 121, 32], [252, 32, 39], [252, 39, 59], [252, 59, 121], [253, 120, 47], [253, 47, 32], [253, 32, 44], [253, 44, 120], [254, 138, 33], [254, 33, 128], [254, 128, 87], [254, 87, 138], [255, 49, 74], [255, 74, 34], [255, 34, 61], [255, 61, 49], [256, 109, 36], [256, 36, 70], [256, 70, 87], [256, 87, 109], [257, 107, 37], [257, 37, 88], [257, 88, 128], [257, 128, 107], [258, 111, 37], [258, 37, 88], [258, 88, 132], [258, 132, 111], [259, 73, 38], [259, 38, 62], [259, 62, 118], [259, 118, 73], [260, 77, 38], [260, 38, 73], [260, 73, 64], [260, 64, 77], [261, 97, 39], [261, 39, 57], [261, 57, 51], [261, 51, 97], [262, 72, 146], [262, 146, 40], [262, 40, 130], [262, 130, 72], [263, 119, 139], [263, 139, 40], [263, 40, 110], [263, 110, 119], [264, 158, 146], [264, 146, 40], [264, 40, 110], [264, 110, 143], [264, 143, 158], [265, 141, 41], [265, 41, 72], [265, 72, 146], [265, 146, 141], [266, 159, 141], [266, 141, 41], [266, 41, 124], [266, 124, 147], [266, 147, 159], [267, 113, 129], [267, 129, 42], [267, 42, 79], [267, 79, 113], [268, 49, 140], [268, 140, 43], [268, 43, 61], [268, 61, 49], [269, 82, 114], [269, 114, 43], [269, 43, 61], [269, 61, 82], [270, 125, 43], [270, 43, 114], [270, 114, 135], [270, 135, 125], [271, 161, 140], [271, 140, 43], [271, 43, 125], [271, 125, 144], [271, 144, 161], [272, 118, 46], [272, 46, 100], [272, 100, 73], [272, 73, 118], [273, 115, 46], [273, 46, 100], [273, 100, 81], [273, 81, 115], [274, 115, 46], [274, 46, 102], [274, 102, 103], [274, 103, 115], [275, 118, 46], [275, 46, 102], [275, 102, 106], [275, 106, 118], [276, 120, 47], [276, 47, 90], [276, 90, 89], [276, 89, 120], [277, 157, 155], [277, 155, 140], [277, 140, 49], [277, 49, 65], [277, 65, 147], [277, 147, 157], [278, 112, 50], [278, 50, 68], [278, 68, 60], [278, 60, 112], [279, 116, 50], [279, 50, 112], [279, 112, 67], [279, 67, 116], [280, 134, 50], [280, 50, 68], [280, 68, 139], [280, 139, 134], [281, 112, 98], [281, 98, 52], [281, 52, 67], [281, 67, 112], [282, 131, 52], [282, 52, 67], [282, 67, 116], [282, 116, 131], [283, 100, 54], [283, 54, 64], [283, 64, 73], [283, 73, 100], [284, 100, 54], [284, 54, 92], [284, 92, 81], [284, 81, 100], [285, 133, 85], [285, 85, 122], [285, 122, 58], [285, 58, 93], [285, 93, 80], [285, 80, 133], [286, 104, 59], [286, 59, 85], [286, 85, 133], [286, 133, 104], [287, 121, 59], [287, 59, 85], [287, 85, 122], [287, 122, 121], [288, 129, 63], [288, 63, 105], [288, 105, 69], [288, 69, 129], [289, 76, 117], [289, 117, 63], [289, 63, 95], [289, 95, 76], [290, 123, 105], [290, 105, 63], [290, 63, 83], [290, 83, 123], [291, 132, 117], [291, 117, 63], [291, 63, 83], [291, 83, 132], [292, 80, 64], [292, 64, 77], [292, 77, 133], [292, 133, 80], [293, 147, 65], [293, 65, 101], [293, 101, 124], [293, 124, 147], [294, 113, 129], [294, 129, 69], [294, 69, 75], [294, 75, 113], [295, 105, 69], [295, 69, 90], [295, 90, 99], [295, 99, 105], [296, 107, 70], [296, 70, 87], [296, 87, 128], [296, 128, 107], [297, 123, 108], [297, 108, 104], [297, 104, 133], [297, 133, 77], [297, 77, 111], [297, 111, 132], [297, 132, 83], [297, 83, 123], [298, 126, 103], [298, 103, 78], [298, 78, 94], [298, 94, 126], [299, 103, 126], [299, 126, 84], [299, 84, 115], [299, 115, 103], [300, 138, 87], [300, 87, 109], [300, 109, 130], [300, 130, 138], [301, 151, 162], [301, 162, 143], [301, 143, 110], [301, 110, 119], [301, 119, 145], [301, 145, 151], [302, 156, 145], [302, 145, 119], [302, 119, 139], [302, 139, 142], [302, 142, 156], [303, 161, 140], [303, 140, 155], [303, 155, 153], [303, 153, 161], [304, 149, 163], [304, 163, 141], [304, 141, 146], [304, 146, 149], [305, 163, 141], [305, 141, 159], [305, 159, 154], [305, 154, 163], [306, 148, 150], [306, 150, 142], [306, 142, 144], [306, 144, 148], [307, 160, 156], [307, 156, 142], [307, 142, 150], [307, 150, 160], [308, 152, 162], [308, 162, 143], [308, 143, 158], [308, 158, 152], [309, 153, 161], [309, 161, 144], [309, 144, 148], [309, 148, 153], [310, 156, 145], [310, 145, 151], [310, 151, 160], [310, 160, 156], [311, 158, 146], [311, 146, 149], [311, 149, 152], [311, 152, 158], [312, 159, 147], [312, 147, 157], [312, 157, 154], [312, 154, 159], [313, 149, 163], [313, 163, 148], [313, 148, 150], [313, 150, 149], [314, 163, 148], [314, 148, 153], [314, 153, 154], [314, 154, 163], [315, 152, 149], [315, 149, 150], [315, 150, 160], [315, 160, 152], [316, 160, 151], [316, 151, 155], [316, 155, 153], [316, 153, 160], [317, 157, 162], [317, 162, 151], [317, 151, 155], [317, 155, 157], [318, 153, 160], [318, 160, 152], [318, 152, 154], [318, 154, 153], [319, 162, 152], [319, 152, 154], [319, 154, 157], [319, 157, 162]] + @test Set(triangles) == Set(trianglesPy) + end +end + +end diff --git a/examples/simplexn-serial_examples.jl b/examples/simplexn-serial_examples.jl new file mode 100644 index 00000000..69f4c39a --- /dev/null +++ b/examples/simplexn-serial_examples.jl @@ -0,0 +1,75 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - serial examples --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +include("../src/simplexn-serial.jl") + +using Test + +VOID = [Int64[]],[[0]] # the empty simplicial model + +@time begin + +@testset "Global Examples" begin + @testset "Simplexn Examples" begin + @testset "Example 1" begin + @test larExtrude1(([[0,0],[1,0],[2,0],[0,1],[1,1],[2,1],[0,2],[1,2],[2,2]],[[0,1,3],[1,2,4],[2,4,5],[3,4,6],[4,6,7],[5,7,8]]), repeat([1,2,-3],4)) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 0, 3], [1, 0, 3], [2, 0, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [0, 0, 6], [1, 0, 6], [2, 0, 6], [0, 1, 6], [1, 1, 6], [2, 1, 6], [0, 2, 6], [1, 2, 6], [2, 2, 6], [0, 0, 7], [1, 0, 7], [2, 0, 7], [0, 1, 7], [1, 1, 7], [2, 1, 7], [0, 2, 7], [1, 2, 7], [2, 2, 7], [0, 0, 9], [1, 0, 9], [2, 0, 9], [0, 1, 9], [1, 1, 9], [2, 1, 9], [0, 2, 9], [1, 2, 9], [2, 2, 9], [0, 0, 12], [1, 0, 12], [2, 0, 12], [0, 1, 12], [1, 1, 12], [2, 1, 12], [0, 2, 12], [1, 2, 12], [2, 2, 12], [0, 0, 13], [1, 0, 13], [2, 0, 13], [0, 1, 13], [1, 1, 13], [2, 1, 13], [0, 2, 13], [1, 2, 13], [2, 2, 13], [0, 0, 15], [1, 0, 15], [2, 0, 15], [0, 1, 15], [1, 1, 15], [2, 1, 15], [0, 2, 15], [1, 2, 15], [2, 2, 15], [0, 0, 18], [1, 0, 18], [2, 0, 18], [0, 1, 18], [1, 1, 18], [2, 1, 18], [0, 2, 18], [1, 2, 18], [2, 2, 18], [0, 0, 19], [1, 0, 19], [2, 0, 19], [0, 1, 19], [1, 1, 19], [2, 1, 19], [0, 2, 19], [1, 2, 19], [2, 2, 19], [0, 0, 21], [1, 0, 21], [2, 0, 21], [0, 1, 21], [1, 1, 21], [2, 1, 21], [0, 2, 21], [1, 2, 21], [2, 2, 21], [0, 0, 24], [1, 0, 24], [2, 0, 24], [0, 1, 24], [1, 1, 24], [2, 1, 24], [0, 2, 24], [1, 2, 24], [2, 2, 24]], [[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11], [4, 5, 11, 13], [5, 11, 13, 14], [3, 4, 6, 12], [4, 6, 12, 13], [6, 12, 13, 15], [4, 6, 7, 13], [6, 7, 13, 15], [7, 13, 15, 16], [5, 7, 8, 14], [7, 8, 14, 16], [8, 14, 16, 17], [9, 10, 12, 18], [10, 12, 18, 19], [12, 18, 19, 21], [10, 11, 13, 19], [11, 13, 19, 20], [13, 19, 20, 22], [11, 13, 14, 20], [13, 14, 20, 22], [14, 20, 22, 23], [12, 13, 15, 21], [13, 15, 21, 22], [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26], [27, 28, 30, 36], [28, 30, 36, 37], [30, 36, 37, 39], [28, 29, 31, 37], [29, 31, 37, 38], [31, 37, 38, 40], [29, 31, 32, 38], [31, 32, 38, 40], [32, 38, 40, 41], [30, 31, 33, 39], [31, 33, 39, 40], [33, 39, 40, 42], [31, 33, 34, 40], [33, 34, 40, 42], [34, 40, 42, 43], [32, 34, 35, 41], [34, 35, 41, 43], [35, 41, 43, 44], [36, 37, 39, 45], [37, 39, 45, 46], [39, 45, 46, 48], [37, 38, 40, 46], [38, 40, 46, 47], [40, 46, 47, 49], [38, 40, 41, 47], [40, 41, 47, 49], [41, 47, 49, 50], [39, 40, 42, 48], [40, 42, 48, 49], [42, 48, 49, 51], [40, 42, 43, 49], [42, 43, 49, 51], [43, 49, 51, 52], [41, 43, 44, 50], [43, 44, 50, 52], [44, 50, 52, 53], [54, 55, 57, 63], [55, 57, 63, 64], [57, 63, 64, 66], [55, 56, 58, 64], [56, 58, 64, 65], [58, 64, 65, 67], [56, 58, 59, 65], [58, 59, 65, 67], [59, 65, 67, 68], [57, 58, 60, 66], [58, 60, 66, 67], [60, 66, 67, 69], [58, 60, 61, 67], [60, 61, 67, 69], [61, 67, 69, 70], [59, 61, 62, 68], [61, 62, 68, 70], [62, 68, 70, 71], [63, 64, 66, 72], [64, 66, 72, 73], [66, 72, 73, 75], [64, 65, 67, 73], [65, 67, 73, 74], [67, 73, 74, 76], [65, 67, 68, 74], [67, 68, 74, 76], [68, 74, 76, 77], [66, 67, 69, 75], [67, 69, 75, 76], [69, 75, 76, 78], [67, 69, 70, 76], [69, 70, 76, 78], [70, 76, 78, 79], [68, 70, 71, 77], [70, 71, 77, 79], [71, 77, 79, 80], [81, 82, 84, 90], [82, 84, 90, 91], [84, 90, 91, 93], [82, 83, 85, 91], [83, 85, 91, 92], [85, 91, 92, 94], [83, 85, 86, 92], [85, 86, 92, 94], [86, 92, 94, 95], [84, 85, 87, 93], [85, 87, 93, 94], [87, 93, 94, 96], [85, 87, 88, 94], [87, 88, 94, 96], [88, 94, 96, 97], [86, 88, 89, 95], [88, 89, 95, 97], [89, 95, 97, 98], [90, 91, 93, 99], [91, 93, 99, 100], [93, 99, 100, 102], [91, 92, 94, 100], [92, 94, 100, 101], [94, 100, 101, 103], [92, 94, 95, 101], [94, 95, 101, 103], [95, 101, 103, 104], [93, 94, 96, 102], [94, 96, 102, 103], [96, 102, 103, 105], [94, 96, 97, 103], [96, 97, 103, 105], [97, 103, 105, 106], [95, 97, 98, 104], [97, 98, 104, 106], [98, 104, 106, 107]]) + end + @testset "Example 2" begin + model = larExtrude1(VOID, repeat([1],10)) + @test model == ([[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) + + model = larExtrude1(model, repeat([1],10)) + @test model == ([[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4], [0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [9, 6], [10, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 7], [9, 7], [10, 7], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [9, 8], [10, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10], [10, 10]], [[0, 1, 11], [1, 11, 12], [1, 2, 12], [2, 12, 13], [2, 3, 13], [3, 13, 14], [3, 4, 14], [4, 14, 15], [4, 5, 15], [5, 15, 16], [5, 6, 16], [6, 16, 17], [6, 7, 17], [7, 17, 18], [7, 8, 18], [8, 18, 19], [8, 9, 19], [9, 19, 20], [9, 10, 20], [10, 20, 21], [11, 12, 22], [12, 22, 23], [12, 13, 23], [13, 23, 24], [13, 14, 24], [14, 24, 25], [14, 15, 25], [15, 25, 26], [15, 16, 26], [16, 26, 27], [16, 17, 27], [17, 27, 28], [17, 18, 28], [18, 28, 29], [18, 19, 29], [19, 29, 30], [19, 20, 30], [20, 30, 31], [20, 21, 31], [21, 31, 32], [22, 23, 33], [23, 33, 34], [23, 24, 34], [24, 34, 35], [24, 25, 35], [25, 35, 36], [25, 26, 36], [26, 36, 37], [26, 27, 37], [27, 37, 38], [27, 28, 38], [28, 38, 39], [28, 29, 39], [29, 39, 40], [29, 30, 40], [30, 40, 41], [30, 31, 41], [31, 41, 42], [31, 32, 42], [32, 42, 43], [33, 34, 44], [34, 44, 45], [34, 35, 45], [35, 45, 46], [35, 36, 46], [36, 46, 47], [36, 37, 47], [37, 47, 48], [37, 38, 48], [38, 48, 49], [38, 39, 49], [39, 49, 50], [39, 40, 50], [40, 50, 51], [40, 41, 51], [41, 51, 52], [41, 42, 52], [42, 52, 53], [42, 43, 53], [43, 53, 54], [44, 45, 55], [45, 55, 56], [45, 46, 56], [46, 56, 57], [46, 47, 57], [47, 57, 58], [47, 48, 58], [48, 58, 59], [48, 49, 59], [49, 59, 60], [49, 50, 60], [50, 60, 61], [50, 51, 61], [51, 61, 62], [51, 52, 62], [52, 62, 63], [52, 53, 63], [53, 63, 64], [53, 54, 64], [54, 64, 65], [55, 56, 66], [56, 66, 67], [56, 57, 67], [57, 67, 68], [57, 58, 68], [58, 68, 69], [58, 59, 69], [59, 69, 70], [59, 60, 70], [60, 70, 71], [60, 61, 71], [61, 71, 72], [61, 62, 72], [62, 72, 73], [62, 63, 73], [63, 73, 74], [63, 64, 74], [64, 74, 75], [64, 65, 75], [65, 75, 76], [66, 67, 77], [67, 77, 78], [67, 68, 78], [68, 78, 79], [68, 69, 79], [69, 79, 80], [69, 70, 80], [70, 80, 81], [70, 71, 81], [71, 81, 82], [71, 72, 82], [72, 82, 83], [72, 73, 83], [73, 83, 84], [73, 74, 84], [74, 84, 85], [74, 75, 85], [75, 85, 86], [75, 76, 86], [76, 86, 87], [77, 78, 88], [78, 88, 89], [78, 79, 89], [79, 89, 90], [79, 80, 90], [80, 90, 91], [80, 81, 91], [81, 91, 92], [81, 82, 92], [82, 92, 93], [82, 83, 93], [83, 93, 94], [83, 84, 94], [84, 94, 95], [84, 85, 95], [85, 95, 96], [85, 86, 96], [86, 96, 97], [86, 87, 97], [87, 97, 98], [88, 89, 99], [89, 99, 100], [89, 90, 100], [90, 100, 101], [90, 91, 101], [91, 101, 102], [91, 92, 102], [92, 102, 103], [92, 93, 103], [93, 103, 104], [93, 94, 104], [94, 104, 105], [94, 95, 105], [95, 105, 106], [95, 96, 106], [96, 106, 107], [96, 97, 107], [97, 107, 108], [97, 98, 108], [98, 108, 109], [99, 100, 110], [100, 110, 111], [100, 101, 111], [101, 111, 112], [101, 102, 112], [102, 112, 113], [102, 103, 113], [103, 113, 114], [103, 104, 114], [104, 114, 115], [104, 105, 115], [105, 115, 116], [105, 106, 116], [106, 116, 117], [106, 107, 117], [107, 117, 118], [107, 108, 118], [108, 118, 119], [108, 109, 119], [109, 119, 120]]) + + @test larExtrude1(model, repeat([1],10)) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [4, 0, 0], [5, 0, 0], [6, 0, 0], [7, 0, 0], [8, 0, 0], [9, 0, 0], [10, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [4, 1, 0], [5, 1, 0], [6, 1, 0], [7, 1, 0], [8, 1, 0], [9, 1, 0], [10, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [4, 2, 0], [5, 2, 0], [6, 2, 0], [7, 2, 0], [8, 2, 0], [9, 2, 0], [10, 2, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [4, 3, 0], [5, 3, 0], [6, 3, 0], [7, 3, 0], [8, 3, 0], [9, 3, 0], [10, 3, 0], [0, 4, 0], [1, 4, 0], [2, 4, 0], [3, 4, 0], [4, 4, 0], [5, 4, 0], [6, 4, 0], [7, 4, 0], [8, 4, 0], [9, 4, 0], [10, 4, 0], [0, 5, 0], [1, 5, 0], [2, 5, 0], [3, 5, 0], [4, 5, 0], [5, 5, 0], [6, 5, 0], [7, 5, 0], [8, 5, 0], [9, 5, 0], [10, 5, 0], [0, 6, 0], [1, 6, 0], [2, 6, 0], [3, 6, 0], [4, 6, 0], [5, 6, 0], [6, 6, 0], [7, 6, 0], [8, 6, 0], [9, 6, 0], [10, 6, 0], [0, 7, 0], [1, 7, 0], [2, 7, 0], [3, 7, 0], [4, 7, 0], [5, 7, 0], [6, 7, 0], [7, 7, 0], [8, 7, 0], [9, 7, 0], [10, 7, 0], [0, 8, 0], [1, 8, 0], [2, 8, 0], [3, 8, 0], [4, 8, 0], [5, 8, 0], [6, 8, 0], [7, 8, 0], [8, 8, 0], [9, 8, 0], [10, 8, 0], [0, 9, 0], [1, 9, 0], [2, 9, 0], [3, 9, 0], [4, 9, 0], [5, 9, 0], [6, 9, 0], [7, 9, 0], [8, 9, 0], [9, 9, 0], [10, 9, 0], [0, 10, 0], [1, 10, 0], [2, 10, 0], [3, 10, 0], [4, 10, 0], [5, 10, 0], [6, 10, 0], [7, 10, 0], [8, 10, 0], [9, 10, 0], [10, 10, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [4, 0, 1], [5, 0, 1], [6, 0, 1], [7, 0, 1], [8, 0, 1], [9, 0, 1], [10, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [4, 1, 1], [5, 1, 1], [6, 1, 1], [7, 1, 1], [8, 1, 1], [9, 1, 1], [10, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [4, 2, 1], [5, 2, 1], [6, 2, 1], [7, 2, 1], [8, 2, 1], [9, 2, 1], [10, 2, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [4, 3, 1], [5, 3, 1], [6, 3, 1], [7, 3, 1], [8, 3, 1], [9, 3, 1], [10, 3, 1], [0, 4, 1], [1, 4, 1], [2, 4, 1], [3, 4, 1], [4, 4, 1], [5, 4, 1], [6, 4, 1], [7, 4, 1], [8, 4, 1], [9, 4, 1], [10, 4, 1], [0, 5, 1], [1, 5, 1], [2, 5, 1], [3, 5, 1], [4, 5, 1], [5, 5, 1], [6, 5, 1], [7, 5, 1], [8, 5, 1], [9, 5, 1], [10, 5, 1], [0, 6, 1], [1, 6, 1], [2, 6, 1], [3, 6, 1], [4, 6, 1], [5, 6, 1], [6, 6, 1], [7, 6, 1], [8, 6, 1], [9, 6, 1], [10, 6, 1], [0, 7, 1], [1, 7, 1], [2, 7, 1], [3, 7, 1], [4, 7, 1], [5, 7, 1], [6, 7, 1], [7, 7, 1], [8, 7, 1], [9, 7, 1], [10, 7, 1], [0, 8, 1], [1, 8, 1], [2, 8, 1], [3, 8, 1], [4, 8, 1], [5, 8, 1], [6, 8, 1], [7, 8, 1], [8, 8, 1], [9, 8, 1], [10, 8, 1], [0, 9, 1], [1, 9, 1], [2, 9, 1], [3, 9, 1], [4, 9, 1], [5, 9, 1], [6, 9, 1], [7, 9, 1], [8, 9, 1], [9, 9, 1], [10, 9, 1], [0, 10, 1], [1, 10, 1], [2, 10, 1], [3, 10, 1], [4, 10, 1], [5, 10, 1], [6, 10, 1], [7, 10, 1], [8, 10, 1], [9, 10, 1], [10, 10, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [4, 0, 2], [5, 0, 2], [6, 0, 2], [7, 0, 2], [8, 0, 2], [9, 0, 2], [10, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [4, 1, 2], [5, 1, 2], [6, 1, 2], [7, 1, 2], [8, 1, 2], [9, 1, 2], [10, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [4, 2, 2], [5, 2, 2], [6, 2, 2], [7, 2, 2], [8, 2, 2], [9, 2, 2], [10, 2, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [4, 3, 2], [5, 3, 2], [6, 3, 2], [7, 3, 2], [8, 3, 2], [9, 3, 2], [10, 3, 2], [0, 4, 2], [1, 4, 2], [2, 4, 2], [3, 4, 2], [4, 4, 2], [5, 4, 2], [6, 4, 2], [7, 4, 2], [8, 4, 2], [9, 4, 2], [10, 4, 2], [0, 5, 2], [1, 5, 2], [2, 5, 2], [3, 5, 2], [4, 5, 2], [5, 5, 2], [6, 5, 2], [7, 5, 2], [8, 5, 2], [9, 5, 2], [10, 5, 2], [0, 6, 2], [1, 6, 2], [2, 6, 2], [3, 6, 2], [4, 6, 2], [5, 6, 2], [6, 6, 2], [7, 6, 2], [8, 6, 2], [9, 6, 2], [10, 6, 2], [0, 7, 2], [1, 7, 2], [2, 7, 2], [3, 7, 2], [4, 7, 2], [5, 7, 2], [6, 7, 2], [7, 7, 2], [8, 7, 2], [9, 7, 2], [10, 7, 2], [0, 8, 2], [1, 8, 2], [2, 8, 2], [3, 8, 2], [4, 8, 2], [5, 8, 2], [6, 8, 2], [7, 8, 2], [8, 8, 2], [9, 8, 2], [10, 8, 2], [0, 9, 2], [1, 9, 2], [2, 9, 2], [3, 9, 2], [4, 9, 2], [5, 9, 2], [6, 9, 2], [7, 9, 2], [8, 9, 2], [9, 9, 2], [10, 9, 2], [0, 10, 2], [1, 10, 2], [2, 10, 2], [3, 10, 2], [4, 10, 2], [5, 10, 2], [6, 10, 2], [7, 10, 2], [8, 10, 2], [9, 10, 2], [10, 10, 2], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [4, 0, 3], [5, 0, 3], [6, 0, 3], [7, 0, 3], [8, 0, 3], [9, 0, 3], [10, 0, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [4, 1, 3], [5, 1, 3], [6, 1, 3], [7, 1, 3], [8, 1, 3], [9, 1, 3], [10, 1, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [4, 2, 3], [5, 2, 3], [6, 2, 3], [7, 2, 3], [8, 2, 3], [9, 2, 3], [10, 2, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3], [4, 3, 3], [5, 3, 3], [6, 3, 3], [7, 3, 3], [8, 3, 3], [9, 3, 3], [10, 3, 3], [0, 4, 3], [1, 4, 3], [2, 4, 3], [3, 4, 3], [4, 4, 3], [5, 4, 3], [6, 4, 3], [7, 4, 3], [8, 4, 3], [9, 4, 3], [10, 4, 3], [0, 5, 3], [1, 5, 3], [2, 5, 3], [3, 5, 3], [4, 5, 3], [5, 5, 3], [6, 5, 3], [7, 5, 3], [8, 5, 3], [9, 5, 3], [10, 5, 3], [0, 6, 3], [1, 6, 3], [2, 6, 3], [3, 6, 3], [4, 6, 3], [5, 6, 3], [6, 6, 3], [7, 6, 3], [8, 6, 3], [9, 6, 3], [10, 6, 3], [0, 7, 3], [1, 7, 3], [2, 7, 3], [3, 7, 3], [4, 7, 3], [5, 7, 3], [6, 7, 3], [7, 7, 3], [8, 7, 3], [9, 7, 3], [10, 7, 3], [0, 8, 3], [1, 8, 3], [2, 8, 3], [3, 8, 3], [4, 8, 3], [5, 8, 3], [6, 8, 3], [7, 8, 3], [8, 8, 3], [9, 8, 3], [10, 8, 3], [0, 9, 3], [1, 9, 3], [2, 9, 3], [3, 9, 3], [4, 9, 3], [5, 9, 3], [6, 9, 3], [7, 9, 3], [8, 9, 3], [9, 9, 3], [10, 9, 3], [0, 10, 3], [1, 10, 3], [2, 10, 3], [3, 10, 3], [4, 10, 3], [5, 10, 3], [6, 10, 3], [7, 10, 3], [8, 10, 3], [9, 10, 3], [10, 10, 3], [0, 0, 4], [1, 0, 4], [2, 0, 4], [3, 0, 4], [4, 0, 4], [5, 0, 4], [6, 0, 4], [7, 0, 4], [8, 0, 4], [9, 0, 4], [10, 0, 4], [0, 1, 4], [1, 1, 4], [2, 1, 4], [3, 1, 4], [4, 1, 4], [5, 1, 4], [6, 1, 4], [7, 1, 4], [8, 1, 4], [9, 1, 4], [10, 1, 4], [0, 2, 4], [1, 2, 4], [2, 2, 4], [3, 2, 4], [4, 2, 4], [5, 2, 4], [6, 2, 4], [7, 2, 4], [8, 2, 4], [9, 2, 4], [10, 2, 4], [0, 3, 4], [1, 3, 4], [2, 3, 4], [3, 3, 4], [4, 3, 4], [5, 3, 4], [6, 3, 4], [7, 3, 4], [8, 3, 4], [9, 3, 4], [10, 3, 4], [0, 4, 4], [1, 4, 4], [2, 4, 4], [3, 4, 4], [4, 4, 4], [5, 4, 4], [6, 4, 4], [7, 4, 4], [8, 4, 4], [9, 4, 4], [10, 4, 4], [0, 5, 4], [1, 5, 4], [2, 5, 4], [3, 5, 4], [4, 5, 4], [5, 5, 4], [6, 5, 4], [7, 5, 4], [8, 5, 4], [9, 5, 4], [10, 5, 4], [0, 6, 4], [1, 6, 4], [2, 6, 4], [3, 6, 4], [4, 6, 4], [5, 6, 4], [6, 6, 4], [7, 6, 4], [8, 6, 4], [9, 6, 4], [10, 6, 4], [0, 7, 4], [1, 7, 4], [2, 7, 4], [3, 7, 4], [4, 7, 4], [5, 7, 4], [6, 7, 4], [7, 7, 4], [8, 7, 4], [9, 7, 4], [10, 7, 4], [0, 8, 4], [1, 8, 4], [2, 8, 4], [3, 8, 4], [4, 8, 4], [5, 8, 4], [6, 8, 4], [7, 8, 4], [8, 8, 4], [9, 8, 4], [10, 8, 4], [0, 9, 4], [1, 9, 4], [2, 9, 4], [3, 9, 4], [4, 9, 4], [5, 9, 4], [6, 9, 4], [7, 9, 4], [8, 9, 4], [9, 9, 4], [10, 9, 4], [0, 10, 4], [1, 10, 4], [2, 10, 4], [3, 10, 4], [4, 10, 4], [5, 10, 4], [6, 10, 4], [7, 10, 4], [8, 10, 4], [9, 10, 4], [10, 10, 4], [0, 0, 5], [1, 0, 5], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 5], [7, 0, 5], [8, 0, 5], [9, 0, 5], [10, 0, 5], [0, 1, 5], [1, 1, 5], [2, 1, 5], [3, 1, 5], [4, 1, 5], [5, 1, 5], [6, 1, 5], [7, 1, 5], [8, 1, 5], [9, 1, 5], [10, 1, 5], [0, 2, 5], [1, 2, 5], [2, 2, 5], [3, 2, 5], [4, 2, 5], [5, 2, 5], [6, 2, 5], [7, 2, 5], [8, 2, 5], [9, 2, 5], [10, 2, 5], [0, 3, 5], [1, 3, 5], [2, 3, 5], [3, 3, 5], [4, 3, 5], [5, 3, 5], [6, 3, 5], [7, 3, 5], [8, 3, 5], [9, 3, 5], [10, 3, 5], [0, 4, 5], [1, 4, 5], [2, 4, 5], [3, 4, 5], [4, 4, 5], [5, 4, 5], [6, 4, 5], [7, 4, 5], [8, 4, 5], [9, 4, 5], [10, 4, 5], [0, 5, 5], [1, 5, 5], [2, 5, 5], [3, 5, 5], [4, 5, 5], [5, 5, 5], [6, 5, 5], [7, 5, 5], [8, 5, 5], [9, 5, 5], [10, 5, 5], [0, 6, 5], [1, 6, 5], [2, 6, 5], [3, 6, 5], [4, 6, 5], [5, 6, 5], [6, 6, 5], [7, 6, 5], [8, 6, 5], [9, 6, 5], [10, 6, 5], [0, 7, 5], [1, 7, 5], [2, 7, 5], [3, 7, 5], [4, 7, 5], [5, 7, 5], [6, 7, 5], [7, 7, 5], [8, 7, 5], [9, 7, 5], [10, 7, 5], [0, 8, 5], [1, 8, 5], [2, 8, 5], [3, 8, 5], [4, 8, 5], [5, 8, 5], [6, 8, 5], [7, 8, 5], [8, 8, 5], [9, 8, 5], [10, 8, 5], [0, 9, 5], [1, 9, 5], [2, 9, 5], [3, 9, 5], [4, 9, 5], [5, 9, 5], [6, 9, 5], [7, 9, 5], [8, 9, 5], [9, 9, 5], [10, 9, 5], [0, 10, 5], [1, 10, 5], [2, 10, 5], [3, 10, 5], [4, 10, 5], [5, 10, 5], [6, 10, 5], [7, 10, 5], [8, 10, 5], [9, 10, 5], [10, 10, 5], [0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6], [6, 0, 6], [7, 0, 6], [8, 0, 6], [9, 0, 6], [10, 0, 6], [0, 1, 6], [1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 6], [6, 1, 6], [7, 1, 6], [8, 1, 6], [9, 1, 6], [10, 1, 6], [0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6], [4, 2, 6], [5, 2, 6], [6, 2, 6], [7, 2, 6], [8, 2, 6], [9, 2, 6], [10, 2, 6], [0, 3, 6], [1, 3, 6], [2, 3, 6], [3, 3, 6], [4, 3, 6], [5, 3, 6], [6, 3, 6], [7, 3, 6], [8, 3, 6], [9, 3, 6], [10, 3, 6], [0, 4, 6], [1, 4, 6], [2, 4, 6], [3, 4, 6], [4, 4, 6], [5, 4, 6], [6, 4, 6], [7, 4, 6], [8, 4, 6], [9, 4, 6], [10, 4, 6], [0, 5, 6], [1, 5, 6], [2, 5, 6], [3, 5, 6], [4, 5, 6], [5, 5, 6], [6, 5, 6], [7, 5, 6], [8, 5, 6], [9, 5, 6], [10, 5, 6], [0, 6, 6], [1, 6, 6], [2, 6, 6], [3, 6, 6], [4, 6, 6], [5, 6, 6], [6, 6, 6], [7, 6, 6], [8, 6, 6], [9, 6, 6], [10, 6, 6], [0, 7, 6], [1, 7, 6], [2, 7, 6], [3, 7, 6], [4, 7, 6], [5, 7, 6], [6, 7, 6], [7, 7, 6], [8, 7, 6], [9, 7, 6], [10, 7, 6], [0, 8, 6], [1, 8, 6], [2, 8, 6], [3, 8, 6], [4, 8, 6], [5, 8, 6], [6, 8, 6], [7, 8, 6], [8, 8, 6], [9, 8, 6], [10, 8, 6], [0, 9, 6], [1, 9, 6], [2, 9, 6], [3, 9, 6], [4, 9, 6], [5, 9, 6], [6, 9, 6], [7, 9, 6], [8, 9, 6], [9, 9, 6], [10, 9, 6], [0, 10, 6], [1, 10, 6], [2, 10, 6], [3, 10, 6], [4, 10, 6], [5, 10, 6], [6, 10, 6], [7, 10, 6], [8, 10, 6], [9, 10, 6], [10, 10, 6], [0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 0, 7], [7, 0, 7], [8, 0, 7], [9, 0, 7], [10, 0, 7], [0, 1, 7], [1, 1, 7], [2, 1, 7], [3, 1, 7], [4, 1, 7], [5, 1, 7], [6, 1, 7], [7, 1, 7], [8, 1, 7], [9, 1, 7], [10, 1, 7], [0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7], [4, 2, 7], [5, 2, 7], [6, 2, 7], [7, 2, 7], [8, 2, 7], [9, 2, 7], [10, 2, 7], [0, 3, 7], [1, 3, 7], [2, 3, 7], [3, 3, 7], [4, 3, 7], [5, 3, 7], [6, 3, 7], [7, 3, 7], [8, 3, 7], [9, 3, 7], [10, 3, 7], [0, 4, 7], [1, 4, 7], [2, 4, 7], [3, 4, 7], [4, 4, 7], [5, 4, 7], [6, 4, 7], [7, 4, 7], [8, 4, 7], [9, 4, 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1137, 1247], [1127, 1137, 1247, 1248], [1137, 1247, 1248, 1258], [1127, 1137, 1138, 1248], [1137, 1138, 1248, 1258], [1138, 1248, 1258, 1259], [1127, 1128, 1138, 1248], [1128, 1138, 1248, 1249], [1138, 1248, 1249, 1259], [1128, 1138, 1139, 1249], [1138, 1139, 1249, 1259], [1139, 1249, 1259, 1260], [1128, 1129, 1139, 1249], [1129, 1139, 1249, 1250], [1139, 1249, 1250, 1260], [1129, 1139, 1140, 1250], [1139, 1140, 1250, 1260], [1140, 1250, 1260, 1261], [1129, 1130, 1140, 1250], [1130, 1140, 1250, 1251], [1140, 1250, 1251, 1261], [1130, 1140, 1141, 1251], [1140, 1141, 1251, 1261], [1141, 1251, 1261, 1262], [1130, 1131, 1141, 1251], [1131, 1141, 1251, 1252], [1141, 1251, 1252, 1262], [1131, 1141, 1142, 1252], [1141, 1142, 1252, 1262], [1142, 1252, 1262, 1263], [1131, 1132, 1142, 1252], [1132, 1142, 1252, 1253], [1142, 1252, 1253, 1263], [1132, 1142, 1143, 1253], [1142, 1143, 1253, 1263], [1143, 1253, 1263, 1264], [1133, 1134, 1144, 1254], [1134, 1144, 1254, 1255], [1144, 1254, 1255, 1265], [1134, 1144, 1145, 1255], [1144, 1145, 1255, 1265], [1145, 1255, 1265, 1266], [1134, 1135, 1145, 1255], [1135, 1145, 1255, 1256], [1145, 1255, 1256, 1266], [1135, 1145, 1146, 1256], [1145, 1146, 1256, 1266], [1146, 1256, 1266, 1267], [1135, 1136, 1146, 1256], [1136, 1146, 1256, 1257], [1146, 1256, 1257, 1267], [1136, 1146, 1147, 1257], [1146, 1147, 1257, 1267], [1147, 1257, 1267, 1268], [1136, 1137, 1147, 1257], [1137, 1147, 1257, 1258], [1147, 1257, 1258, 1268], [1137, 1147, 1148, 1258], [1147, 1148, 1258, 1268], [1148, 1258, 1268, 1269], [1137, 1138, 1148, 1258], [1138, 1148, 1258, 1259], [1148, 1258, 1259, 1269], [1138, 1148, 1149, 1259], [1148, 1149, 1259, 1269], [1149, 1259, 1269, 1270], [1138, 1139, 1149, 1259], [1139, 1149, 1259, 1260], [1149, 1259, 1260, 1270], [1139, 1149, 1150, 1260], [1149, 1150, 1260, 1270], [1150, 1260, 1270, 1271], [1139, 1140, 1150, 1260], [1140, 1150, 1260, 1261], [1150, 1260, 1261, 1271], [1140, 1150, 1151, 1261], [1150, 1151, 1261, 1271], [1151, 1261, 1271, 1272], [1140, 1141, 1151, 1261], [1141, 1151, 1261, 1262], [1151, 1261, 1262, 1272], [1141, 1151, 1152, 1262], [1151, 1152, 1262, 1272], [1152, 1262, 1272, 1273], [1141, 1142, 1152, 1262], [1142, 1152, 1262, 1263], [1152, 1262, 1263, 1273], [1142, 1152, 1153, 1263], [1152, 1153, 1263, 1273], [1153, 1263, 1273, 1274], [1142, 1143, 1153, 1263], [1143, 1153, 1263, 1264], [1153, 1263, 1264, 1274], [1143, 1153, 1154, 1264], [1153, 1154, 1264, 1274], [1154, 1264, 1274, 1275], [1144, 1145, 1155, 1265], [1145, 1155, 1265, 1266], [1155, 1265, 1266, 1276], [1145, 1155, 1156, 1266], [1155, 1156, 1266, 1276], [1156, 1266, 1276, 1277], [1145, 1146, 1156, 1266], [1146, 1156, 1266, 1267], [1156, 1266, 1267, 1277], [1146, 1156, 1157, 1267], [1156, 1157, 1267, 1277], [1157, 1267, 1277, 1278], [1146, 1147, 1157, 1267], [1147, 1157, 1267, 1268], [1157, 1267, 1268, 1278], [1147, 1157, 1158, 1268], [1157, 1158, 1268, 1278], [1158, 1268, 1278, 1279], [1147, 1148, 1158, 1268], [1148, 1158, 1268, 1269], [1158, 1268, 1269, 1279], [1148, 1158, 1159, 1269], [1158, 1159, 1269, 1279], [1159, 1269, 1279, 1280], [1148, 1149, 1159, 1269], [1149, 1159, 1269, 1270], [1159, 1269, 1270, 1280], [1149, 1159, 1160, 1270], [1159, 1160, 1270, 1280], [1160, 1270, 1280, 1281], [1149, 1150, 1160, 1270], [1150, 1160, 1270, 1271], [1160, 1270, 1271, 1281], [1150, 1160, 1161, 1271], [1160, 1161, 1271, 1281], [1161, 1271, 1281, 1282], [1150, 1151, 1161, 1271], [1151, 1161, 1271, 1272], [1161, 1271, 1272, 1282], [1151, 1161, 1162, 1272], [1161, 1162, 1272, 1282], [1162, 1272, 1282, 1283], [1151, 1152, 1162, 1272], [1152, 1162, 1272, 1273], [1162, 1272, 1273, 1283], [1152, 1162, 1163, 1273], [1162, 1163, 1273, 1283], [1163, 1273, 1283, 1284], [1152, 1153, 1163, 1273], [1153, 1163, 1273, 1274], [1163, 1273, 1274, 1284], [1153, 1163, 1164, 1274], [1163, 1164, 1274, 1284], [1164, 1274, 1284, 1285], [1153, 1154, 1164, 1274], [1154, 1164, 1274, 1275], [1164, 1274, 1275, 1285], [1154, 1164, 1165, 1275], [1164, 1165, 1275, 1285], [1165, 1275, 1285, 1286], [1155, 1156, 1166, 1276], [1156, 1166, 1276, 1277], [1166, 1276, 1277, 1287], [1156, 1166, 1167, 1277], [1166, 1167, 1277, 1287], [1167, 1277, 1287, 1288], [1156, 1157, 1167, 1277], [1157, 1167, 1277, 1278], [1167, 1277, 1278, 1288], [1157, 1167, 1168, 1278], [1167, 1168, 1278, 1288], [1168, 1278, 1288, 1289], [1157, 1158, 1168, 1278], [1158, 1168, 1278, 1279], [1168, 1278, 1279, 1289], [1158, 1168, 1169, 1279], [1168, 1169, 1279, 1289], [1169, 1279, 1289, 1290], [1158, 1159, 1169, 1279], [1159, 1169, 1279, 1280], [1169, 1279, 1280, 1290], [1159, 1169, 1170, 1280], [1169, 1170, 1280, 1290], [1170, 1280, 1290, 1291], [1159, 1160, 1170, 1280], [1160, 1170, 1280, 1281], [1170, 1280, 1281, 1291], [1160, 1170, 1171, 1281], [1170, 1171, 1281, 1291], [1171, 1281, 1291, 1292], [1160, 1161, 1171, 1281], [1161, 1171, 1281, 1282], [1171, 1281, 1282, 1292], [1161, 1171, 1172, 1282], [1171, 1172, 1282, 1292], [1172, 1282, 1292, 1293], [1161, 1162, 1172, 1282], [1162, 1172, 1282, 1283], [1172, 1282, 1283, 1293], [1162, 1172, 1173, 1283], [1172, 1173, 1283, 1293], [1173, 1283, 1293, 1294], [1162, 1163, 1173, 1283], [1163, 1173, 1283, 1284], [1173, 1283, 1284, 1294], [1163, 1173, 1174, 1284], [1173, 1174, 1284, 1294], [1174, 1284, 1294, 1295], [1163, 1164, 1174, 1284], [1164, 1174, 1284, 1285], [1174, 1284, 1285, 1295], [1164, 1174, 1175, 1285], [1174, 1175, 1285, 1295], [1175, 1285, 1295, 1296], [1164, 1165, 1175, 1285], [1165, 1175, 1285, 1286], [1175, 1285, 1286, 1296], [1165, 1175, 1176, 1286], [1175, 1176, 1286, 1296], [1176, 1286, 1296, 1297], [1166, 1167, 1177, 1287], [1167, 1177, 1287, 1288], [1177, 1287, 1288, 1298], [1167, 1177, 1178, 1288], [1177, 1178, 1288, 1298], [1178, 1288, 1298, 1299], [1167, 1168, 1178, 1288], [1168, 1178, 1288, 1289], [1178, 1288, 1289, 1299], [1168, 1178, 1179, 1289], [1178, 1179, 1289, 1299], [1179, 1289, 1299, 1300], [1168, 1169, 1179, 1289], [1169, 1179, 1289, 1290], [1179, 1289, 1290, 1300], [1169, 1179, 1180, 1290], [1179, 1180, 1290, 1300], [1180, 1290, 1300, 1301], [1169, 1170, 1180, 1290], [1170, 1180, 1290, 1291], [1180, 1290, 1291, 1301], [1170, 1180, 1181, 1291], [1180, 1181, 1291, 1301], [1181, 1291, 1301, 1302], [1170, 1171, 1181, 1291], [1171, 1181, 1291, 1292], [1181, 1291, 1292, 1302], [1171, 1181, 1182, 1292], [1181, 1182, 1292, 1302], [1182, 1292, 1302, 1303], [1171, 1172, 1182, 1292], [1172, 1182, 1292, 1293], [1182, 1292, 1293, 1303], [1172, 1182, 1183, 1293], [1182, 1183, 1293, 1303], [1183, 1293, 1303, 1304], [1172, 1173, 1183, 1293], [1173, 1183, 1293, 1294], [1183, 1293, 1294, 1304], [1173, 1183, 1184, 1294], [1183, 1184, 1294, 1304], [1184, 1294, 1304, 1305], [1173, 1174, 1184, 1294], [1174, 1184, 1294, 1295], [1184, 1294, 1295, 1305], [1174, 1184, 1185, 1295], [1184, 1185, 1295, 1305], [1185, 1295, 1305, 1306], [1174, 1175, 1185, 1295], [1175, 1185, 1295, 1296], [1185, 1295, 1296, 1306], [1175, 1185, 1186, 1296], [1185, 1186, 1296, 1306], [1186, 1296, 1306, 1307], [1175, 1176, 1186, 1296], [1176, 1186, 1296, 1297], [1186, 1296, 1297, 1307], [1176, 1186, 1187, 1297], [1186, 1187, 1297, 1307], [1187, 1297, 1307, 1308], [1177, 1178, 1188, 1298], [1178, 1188, 1298, 1299], [1188, 1298, 1299, 1309], [1178, 1188, 1189, 1299], [1188, 1189, 1299, 1309], [1189, 1299, 1309, 1310], [1178, 1179, 1189, 1299], [1179, 1189, 1299, 1300], [1189, 1299, 1300, 1310], [1179, 1189, 1190, 1300], [1189, 1190, 1300, 1310], [1190, 1300, 1310, 1311], [1179, 1180, 1190, 1300], [1180, 1190, 1300, 1301], [1190, 1300, 1301, 1311], [1180, 1190, 1191, 1301], [1190, 1191, 1301, 1311], [1191, 1301, 1311, 1312], [1180, 1181, 1191, 1301], [1181, 1191, 1301, 1302], [1191, 1301, 1302, 1312], [1181, 1191, 1192, 1302], [1191, 1192, 1302, 1312], [1192, 1302, 1312, 1313], [1181, 1182, 1192, 1302], [1182, 1192, 1302, 1303], [1192, 1302, 1303, 1313], [1182, 1192, 1193, 1303], [1192, 1193, 1303, 1313], [1193, 1303, 1313, 1314], [1182, 1183, 1193, 1303], [1183, 1193, 1303, 1304], [1193, 1303, 1304, 1314], [1183, 1193, 1194, 1304], [1193, 1194, 1304, 1314], [1194, 1304, 1314, 1315], [1183, 1184, 1194, 1304], [1184, 1194, 1304, 1305], [1194, 1304, 1305, 1315], [1184, 1194, 1195, 1305], [1194, 1195, 1305, 1315], [1195, 1305, 1315, 1316], [1184, 1185, 1195, 1305], [1185, 1195, 1305, 1306], [1195, 1305, 1306, 1316], [1185, 1195, 1196, 1306], [1195, 1196, 1306, 1316], [1196, 1306, 1316, 1317], [1185, 1186, 1196, 1306], [1186, 1196, 1306, 1307], [1196, 1306, 1307, 1317], [1186, 1196, 1197, 1307], [1196, 1197, 1307, 1317], [1197, 1307, 1317, 1318], [1186, 1187, 1197, 1307], [1187, 1197, 1307, 1308], [1197, 1307, 1308, 1318], [1187, 1197, 1198, 1308], [1197, 1198, 1308, 1318], [1198, 1308, 1318, 1319], [1188, 1189, 1199, 1309], [1189, 1199, 1309, 1310], [1199, 1309, 1310, 1320], [1189, 1199, 1200, 1310], [1199, 1200, 1310, 1320], [1200, 1310, 1320, 1321], [1189, 1190, 1200, 1310], [1190, 1200, 1310, 1311], [1200, 1310, 1311, 1321], [1190, 1200, 1201, 1311], [1200, 1201, 1311, 1321], [1201, 1311, 1321, 1322], [1190, 1191, 1201, 1311], [1191, 1201, 1311, 1312], [1201, 1311, 1312, 1322], [1191, 1201, 1202, 1312], [1201, 1202, 1312, 1322], [1202, 1312, 1322, 1323], [1191, 1192, 1202, 1312], [1192, 1202, 1312, 1313], [1202, 1312, 1313, 1323], [1192, 1202, 1203, 1313], [1202, 1203, 1313, 1323], [1203, 1313, 1323, 1324], [1192, 1193, 1203, 1313], [1193, 1203, 1313, 1314], [1203, 1313, 1314, 1324], [1193, 1203, 1204, 1314], [1203, 1204, 1314, 1324], [1204, 1314, 1324, 1325], [1193, 1194, 1204, 1314], [1194, 1204, 1314, 1315], [1204, 1314, 1315, 1325], [1194, 1204, 1205, 1315], [1204, 1205, 1315, 1325], [1205, 1315, 1325, 1326], [1194, 1195, 1205, 1315], [1195, 1205, 1315, 1316], [1205, 1315, 1316, 1326], [1195, 1205, 1206, 1316], [1205, 1206, 1316, 1326], [1206, 1316, 1326, 1327], [1195, 1196, 1206, 1316], [1196, 1206, 1316, 1317], [1206, 1316, 1317, 1327], [1196, 1206, 1207, 1317], [1206, 1207, 1317, 1327], [1207, 1317, 1327, 1328], [1196, 1197, 1207, 1317], [1197, 1207, 1317, 1318], [1207, 1317, 1318, 1328], [1197, 1207, 1208, 1318], [1207, 1208, 1318, 1328], [1208, 1318, 1328, 1329], [1197, 1198, 1208, 1318], [1198, 1208, 1318, 1319], [1208, 1318, 1319, 1329], [1198, 1208, 1209, 1319], [1208, 1209, 1319, 1329], [1209, 1319, 1329, 1330]]) + end + @testset "Example 3" begin + model = larExtrude1(VOID, repeat([1,-1],10)) + @test model == ([[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]], [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19]]) + + @test larExtrude1(model, repeat([1],10)) == ([[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0], [20, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2], [16, 2], [17, 2], [18, 2], [19, 2], [20, 2], [0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [11, 3], [12, 3], [13, 3], [14, 3], [15, 3], [16, 3], [17, 3], [18, 3], [19, 3], [20, 3], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4], [11, 4], [12, 4], [13, 4], [14, 4], [15, 4], [16, 4], [17, 4], [18, 4], [19, 4], [20, 4], [0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5], [12, 5], [13, 5], [14, 5], [15, 5], [16, 5], [17, 5], [18, 5], [19, 5], [20, 5], [0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [9, 6], [10, 6], [11, 6], [12, 6], [13, 6], [14, 6], [15, 6], [16, 6], [17, 6], [18, 6], [19, 6], [20, 6], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 7], [9, 7], [10, 7], [11, 7], [12, 7], [13, 7], [14, 7], [15, 7], [16, 7], [17, 7], [18, 7], [19, 7], [20, 7], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [9, 8], [10, 8], [11, 8], [12, 8], [13, 8], [14, 8], [15, 8], [16, 8], [17, 8], [18, 8], [19, 8], [20, 8], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [16, 9], [17, 9], [18, 9], [19, 9], [20, 9], [0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10], [10, 10], [11, 10], [12, 10], [13, 10], [14, 10], [15, 10], [16, 10], [17, 10], [18, 10], [19, 10], [20, 10]], [[0, 1, 21], [1, 21, 22], [2, 3, 23], [3, 23, 24], [4, 5, 25], [5, 25, 26], [6, 7, 27], [7, 27, 28], [8, 9, 29], [9, 29, 30], [10, 11, 31], [11, 31, 32], [12, 13, 33], [13, 33, 34], [14, 15, 35], [15, 35, 36], [16, 17, 37], [17, 37, 38], [18, 19, 39], [19, 39, 40], [21, 22, 42], [22, 42, 43], [23, 24, 44], [24, 44, 45], [25, 26, 46], [26, 46, 47], [27, 28, 48], [28, 48, 49], [29, 30, 50], [30, 50, 51], [31, 32, 52], [32, 52, 53], [33, 34, 54], [34, 54, 55], [35, 36, 56], [36, 56, 57], [37, 38, 58], [38, 58, 59], [39, 40, 60], [40, 60, 61], [42, 43, 63], [43, 63, 64], [44, 45, 65], [45, 65, 66], [46, 47, 67], [47, 67, 68], [48, 49, 69], [49, 69, 70], [50, 51, 71], [51, 71, 72], [52, 53, 73], [53, 73, 74], [54, 55, 75], [55, 75, 76], [56, 57, 77], [57, 77, 78], [58, 59, 79], [59, 79, 80], [60, 61, 81], [61, 81, 82], [63, 64, 84], [64, 84, 85], [65, 66, 86], [66, 86, 87], [67, 68, 88], [68, 88, 89], [69, 70, 90], [70, 90, 91], [71, 72, 92], [72, 92, 93], [73, 74, 94], [74, 94, 95], [75, 76, 96], [76, 96, 97], [77, 78, 98], [78, 98, 99], [79, 80, 100], [80, 100, 101], [81, 82, 102], [82, 102, 103], [84, 85, 105], [85, 105, 106], [86, 87, 107], [87, 107, 108], [88, 89, 109], [89, 109, 110], [90, 91, 111], [91, 111, 112], [92, 93, 113], [93, 113, 114], [94, 95, 115], [95, 115, 116], [96, 97, 117], [97, 117, 118], [98, 99, 119], [99, 119, 120], [100, 101, 121], [101, 121, 122], [102, 103, 123], [103, 123, 124], [105, 106, 126], [106, 126, 127], [107, 108, 128], [108, 128, 129], [109, 110, 130], [110, 130, 131], [111, 112, 132], [112, 132, 133], [113, 114, 134], [114, 134, 135], [115, 116, 136], [116, 136, 137], [117, 118, 138], [118, 138, 139], [119, 120, 140], [120, 140, 141], [121, 122, 142], [122, 142, 143], [123, 124, 144], [124, 144, 145], [126, 127, 147], [127, 147, 148], [128, 129, 149], [129, 149, 150], [130, 131, 151], [131, 151, 152], [132, 133, 153], [133, 153, 154], [134, 135, 155], [135, 155, 156], [136, 137, 157], [137, 157, 158], [138, 139, 159], [139, 159, 160], [140, 141, 161], [141, 161, 162], [142, 143, 163], [143, 163, 164], [144, 145, 165], [145, 165, 166], [147, 148, 168], [148, 168, 169], [149, 150, 170], [150, 170, 171], [151, 152, 172], [152, 172, 173], [153, 154, 174], [154, 174, 175], [155, 156, 176], [156, 176, 177], [157, 158, 178], [158, 178, 179], [159, 160, 180], [160, 180, 181], [161, 162, 182], [162, 182, 183], [163, 164, 184], [164, 184, 185], [165, 166, 186], [166, 186, 187], [168, 169, 189], [169, 189, 190], [170, 171, 191], [171, 191, 192], [172, 173, 193], [173, 193, 194], [174, 175, 195], [175, 195, 196], [176, 177, 197], [177, 197, 198], [178, 179, 199], [179, 199, 200], [180, 181, 201], [181, 201, 202], [182, 183, 203], [183, 203, 204], [184, 185, 205], [185, 205, 206], [186, 187, 207], [187, 207, 208], [189, 190, 210], [190, 210, 211], [191, 192, 212], [192, 212, 213], [193, 194, 214], [194, 214, 215], [195, 196, 216], [196, 216, 217], [197, 198, 218], [198, 218, 219], [199, 200, 220], [200, 220, 221], [201, 202, 222], [202, 222, 223], [203, 204, 224], [204, 224, 225], [205, 206, 226], [206, 226, 227], [207, 208, 228], [208, 228, 229]]) + + @test larSimplexGrid1([3,3]) == ([[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2], [0, 3], [1, 3], [2, 3], [3, 3]], [[0, 1, 4], [1, 4, 5], [1, 2, 5], [2, 5, 6], [2, 3, 6], [3, 6, 7], [4, 5, 8], [5, 8, 9], [5, 6, 9], [6, 9, 10], [6, 7, 10], [7, 10, 11], [8, 9, 12], [9, 12, 13], [9, 10, 13], [10, 13, 14], [10, 11, 14], [11, 14, 15]]) + + @test larSimplexGrid1([2,3,4]) == ([[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [0, 0, 3], [1, 0, 3], [2, 0, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [0, 0, 4], [1, 0, 4], [2, 0, 4], [0, 1, 4], [1, 1, 4], [2, 1, 4], [0, 2, 4], [1, 2, 4], [2, 2, 4], [0, 3, 4], [1, 3, 4], [2, 3, 4]], [[0, 1, 3, 12], [1, 3, 12, 13], [3, 12, 13, 15], [1, 3, 4, 13], [3, 4, 13, 15], [4, 13, 15, 16], [1, 2, 4, 13], [2, 4, 13, 14], [4, 13, 14, 16], [2, 4, 5, 14], [4, 5, 14, 16], [5, 14, 16, 17], [3, 4, 6, 15], [4, 6, 15, 16], [6, 15, 16, 18], [4, 6, 7, 16], [6, 7, 16, 18], [7, 16, 18, 19], [4, 5, 7, 16], [5, 7, 16, 17], [7, 16, 17, 19], [5, 7, 8, 17], [7, 8, 17, 19], [8, 17, 19, 20], [6, 7, 9, 18], [7, 9, 18, 19], [9, 18, 19, 21], [7, 9, 10, 19], [9, 10, 19, 21], [10, 19, 21, 22], [7, 8, 10, 19], [8, 10, 19, 20], [10, 19, 20, 22], [8, 10, 11, 20], [10, 11, 20, 22], [11, 20, 22, 23], [12, 13, 15, 24], [13, 15, 24, 25], [15, 24, 25, 27], [13, 15, 16, 25], [15, 16, 25, 27], [16, 25, 27, 28], [13, 14, 16, 25], [14, 16, 25, 26], [16, 25, 26, 28], [14, 16, 17, 26], [16, 17, 26, 28], [17, 26, 28, 29], [15, 16, 18, 27], [16, 18, 27, 28], [18, 27, 28, 30], [16, 18, 19, 28], [18, 19, 28, 30], [19, 28, 30, 31], [16, 17, 19, 28], [17, 19, 28, 29], [19, 28, 29, 31], [17, 19, 20, 29], [19, 20, 29, 31], [20, 29, 31, 32], [18, 19, 21, 30], [19, 21, 30, 31], [21, 30, 31, 33], [19, 21, 22, 31], [21, 22, 31, 33], [22, 31, 33, 34], [19, 20, 22, 31], [20, 22, 31, 32], [22, 31, 32, 34], [20, 22, 23, 32], [22, 23, 32, 34], [23, 32, 34, 35], [24, 25, 27, 36], [25, 27, 36, 37], [27, 36, 37, 39], [25, 27, 28, 37], [27, 28, 37, 39], [28, 37, 39, 40], [25, 26, 28, 37], [26, 28, 37, 38], [28, 37, 38, 40], [26, 28, 29, 38], [28, 29, 38, 40], [29, 38, 40, 41], [27, 28, 30, 39], [28, 30, 39, 40], [30, 39, 40, 42], [28, 30, 31, 40], [30, 31, 40, 42], [31, 40, 42, 43], [28, 29, 31, 40], [29, 31, 40, 41], [31, 40, 41, 43], [29, 31, 32, 41], [31, 32, 41, 43], [32, 41, 43, 44], [30, 31, 33, 42], [31, 33, 42, 43], [33, 42, 43, 45], [31, 33, 34, 43], [33, 34, 43, 45], [34, 43, 45, 46], [31, 32, 34, 43], [32, 34, 43, 44], [34, 43, 44, 46], [32, 34, 35, 44], [34, 35, 44, 46], [35, 44, 46, 47], [36, 37, 39, 48], [37, 39, 48, 49], [39, 48, 49, 51], [37, 39, 40, 49], [39, 40, 49, 51], [40, 49, 51, 52], [37, 38, 40, 49], [38, 40, 49, 50], [40, 49, 50, 52], [38, 40, 41, 50], [40, 41, 50, 52], [41, 50, 52, 53], [39, 40, 42, 51], [40, 42, 51, 52], [42, 51, 52, 54], [40, 42, 43, 52], [42, 43, 52, 54], [43, 52, 54, 55], [40, 41, 43, 52], [41, 43, 52, 53], [43, 52, 53, 55], [41, 43, 44, 53], [43, 44, 53, 55], [44, 53, 55, 56], [42, 43, 45, 54], [43, 45, 54, 55], [45, 54, 55, 57], [43, 45, 46, 55], [45, 46, 55, 57], [46, 55, 57, 58], [43, 44, 46, 55], [44, 46, 55, 56], [46, 55, 56, 58], [44, 46, 47, 56], [46, 47, 56, 58], [47, 56, 58, 59]]) + + V, CV = larSimplexGrid1([1,1,1]) + @test (V, CV) == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1, 2, 4], [1, 2, 4, 5], [2, 4, 5, 6], [1, 2, 3, 5], [2, 3, 5, 6], [3, 5, 6, 7]]) + + SK2 = (V,larSimplexFacets(CV)) + @test SK2 == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1, 2], [0, 1, 4], [0, 2, 4], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 5], [1, 4, 5], [2, 3, 5], [2, 3, 6], [2, 4, 5], [2, 4, 6], [2, 5, 6], [3, 5, 6], [3, 5, 7], [3, 6, 7], [4, 5, 6], [5, 6, 7]]) + + @test (V,larSimplexFacets(SK2[2])) == ([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [2, 6], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [5, 6], [5, 7], [6, 7]]) + end + end + @testset "Simplexn Tests" begin + @testset "2D example" begin + V, FV = larSimplexGrid1([3,3]) + @test V == [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2], [0, 3], [1, 3], [2, 3], [3, 3]] + @test FV == [[0, 1, 4], [1, 4, 5], [1, 2, 5], [2, 5, 6], [2, 3, 6], [3, 6, 7], [4, 5, 8], [5, 8, 9], [5, 6, 9], [6, 9, 10], [6, 7, 10], [7, 10, 11], [8, 9, 12], [9, 12, 13], [9, 10, 13], [10, 13, 14], [10, 11, 14], [11, 14, 15]] + + @test larSimplexFacets(FV) == [[0, 1], [0, 4], [1, 2], [1, 4], [1, 5], [2, 3], [2, 5], [2, 6], [3, 6], [3, 7], [4, 5], [4, 8], [5, 6], [5, 8], [5, 9], [6, 7], [6, 9], [6, 10], [7, 10], [7, 11], [8, 9], [8, 12], [9, 10], [9, 12], [9, 13], [10, 11], [10, 13], [10, 14], [11, 14], [11, 15], [12, 13], [13, 14], [14, 15]] + end + @testset "3D example" begin + V, CV = larSimplexGrid1([2,2,2]) + @test V == [[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1], [1, 0, 1], [2, 0, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + @test CV == [[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 3, 4, 10], [3, 4, 10, 12], [4, 10, 12, 13], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11], [4, 5, 11, 13], [5, 11, 13, 14], [3, 4, 6, 12], [4, 6, 12, 13], [6, 12, 13, 15], [4, 6, 7, 13], [6, 7, 13, 15], [7, 13, 15, 16], [4, 5, 7, 13], [5, 7, 13, 14], [7, 13, 14, 16], [5, 7, 8, 14], [7, 8, 14, 16], [8, 14, 16, 17], [9, 10, 12, 18], [10, 12, 18, 19], [12, 18, 19, 21], [10, 12, 13, 19], [12, 13, 19, 21], [13, 19, 21, 22], [10, 11, 13, 19], [11, 13, 19, 20], [13, 19, 20, 22], [11, 13, 14, 20], [13, 14, 20, 22], [14, 20, 22, 23], [12, 13, 15, 21], [13, 15, 21, 22], [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [13, 14, 16, 22], [14, 16, 22, 23], [16, 22, 23, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26]] + + FV = larSimplexFacets(CV) + @test FV == [[0, 1, 3], [0, 1, 9], [0, 3, 9], [1, 2, 4], [1, 2, 10], [1, 3, 4], [1, 3, 9], [1, 3, 10], [1, 4, 10], [1, 9, 10], [2, 4, 5], [2, 4, 10], [2, 4, 11], [2, 5, 11], [2, 10, 11], [3, 4, 6], [3, 4, 10], [3, 4, 12], [3, 6, 12], [3, 9, 10], [3, 9, 12], [3, 10, 12], [4, 5, 7], [4, 5, 11], [4, 5, 13], [4, 6, 7], [4, 6, 12], [4, 6, 13], [4, 7, 13], [4, 10, 11], [4, 10, 12], [4, 10, 13], [4, 11, 13], [4, 12, 13], [5, 7, 8], [5, 7, 13], [5, 7, 14], [5, 8, 14], [5, 11, 13], [5, 11, 14], [5, 13, 14], [6, 7, 13], [6, 7, 15], [6, 12, 13], [6, 12, 15], [6, 13, 15], [7, 8, 14], [7, 8, 16], [7, 13, 14], [7, 13, 15], [7, 13, 16], [7, 14, 16], [7, 15, 16], [8, 14, 16], [8, 14, 17], [8, 16, 17], [9, 10, 12], [9, 10, 18], [9, 12, 18], [10, 11, 13], [10, 11, 19], [10, 12, 13], [10, 12, 18], [10, 12, 19], [10, 13, 19], [10, 18, 19], [11, 13, 14], [11, 13, 19], [11, 13, 20], [11, 14, 20], [11, 19, 20], [12, 13, 15], [12, 13, 19], [12, 13, 21], [12, 15, 21], [12, 18, 19], [12, 18, 21], [12, 19, 21], [13, 14, 16], [13, 14, 20], [13, 14, 22], [13, 15, 16], [13, 15, 21], [13, 15, 22], [13, 16, 22], [13, 19, 20], [13, 19, 21], [13, 19, 22], [13, 20, 22], [13, 21, 22], [14, 16, 17], [14, 16, 22], [14, 16, 23], [14, 17, 23], [14, 20, 22], [14, 20, 23], [14, 22, 23], [15, 16, 22], [15, 16, 24], [15, 21, 22], [15, 21, 24], [15, 22, 24], [16, 17, 23], [16, 17, 25], [16, 22, 23], [16, 22, 24], [16, 22, 25], [16, 23, 25], [16, 24, 25], [17, 23, 25], [17, 23, 26], [17, 25, 26], [18, 19, 21], [19, 20, 22], [19, 21, 22], [20, 22, 23], [21, 22, 24], [22, 23, 25], [22, 24, 25], [23, 25, 26]] + + @test larSimplexFacets(FV) == [[0, 1], [0, 3], [0, 9], [1, 2], [1, 3], [1, 4], [1, 9], [1, 10], [2, 4], [2, 5], [2, 10], [2, 11], [3, 4], [3, 6], [3, 9], [3, 10], [3, 12], [4, 5], [4, 6], [4, 7], [4, 10], [4, 11], [4, 12], [4, 13], [5, 7], [5, 8], [5, 11], [5, 13], [5, 14], [6, 7], [6, 12], [6, 13], [6, 15], [7, 8], [7, 13], [7, 14], [7, 15], [7, 16], [8, 14], [8, 16], [8, 17], [9, 10], [9, 12], [9, 18], [10, 11], [10, 12], [10, 13], [10, 18], [10, 19], [11, 13], [11, 14], [11, 19], [11, 20], [12, 13], [12, 15], [12, 18], [12, 19], [12, 21], [13, 14], [13, 15], [13, 16], [13, 19], [13, 20], [13, 21], [13, 22], [14, 16], [14, 17], [14, 20], [14, 22], [14, 23], [15, 16], [15, 21], [15, 22], [15, 24], [16, 17], [16, 22], [16, 23], [16, 24], [16, 25], [17, 23], [17, 25], [17, 26], [18, 19], [18, 21], [19, 20], [19, 21], [19, 22], [20, 22], [20, 23], [21, 22], [21, 24], [22, 23], [22, 24], [22, 25], [23, 25], [23, 26], [24, 25], [25, 26]] + end + end + @testset "quads2tria Test" begin + verts, triangles = quads2tria(([[8.6, 7.3, 3.0], [0.0, 0.0, 3.0], [3.6, 4.3, 0.0], [8.6, 7.6, 3.0], [3.6, 4.4, 0.3], [3.5, 0.3, 3.0], [0.3, 0.3, 0.3], [0.0, 0.3, 3.0], [0.0, 7.3, 0.3], [3.6, 7.3, 2.7], [8.6, 4.4, 0.0], [6.2, 7.6, 3.0], [6.0, 7.6, 2.7], [8.9, 7.6, 3.0], [5.1, 7.6, 3.0], [3.5, 7.3, 3.0], [8.9, 0.3, 0.3], [8.6, 4.4, 3.0], [6.0, 7.6, 3.0], [0.3, 4.3, 0.3], [0.3, 0.3, 0.0], [0.0, 7.3, 3.0], [6.0, 7.3, 1.3], [6.0, 7.6, 1.3], [6.0, 7.3, 0.3], [0.0, 0.0, 0.3], [7.1, 7.6, 3.0], [7.1, 7.3, 2.7], [0.3, 7.6, 0.3], [0.0, 4.3, 3.0], [8.6, 0.3, 0.0], [8.6, 7.3, 0.0], [5.1, 7.3, 2.7], [8.9, 7.3, 3.0], [3.5, 0.3, 0.0], [8.9, 0.3, 0.0], [8.9, 4.3, 0.0], [8.9, 7.6, 0.0], [3.6, 7.3, 0.0], [5.1, 7.3, 1.3], [8.6, 4.3, 3.0], [8.9, 0.0, 3.0], [8.6, 7.3, 1.3], [3.5, 0.0, 0.3], [5.1, 7.3, 3.0], [0.0, 7.6, 0.3], [0.3, 4.4, 0.0], [6.0, 7.3, 2.7], [8.6, 4.3, 0.0], [3.6, 0.0, 0.0], [3.5, 4.4, 3.0], [3.6, 7.3, 0.3], [0.3, 7.3, 0.3], [3.5, 0.3, 0.3], [0.3, 7.6, 0.0], [3.5, 4.3, 0.3], [8.6, 4.4, 0.3], [3.6, 7.3, 1.3], [3.6, 7.6, 3.0], [5.1, 7.6, 1.3], [0.3, 4.3, 3.0], [3.5, 0.0, 0.0], [3.6, 4.4, 0.0], [7.1, 7.6, 1.3], [3.5, 7.6, 0.0], [8.6, 0.0, 0.0], [0.0, 4.4, 3.0], [0.3, 4.4, 0.3], [3.5, 4.3, 3.0], [6.2, 7.3, 1.3], [8.9, 4.4, 0.0], [8.6, 7.3, 2.7], [8.9, 0.3, 3.0], [3.5, 7.3, 0.0], [3.6, 0.3, 0.0], [6.2, 7.3, 0.3], [8.6, 7.6, 2.7], [3.6, 7.6, 0.0], [0.0, 0.3, 0.0], [8.6, 7.3, 0.3], [3.5, 7.6, 0.3], [0.0, 7.3, 0.0], [0.3, 0.0, 0.0], [7.1, 7.6, 0.3], [0.0, 4.4, 0.3], [3.6, 7.6, 1.3], [0.0, 0.0, 0.0], [8.9, 4.4, 0.3], [8.9, 7.6, 0.3], [6.2, 7.3, 3.0], [6.2, 7.3, 2.7], [7.1, 7.3, 3.0], [0.0, 7.6, 0.0], [3.5, 7.6, 3.0], [0.0, 0.3, 0.3], [7.1, 7.6, 2.7], [3.6, 7.3, 3.0], [5.1, 7.3, 0.3], [0.3, 7.3, 3.0], [6.2, 7.6, 2.7], [0.3, 7.3, 0.0], [8.9, 0.0, 0.0], [0.3, 4.3, 0.0], [0.0, 4.3, 0.0], [5.1, 7.6, 0.3], [6.2, 7.6, 1.3], [3.5, 4.3, 0.0], [8.9, 7.3, 0.0], [6.0, 7.6, 0.3], [8.9, 4.3, 0.3], [8.6, 4.3, 0.3], [8.6, 7.6, 0.0], [0.3, 4.4, 3.0], [7.1, 7.3, 0.3], [0.3, 0.0, 0.3], [0.0, 4.4, 0.0], [3.5, 4.4, 0.3], [8.6, 7.6, 1.3], [3.5, 4.4, 0.0], [3.6, 4.3, 0.3], [6.0, 7.3, 3.0], [5.1, 7.6, 2.7], [3.6, 7.6, 2.7], [6.2, 7.6, 0.3], [8.9, 0.0, 0.3], [3.5, 0.0, 3.0], [0.0, 4.3, 0.3], [0.0, 7.6, 3.0], [8.9, 7.3, 0.3], [7.1, 7.3, 1.3], [8.9, 4.3, 3.0], [3.5, 7.3, 0.3], [8.6, 7.6, 0.3], [3.6, 7.6, 0.3], [3.6, 4.4, 3.0], [0.3, 0.0, 3.0], [0.3, 0.3, 3.0], [0.3, 7.6, 3.0], [8.9, 4.4, 3.0], [3.6, 4.3, 3.0], [3.6, 0.0, 0.3], [8.6, 0.0, 3.0], [3.6, 0.3, 3.0], [8.6, 0.3, 0.3], [3.6, 0.0, 3.0], [3.6, 0.3, 0.3], [8.6, 0.3, 3.0], [8.6, 0.0, 0.3], [5.6, 0.0, 3.0], [6.6, 0.3, 3.0], [5.6, 0.3, 3.0], [5.6, 0.3, 0.3], [6.6, 0.3, 2.5], [5.6, 0.0, 2.5], [6.6, 0.0, 2.5], [5.6, 0.0, 0.3], [3.6, 0.3, 2.5], [6.6, 0.0, 0.3], [8.6, 0.3, 2.5], [8.6, 0.0, 2.5], [5.6, 0.3, 2.5], [3.6, 0.0, 2.5], [6.6, 0.3, 0.3], [6.6, 0.0, 3.0]], [[0, 3, 13, 33], [0, 3, 26, 91], [0, 17, 33, 138], [0, 17, 42, 56, 71, 79], [0, 27, 71, 91], [1, 7, 25, 94], [1, 7, 135, 136], [1, 25, 114, 135], [2, 10, 48, 62], [2, 30, 48, 74], [2, 34, 74, 106], [2, 62, 106, 118], [3, 13, 76, 88, 117, 132], [3, 26, 76, 95], [4, 9, 51, 57, 96, 134], [4, 17, 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1.8199999999999998], [4.6, 0.0, 1.4], [7.6, 0.15, 3.0], [7.6, 0.0, 2.75], [4.6, 0.15, 3.0], [4.6, 0.3, 2.75], [7.6, 0.3, 1.4], [4.6, 0.0, 2.75], [4.6, 0.3, 1.4], [7.6, 0.3, 2.75], [7.6, 0.0, 1.4], [6.1, 0.15, 3.0], [6.1, 0.0, 2.75], [6.1, 0.3, 2.75], [5.6, 0.15, 1.4], [6.1, 0.15, 0.3], [6.1, 0.15, 2.5], [6.6, 0.15, 1.4]] + trianglesPy = [[164, 13, 33], [164, 33, 0], [164, 0, 3], [164, 3, 13], [165, 26, 91], [165, 91, 0], [165, 0, 3], [165, 3, 26], [166, 33, 0], [166, 0, 17], [166, 17, 138], [166, 138, 33], [167, 79, 42], [167, 42, 71], [167, 71, 0], [167, 0, 17], [167, 17, 56], [167, 56, 79], [168, 27, 91], [168, 91, 0], [168, 0, 71], [168, 71, 27], [169, 25, 1], [169, 1, 7], [169, 7, 94], [169, 94, 25], [170, 136, 135], [170, 135, 1], [170, 1, 7], [170, 7, 136], [171, 114, 135], [171, 135, 1], [171, 1, 25], [171, 25, 114], [172, 62, 2], [172, 2, 48], [172, 48, 10], [172, 10, 62], [173, 74, 2], [173, 2, 48], [173, 48, 30], [173, 30, 74], [174, 106, 2], [174, 2, 74], [174, 74, 34], [174, 34, 106], [175, 106, 2], [175, 2, 62], [175, 62, 118], [175, 118, 106], [176, 132, 117], [176, 117, 76], [176, 76, 3], [176, 3, 13], [176, 13, 88], [176, 88, 132], [177, 76, 3], [177, 3, 26], [177, 26, 95], [177, 95, 76], [178, 57, 51], [178, 51, 4], [178, 4, 134], [178, 134, 96], [178, 96, 9], [178, 9, 57], [179, 134, 4], [179, 4, 56], [179, 56, 17], [179, 17, 134], [180, 113, 79], [180, 79, 56], [180, 56, 4], [180, 4, 51], [180, 51, 97], [180, 97, 24], [180, 24, 75], [180, 75, 113], [181, 6, 136], [181, 136, 5], [181, 5, 53], [181, 53, 6], [182, 55, 68], [182, 68, 5], [182, 5, 53], [182, 53, 55], [183, 142, 5], [183, 5, 68], [183, 68, 139], [183, 139, 142], [184, 135, 136], [184, 136, 5], [184, 5, 125], [184, 125, 135], [185, 144, 142], [185, 142, 5], [185, 5, 125], [185, 125, 144], [186, 53, 6], [186, 6, 19], [186, 19, 55], [186, 55, 53], [187, 136, 6], [187, 6, 19], [187, 19, 60], [187, 60, 136], [188, 136, 7], [188, 7, 29], [188, 29, 60], [188, 60, 136], [189, 94, 7], [189, 7, 29], [189, 29, 126], [189, 126, 94], [190, 127, 45], [190, 45, 8], [190, 8, 21], [190, 21, 127], [191, 84, 8], [191, 8, 21], [191, 21, 66], [191, 66, 84], [192, 81, 8], [192, 8, 45], [192, 45, 92], [192, 92, 81], [193, 84, 8], [193, 8, 81], [193, 81, 115], [193, 115, 84], [194, 57, 9], [194, 9, 32], [194, 32, 39], [194, 39, 57], [195, 96, 9], [195, 9, 32], [195, 32, 44], [195, 44, 96], [196, 38, 62], [196, 62, 10], [196, 10, 31], [196, 31, 38], [197, 70, 10], [197, 10, 31], [197, 31, 107], [197, 107, 70], [198, 70, 10], [198, 10, 48], [198, 48, 36], [198, 36, 70], [199, 99, 11], [199, 11, 18], [199, 18, 12], [199, 12, 99], [200, 89, 11], [200, 11, 18], [200, 18, 120], [200, 120, 89], [201, 89, 11], [201, 11, 26], [201, 26, 91], [201, 91, 89], [202, 99, 11], [202, 11, 26], [202, 26, 95], [202, 95, 99], [203, 14, 121], [203, 121, 12], [203, 12, 18], [203, 18, 14], [204, 47, 12], [204, 12, 23], [204, 23, 22], [204, 22, 47], [205, 99, 12], [205, 12, 23], [205, 23, 105], [205, 105, 99], [206, 32, 121], [206, 121, 12], [206, 12, 47], [206, 47, 32], [207, 88, 13], [207, 13, 33], [207, 33, 128], [207, 128, 88], [208, 44, 14], [208, 14, 18], [208, 18, 120], [208, 120, 44], [209, 96, 58], [209, 58, 14], [209, 14, 44], [209, 44, 96], [210, 121, 14], [210, 14, 58], [210, 58, 122], [210, 122, 121], [211, 96, 15], [211, 15, 50], [211, 50, 134], [211, 134, 96], [212, 116, 131], [212, 131, 15], [212, 15, 50], [212, 50, 116], [213, 131, 15], [213, 15, 98], [213, 98, 52], [213, 52, 131], [214, 58, 96], [214, 96, 15], [214, 15, 93], [214, 93, 58], [215, 137, 98], [215, 98, 15], [215, 15, 93], [215, 93, 137], [216, 36, 109], [216, 109, 16], [216, 16, 35], [216, 35, 36], [217, 124, 16], [217, 16, 35], [217, 35, 101], [217, 101, 124], [218, 41, 124], [218, 124, 16], [218, 16, 72], [218, 72, 41], [219, 130, 109], [219, 109, 16], [219, 16, 72], [219, 72, 130], [220, 138, 17], [220, 17, 40], [220, 40, 130], [220, 130, 138], [221, 139, 134], [221, 134, 17], [221, 17, 40], [221, 40, 139], [222, 60, 19], [222, 19, 55], [222, 55, 68], [222, 68, 60], [223, 82, 20], [223, 20, 34], [223, 34, 61], [223, 61, 82], [224, 102, 20], [224, 20, 34], [224, 34, 106], [224, 106, 102], [225, 82, 20], [225, 20, 78], [225, 78, 86], [225, 86, 82], [226, 103, 102], [226, 102, 20], [226, 20, 78], [226, 78, 103], [227, 98, 21], [227, 21, 66], [227, 66, 112], [227, 112, 98], [228, 127, 21], [228, 21, 98], [228, 98, 137], [228, 137, 127], [229, 59, 39], [229, 39, 22], [229, 22, 23], [229, 23, 59], [230, 97, 39], [230, 39, 22], [230, 22, 24], [230, 24, 97], [231, 69, 22], [231, 22, 24], [231, 24, 75], [231, 75, 69], [232, 69, 22], [232, 22, 47], [232, 47, 90], [232, 90, 69], [233, 108, 23], [233, 23, 59], [233, 59, 104], [233, 104, 108], [234, 108, 23], [234, 23, 105], [234, 105, 123], [234, 123, 108], [235, 94, 25], [235, 25, 86], [235, 86, 78], [235, 78, 94], [236, 114, 25], [236, 25, 86], [236, 86, 82], [236, 82, 114], [237, 129, 27], [237, 27, 71], [237, 71, 42], [237, 42, 129], [238, 63, 129], [238, 129, 27], [238, 27, 95], [238, 95, 63], [239, 91, 27], [239, 27, 90], [239, 90, 89], [239, 89, 91], [240, 95, 27], [240, 27, 90], [240, 90, 99], [240, 99, 95], [241, 54, 28], [241, 28, 45], [241, 45, 92], [241, 92, 54], [242, 137, 28], [242, 28, 45], [242, 45, 127], [242, 127, 137], [243, 64, 80], [243, 80, 28], [243, 28, 54], [243, 54, 64], [244, 137, 28], [244, 28, 80], [244, 80, 93], [244, 93, 137], [245, 112, 66], [245, 66, 29], [245, 29, 60], [245, 60, 112], [246, 126, 29], [246, 29, 66], [246, 66, 84], [246, 84, 126], [247, 36, 48], [247, 48, 30], [247, 30, 35], [247, 35, 36], [248, 65, 30], [248, 30, 35], [248, 35, 101], [248, 101, 65], [249, 49, 74], [249, 74, 30], [249, 30, 65], [249, 65, 49], [250, 111, 31], [250, 31, 107], [250, 107, 37], [250, 37, 111], [251, 111, 31], [251, 31, 38], [251, 38, 77], [251, 77, 111], [252, 121, 32], [252, 32, 39], [252, 39, 59], [252, 59, 121], [253, 120, 47], [253, 47, 32], [253, 32, 44], [253, 44, 120], [254, 138, 33], [254, 33, 128], [254, 128, 87], [254, 87, 138], [255, 49, 74], [255, 74, 34], [255, 34, 61], [255, 61, 49], [256, 109, 36], [256, 36, 70], [256, 70, 87], [256, 87, 109], [257, 107, 37], [257, 37, 88], [257, 88, 128], [257, 128, 107], [258, 111, 37], [258, 37, 88], [258, 88, 132], [258, 132, 111], [259, 73, 38], [259, 38, 62], [259, 62, 118], [259, 118, 73], [260, 77, 38], [260, 38, 73], [260, 73, 64], [260, 64, 77], [261, 97, 39], [261, 39, 57], [261, 57, 51], [261, 51, 97], [262, 72, 146], [262, 146, 40], [262, 40, 130], [262, 130, 72], [263, 119, 139], [263, 139, 40], [263, 40, 110], [263, 110, 119], [264, 158, 146], [264, 146, 40], [264, 40, 110], [264, 110, 143], [264, 143, 158], [265, 141, 41], [265, 41, 72], [265, 72, 146], [265, 146, 141], [266, 159, 141], [266, 141, 41], [266, 41, 124], [266, 124, 147], [266, 147, 159], [267, 113, 129], [267, 129, 42], [267, 42, 79], [267, 79, 113], [268, 49, 140], [268, 140, 43], [268, 43, 61], [268, 61, 49], [269, 82, 114], [269, 114, 43], [269, 43, 61], [269, 61, 82], [270, 125, 43], [270, 43, 114], [270, 114, 135], [270, 135, 125], [271, 161, 140], [271, 140, 43], [271, 43, 125], [271, 125, 144], [271, 144, 161], [272, 118, 46], [272, 46, 100], [272, 100, 73], [272, 73, 118], [273, 115, 46], [273, 46, 100], [273, 100, 81], [273, 81, 115], [274, 115, 46], [274, 46, 102], [274, 102, 103], [274, 103, 115], [275, 118, 46], [275, 46, 102], [275, 102, 106], [275, 106, 118], [276, 120, 47], [276, 47, 90], [276, 90, 89], [276, 89, 120], [277, 157, 155], [277, 155, 140], [277, 140, 49], [277, 49, 65], [277, 65, 147], [277, 147, 157], [278, 112, 50], [278, 50, 68], [278, 68, 60], [278, 60, 112], [279, 116, 50], [279, 50, 112], [279, 112, 67], [279, 67, 116], [280, 134, 50], [280, 50, 68], [280, 68, 139], [280, 139, 134], [281, 112, 98], [281, 98, 52], [281, 52, 67], [281, 67, 112], [282, 131, 52], [282, 52, 67], [282, 67, 116], [282, 116, 131], [283, 100, 54], [283, 54, 64], [283, 64, 73], [283, 73, 100], [284, 100, 54], [284, 54, 92], [284, 92, 81], [284, 81, 100], [285, 133, 85], [285, 85, 122], [285, 122, 58], [285, 58, 93], [285, 93, 80], [285, 80, 133], [286, 104, 59], [286, 59, 85], [286, 85, 133], [286, 133, 104], [287, 121, 59], [287, 59, 85], [287, 85, 122], [287, 122, 121], [288, 129, 63], [288, 63, 105], [288, 105, 69], [288, 69, 129], [289, 76, 117], [289, 117, 63], [289, 63, 95], [289, 95, 76], [290, 123, 105], [290, 105, 63], [290, 63, 83], [290, 83, 123], [291, 132, 117], [291, 117, 63], [291, 63, 83], [291, 83, 132], [292, 80, 64], [292, 64, 77], [292, 77, 133], [292, 133, 80], [293, 147, 65], [293, 65, 101], [293, 101, 124], [293, 124, 147], [294, 113, 129], [294, 129, 69], [294, 69, 75], [294, 75, 113], [295, 105, 69], [295, 69, 90], [295, 90, 99], [295, 99, 105], [296, 107, 70], [296, 70, 87], [296, 87, 128], [296, 128, 107], [297, 123, 108], [297, 108, 104], [297, 104, 133], [297, 133, 77], [297, 77, 111], [297, 111, 132], [297, 132, 83], [297, 83, 123], [298, 126, 103], [298, 103, 78], [298, 78, 94], [298, 94, 126], [299, 103, 126], [299, 126, 84], [299, 84, 115], [299, 115, 103], [300, 138, 87], [300, 87, 109], [300, 109, 130], [300, 130, 138], [301, 151, 162], [301, 162, 143], [301, 143, 110], [301, 110, 119], [301, 119, 145], [301, 145, 151], [302, 156, 145], [302, 145, 119], [302, 119, 139], [302, 139, 142], [302, 142, 156], [303, 161, 140], [303, 140, 155], [303, 155, 153], [303, 153, 161], [304, 149, 163], [304, 163, 141], [304, 141, 146], [304, 146, 149], [305, 163, 141], [305, 141, 159], [305, 159, 154], [305, 154, 163], [306, 148, 150], [306, 150, 142], [306, 142, 144], [306, 144, 148], [307, 160, 156], [307, 156, 142], [307, 142, 150], [307, 150, 160], [308, 152, 162], [308, 162, 143], [308, 143, 158], [308, 158, 152], [309, 153, 161], [309, 161, 144], [309, 144, 148], [309, 148, 153], [310, 156, 145], [310, 145, 151], [310, 151, 160], [310, 160, 156], [311, 158, 146], [311, 146, 149], [311, 149, 152], [311, 152, 158], [312, 159, 147], [312, 147, 157], [312, 157, 154], [312, 154, 159], [313, 149, 163], [313, 163, 148], [313, 148, 150], [313, 150, 149], [314, 163, 148], [314, 148, 153], [314, 153, 154], [314, 154, 163], [315, 152, 149], [315, 149, 150], [315, 150, 160], [315, 160, 152], [316, 160, 151], [316, 151, 155], [316, 155, 153], [316, 153, 160], [317, 157, 162], [317, 162, 151], [317, 151, 155], [317, 155, 157], [318, 153, 160], [318, 160, 152], [318, 152, 154], [318, 154, 153], [319, 162, 152], [319, 152, 154], [319, 154, 157], [319, 157, 162]] + @test Set(triangles) == Set(trianglesPy) + end +end + +end diff --git a/examples/simplexn-speedup.jl b/examples/simplexn-speedup.jl new file mode 100644 index 00000000..2a21b116 --- /dev/null +++ b/examples/simplexn-speedup.jl @@ -0,0 +1,75 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - speedup --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +include("../src/simplexn-serial.jl") +include("../src/psimplexn.jl") + +using Statistics +using Plots +Plots.scalefontsizes(0.7) +gr() # loading backend + +VOID = [Int64[]],[[0]] # the empty simplicial model +nt, N = 7, 5 + +# Compute the execution mean time +function timing(f::Function,x,n::Int64) + t = Array{Float64}(undef,n) + f(x...) + for k in 1:n + t[k] = @elapsed f(x...) + end + return mean(t) +end + +# Create and save the plots in the specified folder +function plotting(name::String,timeS::Array{Float64,1},timeP::Array{Float64,1},flag::Int64) + l = max(length(timeS),length(timeP))+1 + pathName = "./"*name + s, p, xlb, ylb, DPI = "Serial", "Parallel", "Input", "Time (seconds)", 150 + plot(timeS,xlims=(1,l),title=name,label=s,xlabel=xlb,ylabel=ylb,dpi=DPI,legend=:topleft) + savefig(pathName*"serial") + plot(timeP,xlims=(1,l),title=name,label=p,xlabel=xlb,ylabel=ylb,dpi=DPI,legend=:topleft) + savefig(pathName*"parallel") + plot([timeS,timeP],xlims=(1,l),title=name,label=[s,p],xlabel=xlb,ylabel=ylb,dpi=DPI,legend=:topleft) + savefig(pathName*"both") +end + +# Create the plots +function plotting(name::String,timeS::Array{Float64,1},timeP::Array{Float64,1}) + l = max(length(timeS),length(timeP))+1 + s, p, xlb, ylb, DPI = "Serial", "Parallel", "Input", "Time (seconds)", 150 + p1 = plot(timeS,label=s,title=name) + p2 = plot(timeP,label=p) + p3 = plot([timeS,timeP],label=[s,p]) + plot(p1,p2,p3,xlims=(1,l),xlabel=xlb,ylabel=ylb,dpi=1.5*DPI,legend=:topleft) +end + + +timeSer = [timing(larExtrude1,[VOID,repeat([1,2,3,4],k^4)],nt) for k in 1:2*N] +timePar = [timing(plarExtrude1,[VOID,repeat([1,2,3,4],k^4)],nt) for k in 1:2*N] +plotting("larExtrude1",timeSer,timePar) + + +simp = [collect(1:500)] +sLen = length(simp[1]) +for k in 2:2*N^2 + push!(simp,simp[end].+sLen) +end +timeSer = [timing(larSimplexFacets,[simp[1:k]],nt) for k in 1:2*N^2] +timePar = [timing(plarSimplexFacets,[simp[1:k]],nt) for k in 1:2*N^2] +plotting("larSimplexFacets",timeSer,timePar) + + +verts, quads = [[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]], [[0,1,2,3],[4,5,6,7]] +len = length(quads[1]) +for k in 2:2*N^2 + append!(verts,map(x->x.+1,verts[end-len+1:end])) + append!(quads,[quads[end].+len]) +end +timeSer = [timing(quads2tria,[(verts[1:len*k],quads[1:k])],nt) for k in 1:2*N^2] +timePar = [timing(pquads2tria,[(verts[1:len*k],quads[1:k])],nt) for k in 1:2*N^2] +plotting("quads2tria",timeSer,timePar) diff --git a/src/psimplexn.jl b/src/psimplexn.jl new file mode 100644 index 00000000..950bd2a8 --- /dev/null +++ b/src/psimplexn.jl @@ -0,0 +1,201 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - parallel version --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +""" + plarExtrude1(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}, pattern::Array{Int64,1}) where T<:Real + ::Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + +Algorithm for multidimensional extrusion of a simplicial complex. +Can be applied to 0-, 1-, 2-, ... simplicial models, to get a 1-, 2-, 3-, ... model. +The pattern `Array` is used to specify how to decompose the added dimension. + +A `model` is a LAR model, i.e. a pair (vertices,cells) to be extruded, whereas pattern is an array of `Int64`, to be used as lateral measures of the *extruded* model. `pattern` elements are assumed as either *solid* or *empty* measures, according to their (+/-) sign. + +# Example +```julia +julia> V = [[0,0], [1,0], [2,0], [0,1], [1,1], [2,1], [0,2], [1,2], [2,2]]; + +julia> FV = [[1,2,4],[2,3,5],[3,5,6],[4,5,7],[5,7,8],[6,8,9]]; + +julia> pattern = repeat([1,2,-3],outer=4); + +julia> model = (V,FV); + +julia> W,FW = plarExtrude1(model, pattern); +``` +""" +# Generation of the output model vertices in a multiple extrusion of a LAR model +using SharedArrays + +@everywhere function plarExtrude1(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}, pattern::Array{Int64,1}) where T<:Real + V, FV = model + d, m = length(FV[1]), length(pattern) + dd1 = d*(d+1) + coords = cumsum(append!([0],abs.(pattern))) # built-in function cumsum + outVertices = @spawn [vcat(v,z) for z in coords for v in V] + offset, outcells, rangelimit = length(V), SharedArray{Int64}(m,dd1*length(FV)), d*m + @sync @distributed for j in 1:length(FV) + tube = [v+k*offset for k in 0:m for v in FV[j]] + celltube = Int64[] + celltube = @sync @distributed (append!) for k in 1:rangelimit + tube[k:k+d] + end + outcells[:,(j-1)*dd1+1:(j-1)*dd1+dd1] = reshape(celltube,dd1,m)' + end + p = convert(SharedArray,findall(x->x>0,pattern)) + cellGroups = SharedArray{Int64}(length(p),size(outcells)[2]) + @sync @distributed for k in 1:length(p) + cellGroups[k,:] = outcells[p[k],:] + end + cellGroupsL = vec(cellGroups') + outCellGroups = Array{Int64,1}[] + outCellGroups = @distributed (append!) for k in 1:d+1:length(cellGroupsL) + [cellGroupsL[k:k+d]] + end + return fetch(outVertices), outCellGroups +end + +""" + plarSimplexGrid1(shape::Array{Int64,1})::Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + +Generate a simplicial complex decomposition of a cubical grid of ``d``-cuboids, where ``d`` is the length of `shape` array. Vertices (0-cells) of the grid have `Int64` coordinates. + +# Example +```julia +julia> plarSimplexGrid1([0]) # 0-dimensional complex +# output +(Array{Int64,1}[[0]], Array{Int64,1}[]) + +julia> V,EV = plarSimplexGrid1([1]) # 1-dimensional complex +# output +(Array{Int64,1}[[0], [1]], Array{Int64,1}[[0, 1]]) + +julia> V,FV = plarSimplexGrid1([1,1]) # 2-dimensional complex +# output +(Array{Int64,1}[[0, 0], [1, 0], [0, 1], [1, 1]], Array{Int64,1}[[0, 1, 2], [1, 2, 3]]) + +julia> V,CV = plarSimplexGrid1([10,10,1]) # 3-dimensional complex +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [4, 0, 0], [5, 0, 0], [6, 0, 0], [7, 0, 0], [8, 0, 0], [9, 0, 0] … [1, 10, 1], [2, 10, 1], [3, 10, 1], [4, 10, 1], [5, 10, 1], [6, 10, 1], [7, 10, 1], [8, 10, 1], [9, 10, 1], [10, 10, 1]], Array{Int64,1}[[0, 1, 11, 121], [1, 11, 121, 122], [11, 121, 122, 132], [1, 11, 12, 122], [11, 12, 122, 132], [12, 122, 132, 133], [1, 2, 12, 122], [2, 12, 122, 123], [12, 122, 123, 133], [2, 12, 13, 123] … [118, 228, 229, 239], [108, 118, 119, 229], [118, 119, 229, 239], [119, 229, 239, 240], [108, 109, 119, 229], [109, 119, 229, 230], [119, 229, 230, 240], [109, 119, 120, 230], [119, 120, 230, 240], [120, 230, 240, 241]]) + +julia> V,HV = plarSimplexGrid1([1,1,1,1]) # 4-dim cellular complex from the 4D simplex +# output +(Array{Int64,1}[[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, 1, 0, 0], [0, 0, 1, 0], [1, 0, 1, 0], [0, 1, 1, 0], [1, 1, 1, 0], [0, 0, 0, 1], [1, 0, 0, 1], [0, 1, 0, 1], [1, 1, 0, 1], [0, 0, 1, 1], [1, 0, 1, 1], [0, 1, 1, 1], [1, 1, 1, 1]], Array{Int64,1}[[0, 1, 2, 4, 8], [1, 2, 4, 8, 9], [2, 4, 8, 9, 10], [4, 8, 9, 10, 12], [1, 2, 4, 5, 9], [2, 4, 5, 9, 10], [4, 5, 9, 10, 12], [5, 9, 10, 12, 13], [2, 4, 5, 6, 10], [4, 5, 6, 10, 12] … [3, 5, 9, 10, 11], [5, 9, 10, 11, 13], [2, 3, 5, 6, 10], [3, 5, 6, 10, 11], [5, 6, 10, 11, 13], [6, 10, 11, 13, 14], [3, 5, 6, 7, 11], [5, 6, 7, 11, 13], [6, 7, 11, 13, 14], [7, 11, 13, 14, 15]]) +``` +""" +# Generation of simplicial grids of any dimension and shape +@everywhere function plarSimplexGrid1(shape::Array{Int64,1}) + model = [Int64[]],[[0]] # the empty simplicial model + for item in shape # no parallel + model = plarExtrude1(model,repeat([1],item)) + end + return model +end + + +""" + plarSimplexFacets(simplices::Array{Array{Int64,1},1})::Array{Array{Int64,1},1} + +Compute the `(d-1)`-skeleton (set of `facets`) of a simplicial `d`-complex. + +# Example +```julia +julia> V,FV = plarSimplexGrid1([1,1]) +# output +(Array{Int64,1}[[0, 0], [1, 0], [0, 1], [1, 1]], Array{Int64,1}[[0, 1, 2], [1, 2, 3]]) + +julia> W,CW = plarExtrude1((V,FV), [1]) +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], Array{Int64,1}[[0, 1, 2, 4], [1, 2, 4, 5], [2, 4, 5, 6], [1, 2, 3, 5], [2, 3, 5, 6], [3, 5, 6, 7]]) + +julia> FW = plarSimplexFacets(CW) +18-element Array{Array{Int64,1},1}: + [0, 1, 2] + [0, 1, 4] + [0, 2, 4] + [1, 2, 3] + [1, 2, 4] + [1, 2, 5] + [1, 3, 5] + [1, 4, 5] + [2, 3, 5] + [2, 3, 6] + [2, 4, 5] + [2, 4, 6] + [2, 5, 6] + [3, 5, 6] + [3, 5, 7] + [3, 6, 7] + [4, 5, 6] + [5, 6, 7] +``` +""" +# Extraction of non-oriented (d-1)-facets of d-dimensional simplices +@everywhere using Combinatorics # for combinations() function + +@everywhere function plarSimplexFacets(simplices::Array{Array{Int64,1},1}) + out = Array{Int64,1}[] + d = length(simplices[1]) + out = @distributed (append!) for simplex in simplices + collect(combinations(simplex,d-1)) + end + return sort!(unique(out),lt=isless) +end + + +""" + pquads2tria(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}) where T<:Real + ::Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + +Give the conversion of a LAR boundary representation (B-Rep), i.e. a LAR model `V, FV` made of 2D faces, usually quads but also general polygons, into a LAR model `verts, triangles` made by triangles. + +# Example +```julia +julia> model = plarSimplexGrid1([2,2,2]) +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1] … [2, 2, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]], Array{Int64,1}[[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 3, 4, 10], [3, 4, 10, 12], [4, 10, 12, 13], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11] … [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [13, 14, 16, 22], [14, 16, 22, 23], [16, 22, 23, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26]]) + +julia> pquads2tria(model) +# output +(Array{Float64,1}[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [0.0, 2.0, 0.0], [1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [0.0, 0.0, 1.0] … [0.25, 1.5, 1.75], [0.75, 1.5, 1.25], [0.5, 1.75, 1.5], [0.75, 1.75, 1.75], [1.25, 1.25, 1.25], [1.5, 1.25, 1.5], [1.25, 1.5, 1.75], [1.75, 1.5, 1.25], [1.5, 1.75, 1.5], [1.75, 1.75, 1.75]], Array{Int64,1}[[27, 3, 9], [27, 9, 0], [27, 0, 1], [27, 1, 3], [28, 9, 10], [28, 10, 1], [28, 1, 3], [28, 3, 9], [29, 10, 12], [29, 12, 3] … [72, 16, 17], [72, 17, 23], [73, 23, 25], [73, 25, 16], [73, 16, 17], [73, 17, 23], [74, 26, 25], [74, 25, 17], [74, 17, 23], [74, 23, 26]]) +``` +""" +# Transformation to triangles by sorting circularly the vertices of faces +using LinearAlgebra + +@everywhere function pquads2tria(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}) where T<:Real + V, FV = model + if typeof(V) != Array{Array{Float64,1},1} + V = convert(Array{Array{Float64,1},1},V) + end + out = Array{Int64,1}[] + nverts = length(V)-1 + for face in FV # no parallel + arr = [V[v+1] for v in face] + centroid = sum(arr)/length(arr) + append!(V,[centroid]) + nverts += 1 + v1, v2 = V[face[1]+1]-centroid, V[face[2]+1]-centroid + v3 = cross(v1,v2) + if norm(v3) < 1/(10^3) + v1, v2 = V[face[1]+1]-centroid, V[face[3]+1]-centroid + v3 = cross(v1,v2) + end + transf = inv(copy(hcat(v1,v2,v3)')) + verts = [(V[v+1]'*transf)'[1:end-1] for v in face] + tcentroid = sum(verts)/length(verts) + tverts = pmap(x->x-tcentroid,verts) + iterator = collect(zip(tverts,face)) + rverts = [[atan(reverse(iterator[i][1])...),iterator[i][2]] for i in 1:length(iterator)] + rvertsS = sort(rverts,lt=(x,y)->isless(x[1],y[1])) + ord = [pair[2] for pair in rvertsS] + append!(ord,ord[1]) + edges = [[i[2],ord[i[1]+1]] for i in enumerate(ord[1:end-1])] + triangles = pmap(x->prepend!(x,nverts),edges) + append!(out,triangles) + end + return V, out +end diff --git a/src/simplexn-serial.jl b/src/simplexn-serial.jl new file mode 100644 index 00000000..212470ce --- /dev/null +++ b/src/simplexn-serial.jl @@ -0,0 +1,200 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - serial version --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + + +""" + larExtrude1(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}, pattern::Array{Int64,1}) where T<:Real + ::Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + +Algorithm for multidimensional extrusion of a simplicial complex. +Can be applied to 0-, 1-, 2-, ... simplicial models, to get a 1-, 2-, 3-, ... model. +The pattern `Array` is used to specify how to decompose the added dimension. + +A `model` is a LAR model, i.e. a pair (vertices,cells) to be extruded, whereas pattern is an array of `Int64`, to be used as lateral measures of the *extruded* model. `pattern` elements are assumed as either *solid* or *empty* measures, according to their (+/-) sign. + +# Example +```julia +julia> V = [[0,0], [1,0], [2,0], [0,1], [1,1], [2,1], [0,2], [1,2], [2,2]]; + +julia> FV = [[1,2,4],[2,3,5],[3,5,6],[4,5,7],[5,7,8],[6,8,9]]; + +julia> pattern = repeat([1,2,-3],outer=4); + +julia> model = (V,FV); + +julia> W,FW = larExtrude1(model, pattern); +``` +""" +# Generation of the output model vertices in a multiple extrusion of a LAR model +function larExtrude1(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}, pattern::Array{Int64,1}) where T<:Real + V, FV = model + d, m = length(FV[1]), length(pattern) + coords = cumsum(append!([0],abs.(pattern))) # built-in function cumsum + offset, outcells, rangelimit = length(V), Array{Int64}(undef,m,0), d*m + for cell in FV + tube = [v+k*offset for k in 0:m for v in cell] + celltube = Int64[] + for k in 1:rangelimit + append!(celltube,tube[k:k+d]) + end + outcells = hcat(outcells,reshape(celltube,d*(d+1),m)') + end + cellGroups = Int64[] + for k in 1:m + if pattern[k]>0 + cellGroups = vcat(cellGroups,outcells[k,:]) + end + end + outVertices = [vcat(v,z) for z in coords for v in V] + outCellGroups = Array{Int64,1}[] + for k in 1:d+1:length(cellGroups) + append!(outCellGroups,[cellGroups[k:k+d]]) + end + return outVertices, outCellGroups +end + + +""" + larSimplexGrid1(shape::Array{Int64,1})::Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + +Generate a simplicial complex decomposition of a cubical grid of ``d``-cuboids, where ``d`` is the length of `shape` array. Vertices (0-cells) of the grid have `Int64` coordinates. + +# Example +```julia +julia> larSimplexGrid1([0]) # 0-dimensional complex +# output +(Array{Int64,1}[[0]], Array{Int64,1}[]) + +julia> V,EV = larSimplexGrid1([1]) # 1-dimensional complex +# output +(Array{Int64,1}[[0], [1]], Array{Int64,1}[[0, 1]]) + +julia> V,FV = larSimplexGrid1([1,1]) # 2-dimensional complex +# output +(Array{Int64,1}[[0, 0], [1, 0], [0, 1], [1, 1]], Array{Int64,1}[[0, 1, 2], [1, 2, 3]]) + +julia> V,CV = larSimplexGrid1([10,10,1]) # 3-dimensional complex +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [4, 0, 0], [5, 0, 0], [6, 0, 0], [7, 0, 0], [8, 0, 0], [9, 0, 0] … [1, 10, 1], [2, 10, 1], [3, 10, 1], [4, 10, 1], [5, 10, 1], [6, 10, 1], [7, 10, 1], [8, 10, 1], [9, 10, 1], [10, 10, 1]], Array{Int64,1}[[0, 1, 11, 121], [1, 11, 121, 122], [11, 121, 122, 132], [1, 11, 12, 122], [11, 12, 122, 132], [12, 122, 132, 133], [1, 2, 12, 122], [2, 12, 122, 123], [12, 122, 123, 133], [2, 12, 13, 123] … [118, 228, 229, 239], [108, 118, 119, 229], [118, 119, 229, 239], [119, 229, 239, 240], [108, 109, 119, 229], [109, 119, 229, 230], [119, 229, 230, 240], [109, 119, 120, 230], [119, 120, 230, 240], [120, 230, 240, 241]]) + +julia> V,HV = larSimplexGrid1([1,1,1,1]) # 4-dim cellular complex from the 4D simplex +# output +(Array{Int64,1}[[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, 1, 0, 0], [0, 0, 1, 0], [1, 0, 1, 0], [0, 1, 1, 0], [1, 1, 1, 0], [0, 0, 0, 1], [1, 0, 0, 1], [0, 1, 0, 1], [1, 1, 0, 1], [0, 0, 1, 1], [1, 0, 1, 1], [0, 1, 1, 1], [1, 1, 1, 1]], Array{Int64,1}[[0, 1, 2, 4, 8], [1, 2, 4, 8, 9], [2, 4, 8, 9, 10], [4, 8, 9, 10, 12], [1, 2, 4, 5, 9], [2, 4, 5, 9, 10], [4, 5, 9, 10, 12], [5, 9, 10, 12, 13], [2, 4, 5, 6, 10], [4, 5, 6, 10, 12] … [3, 5, 9, 10, 11], [5, 9, 10, 11, 13], [2, 3, 5, 6, 10], [3, 5, 6, 10, 11], [5, 6, 10, 11, 13], [6, 10, 11, 13, 14], [3, 5, 6, 7, 11], [5, 6, 7, 11, 13], [6, 7, 11, 13, 14], [7, 11, 13, 14, 15]]) +``` +""" +# Generation of simplicial grids of any dimension and shape +function larSimplexGrid1(shape::Array{Int64,1}) + model = [Int64[]],[[0]] # the empty simplicial model + for item in shape + model = larExtrude1(model,repeat([1],item)) + end + return model +end + + +""" + larSimplexFacets(simplices::Array{Array{Int64,1},1})::Array{Array{Int64,1},1} + +Compute the `(d-1)`-skeleton (set of `facets`) of a simplicial `d`-complex. + +# Example +```julia +julia> V,FV = larSimplexGrid1([1,1]) +# output +(Array{Int64,1}[[0, 0], [1, 0], [0, 1], [1, 1]], Array{Int64,1}[[0, 1, 2], [1, 2, 3]]) + +julia> W,CW = larExtrude1((V,FV), [1]) +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], Array{Int64,1}[[0, 1, 2, 4], [1, 2, 4, 5], [2, 4, 5, 6], [1, 2, 3, 5], [2, 3, 5, 6], [3, 5, 6, 7]]) + +julia> FW = larSimplexFacets(CW) +18-element Array{Array{Int64,1},1}: + [0, 1, 2] + [0, 1, 4] + [0, 2, 4] + [1, 2, 3] + [1, 2, 4] + [1, 2, 5] + [1, 3, 5] + [1, 4, 5] + [2, 3, 5] + [2, 3, 6] + [2, 4, 5] + [2, 4, 6] + [2, 5, 6] + [3, 5, 6] + [3, 5, 7] + [3, 6, 7] + [4, 5, 6] + [5, 6, 7] +``` +""" +# Extraction of non-oriented (d-1)-facets of d-dimensional simplices +using Combinatorics # for combinations() function + +function larSimplexFacets(simplices::Array{Array{Int64,1},1}) + out = Array{Int64,1}[] + d = length(simplices[1]) + for simplex in simplices + append!(out,collect(combinations(simplex,d-1))) + end + return sort!(unique(out),lt=isless) +end + + +""" + quads2tria(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}) where T<:Real + ::Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + +Give the conversion of a LAR boundary representation (B-Rep), i.e. a LAR model `V, FV` made of 2D faces, usually quads but also general polygons, into a LAR model `verts, triangles` made by triangles. + +# Example +```julia +julia> model = larSimplexGrid1([2,2,2]) +# output +(Array{Int64,1}[[0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [0, 0, 1] … [2, 2, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]], Array{Int64,1}[[0, 1, 3, 9], [1, 3, 9, 10], [3, 9, 10, 12], [1, 3, 4, 10], [3, 4, 10, 12], [4, 10, 12, 13], [1, 2, 4, 10], [2, 4, 10, 11], [4, 10, 11, 13], [2, 4, 5, 11] … [15, 21, 22, 24], [13, 15, 16, 22], [15, 16, 22, 24], [16, 22, 24, 25], [13, 14, 16, 22], [14, 16, 22, 23], [16, 22, 23, 25], [14, 16, 17, 23], [16, 17, 23, 25], [17, 23, 25, 26]]) + +julia> quads2tria(model) +# output +(Array{Float64,1}[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [0.0, 2.0, 0.0], [1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [0.0, 0.0, 1.0] … [0.25, 1.5, 1.75], [0.75, 1.5, 1.25], [0.5, 1.75, 1.5], [0.75, 1.75, 1.75], [1.25, 1.25, 1.25], [1.5, 1.25, 1.5], [1.25, 1.5, 1.75], [1.75, 1.5, 1.25], [1.5, 1.75, 1.5], [1.75, 1.75, 1.75]], Array{Int64,1}[[27, 3, 9], [27, 9, 0], [27, 0, 1], [27, 1, 3], [28, 9, 10], [28, 10, 1], [28, 1, 3], [28, 3, 9], [29, 10, 12], [29, 12, 3] … [72, 16, 17], [72, 17, 23], [73, 23, 25], [73, 25, 16], [73, 16, 17], [73, 17, 23], [74, 26, 25], [74, 25, 17], [74, 17, 23], [74, 23, 26]]) +``` +""" +# Transformation to triangles by sorting circularly the vertices of faces +using LinearAlgebra + +function quads2tria(model::Tuple{Array{Array{T,1},1},Array{Array{Int64,1},1}}) where T<:Real + V, FV = model + if typeof(V) != Array{Array{Float64,1},1} + V = convert(Array{Array{Float64,1},1},V) + end + out = Array{Int64,1}[] + nverts = length(V)-1 + for face in FV + arr = [V[v+1] for v in face] + centroid = sum(arr)/length(arr) + append!(V,[centroid]) + nverts += 1 + v1, v2 = V[face[1]+1]-centroid, V[face[2]+1]-centroid + v3 = cross(v1,v2) + if norm(v3) < 1/(10^3) + v1, v2 = V[face[1]+1]-centroid, V[face[3]+1]-centroid + v3 = cross(v1,v2) + end + transf = inv(copy(hcat(v1,v2,v3)')) + verts = [(V[v+1]'*transf)'[1:end-1] for v in face] + tcentroid = sum(verts)/length(verts) + tverts = [v-tcentroid for v in verts] + iterator = collect(zip(tverts,face)) + rverts = [[atan(reverse(iterator[i][1])...),iterator[i][2]] for i in 1:length(iterator)] + rvertsS = sort(rverts,lt=(x,y)->isless(x[1],y[1])) + ord = [pair[2] for pair in rvertsS] + append!(ord,ord[1]) + edges = [[i[2],ord[i[1]+1]] for i in enumerate(ord[1:end-1])] + triangles = [prepend!(edge,nverts) for edge in edges] + append!(out,triangles) + end + return V, out +end diff --git a/test/psimplexn.jl b/test/psimplexn.jl new file mode 100644 index 00000000..c4f1e35e --- /dev/null +++ b/test/psimplexn.jl @@ -0,0 +1,181 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - parallel unit tests --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +include("../src/psimplexn.jl") + +using Test + +println("Checking the number of nodes...") +if nprocs() < 4 + println("The number of nodes is less then 4, you shall not pass!") + sleep(3) + exit(1) +else + println("You have more than 3 nodes, good to go!") +end + +@testset "Unit Tests" begin + @testset "plarExtrude1" begin + VOID = [Int64[]],[[0]] # the empty simplicial model + pattern1 = [1,-1] + model1 = plarExtrude1(VOID,pattern1) # 1D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == length(pattern1)+1 # num of vertices, no rep + @test length(model1[2]) == length(filter(x->x>0,pattern1)) # num of 1D-simplices + + pattern2 = [1,1,1,-1] + model2 = plarExtrude1(VOID,pattern2) # 1D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == length(pattern2)+1 # num of vertices, no rep + @test length(model2[2]) == length(filter(x->x>0,pattern2)) # num of 1D-simplices + + pattern3 = [1,1,1,1,1,-1] + model3 = plarExtrude1(VOID,pattern3) # 1D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == length(pattern3)+1 # num of vertices, no rep + @test length(model3[2]) == length(filter(x->x>0,pattern3)) # num of 1D-simplices + + model1 = plarExtrude1(model1,pattern1) # 2D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == (length(pattern1)+1)^2 # num of vertices, no rep + @test length(model1[2]) == 2*length(filter(x->x>0,pattern1))^2 # num of 2D-simplices + + model2 = plarExtrude1(model2,pattern2) # 2D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == (length(pattern2)+1)^2 # num of vertices, no rep + @test length(model2[2]) == 2*length(filter(x->x>0,pattern2))^2 # num of 2D-simplices + + model3 = plarExtrude1(model3,pattern3) # 2D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == (length(pattern3)+1)^2 # num of vertices, no rep + @test length(model3[2]) == 2*length(filter(x->x>0,pattern3))^2 # num of 2D-simplices + + model1 = plarExtrude1(model1,pattern1) # 3D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == (length(pattern1)+1)^3 # num of vertices, no rep + @test length(model1[2]) == 6*length(filter(x->x>0,pattern1))^3 # num of 3D-simplices + + model2 = plarExtrude1(model2,pattern2) # 3D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == (length(pattern2)+1)^3 # num of vertices, no rep + @test length(model2[2]) == 6*length(filter(x->x>0,pattern2))^3 # num of 3D-simplices + + model3 = plarExtrude1(model3,pattern3) # 3D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == (length(pattern3)+1)^3 # num of vertices, no rep + @test length(model3[2]) == 6*length(filter(x->x>0,pattern3))^3 # num of 3D-simplices + + model = ([[0.0,0],[0,1]],[[1,0],[1,1]]) # 2D with float + @test typeof(model[1]) == Array{Array{Float64,1},1} + model = plarExtrude1(model,pattern1) + #println(model) + @test typeof(model) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + end + @testset "plarSimplexGrid1" begin + shape = [3] # 1D + model1 = plarSimplexGrid1(shape) + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == shape[1]+1 # num of vertices, no rep + @test length(model1[2]) == shape[1] # num of 1D-simplices + + shape = [3,5] # 2D + model2 = plarSimplexGrid1(shape) + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + # (shape[1]+1)*(shape[2]+1) + @test length(model2[1]) == prod(shape)+sum(shape)+1 # num of vertices, no rep + @test length(model2[2]) == 2*prod(shape) # num of 2D-simplices + + shape = [3,5,7] # 3D + model3 = plarSimplexGrid1(shape) + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + # (shape[1]+1)*(shape[2]+1)*(shape[3]+1); num of vertices, no rep + @test length(model3[1]) == prod(shape)+sum(prod.(collect(combinations(shape,2))))+sum(shape)+1 + @test length(model3[2]) == 6*prod(shape) # num of 3D-simplices + end + @testset "plarSimplexFacets" begin + s = plarSimplexGrid1([3])[2] # 1D + #println(s) + sOut = plarSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + + s = plarSimplexGrid1([3,5])[2] # 2D + #println(s) + sOut = plarSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + + s = plarSimplexGrid1([3,5,7])[2] # 3D + #println(s) + sOut = plarSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + end + @testset "pquads2tria" begin + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,2,3]]) # 2D + modOut = pquads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0.5,1.5,0]],[[0,1,2,3,4]]) # 2D + modOut = pquads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,1,2,3,4,5,6,7]]) # 3D + modOut = pquads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[0.5,0.5,1.5]],[[0,1,2,3,4,5,6,7,8]]) # 3D + modOut = pquads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + end +end diff --git a/test/runtests.jl b/test/runtests.jl index 2fa7495f..e475e1f1 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -11,3 +11,6 @@ include("./struct.jl") include("./mapper.jl") include("./integr.jl") include("./simplexn.jl") + +include("./simplexn-serial.jl") +include("./psimplexn.jl") diff --git a/test/simplexn-serial.jl b/test/simplexn-serial.jl new file mode 100644 index 00000000..636e9a9f --- /dev/null +++ b/test/simplexn-serial.jl @@ -0,0 +1,172 @@ +##################################################### +### From Julia 0.6 to Julia 1.0 +### --- SIMPLEXN - serial unit tests --- +### Authors: Fabio Fatelli, Emanuele Loprevite +##################################################### + +include("../src/simplexn-serial.jl") + +using Test + +@testset "Unit Tests" begin + @testset "larExtrude1" begin + VOID = [Int64[]],[[0]] # the empty simplicial model + pattern1 = [1,-1] + model1 = larExtrude1(VOID,pattern1) # 1D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == length(pattern1)+1 # num of vertices, no rep + @test length(model1[2]) == length(filter(x->x>0,pattern1)) # num of 1D-simplices + + pattern2 = [1,1,1,-1] + model2 = larExtrude1(VOID,pattern2) # 1D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == length(pattern2)+1 # num of vertices, no rep + @test length(model2[2]) == length(filter(x->x>0,pattern2)) # num of 1D-simplices + + pattern3 = [1,1,1,1,1,-1] + model3 = larExtrude1(VOID,pattern3) # 1D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == length(pattern3)+1 # num of vertices, no rep + @test length(model3[2]) == length(filter(x->x>0,pattern3)) # num of 1D-simplices + + model1 = larExtrude1(model1,pattern1) # 2D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == (length(pattern1)+1)^2 # num of vertices, no rep + @test length(model1[2]) == 2*length(filter(x->x>0,pattern1))^2 # num of 2D-simplices + + model2 = larExtrude1(model2,pattern2) # 2D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == (length(pattern2)+1)^2 # num of vertices, no rep + @test length(model2[2]) == 2*length(filter(x->x>0,pattern2))^2 # num of 2D-simplices + + model3 = larExtrude1(model3,pattern3) # 2D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == (length(pattern3)+1)^2 # num of vertices, no rep + @test length(model3[2]) == 2*length(filter(x->x>0,pattern3))^2 # num of 2D-simplices + + model1 = larExtrude1(model1,pattern1) # 3D + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == (length(pattern1)+1)^3 # num of vertices, no rep + @test length(model1[2]) == 6*length(filter(x->x>0,pattern1))^3 # num of 3D-simplices + + model2 = larExtrude1(model2,pattern2) # 3D + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model2[1]) == (length(pattern2)+1)^3 # num of vertices, no rep + @test length(model2[2]) == 6*length(filter(x->x>0,pattern2))^3 # num of 3D-simplices + + model3 = larExtrude1(model3,pattern3) # 3D + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model3[1]) == (length(pattern3)+1)^3 # num of vertices, no rep + @test length(model3[2]) == 6*length(filter(x->x>0,pattern3))^3 # num of 3D-simplices + + model = ([[0.0,0],[0,1]],[[1,0],[1,1]]) # 2D with float + @test typeof(model[1]) == Array{Array{Float64,1},1} + model = larExtrude1(model,pattern1) + #println(model) + @test typeof(model) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + end + @testset "larSimplexGrid1" begin + shape = [3] # 1D + model1 = larSimplexGrid1(shape) + #println(model1) + @test typeof(model1) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test length(model1[1]) == shape[1]+1 # num of vertices, no rep + @test length(model1[2]) == shape[1] # num of 1D-simplices + + shape = [3,5] # 2D + model2 = larSimplexGrid1(shape) + #println(model2) + @test typeof(model2) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + # (shape[1]+1)*(shape[2]+1) + @test length(model2[1]) == prod(shape)+sum(shape)+1 # num of vertices, no rep + @test length(model2[2]) == 2*prod(shape) # num of 2D-simplices + + shape = [3,5,7] # 3D + model3 = larSimplexGrid1(shape) + #println(model3) + @test typeof(model3) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + # (shape[1]+1)*(shape[2]+1)*(shape[3]+1); num of vertices, no rep + @test length(model3[1]) == prod(shape)+sum(prod.(collect(combinations(shape,2))))+sum(shape)+1 + @test length(model3[2]) == 6*prod(shape) # num of 3D-simplices + end + @testset "larSimplexFacets" begin + s = larSimplexGrid1([3])[2] # 1D + #println(s) + sOut = larSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + + s = larSimplexGrid1([3,5])[2] # 2D + #println(s) + sOut = larSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + + s = larSimplexGrid1([3,5,7])[2] # 3D + #println(s) + sOut = larSimplexFacets(s) + #println(sOut) + @test typeof(sOut) == Array{Array{Int64,1},1} + d1 = sum([length(s[k]) for k in 1:length(s)])/length(s) + d2 = sum([length(sOut[k]) for k in 1:length(sOut)])/length(sOut) + @test d1-1 == d2 # dimension + # length(s)*binomial(length(s[1]),(length(s[1])-1)) + @test length(sOut) <= length(s)*length(s[1]) # "<=" because no rep + end + @testset "quads2tria" begin + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,2,3]]) # 2D + modOut = quads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0.5,1.5,0]],[[0,1,2,3,4]]) # 2D + modOut = quads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,1,2,3,4,5,6,7]]) # 3D + modOut = quads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Int64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + + modIn = ([[0,0,0],[0,1,0],[1,0,0],[1,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[0.5,0.5,1.5]],[[0,1,2,3,4,5,6,7,8]]) # 3D + modOut = quads2tria(modIn) + #println(modOut) + @test typeof(modIn) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + @test typeof(modOut) == Tuple{Array{Array{Float64,1},1},Array{Array{Int64,1},1}} + edges = 2*sum([length(modIn[2][k]) for k in 1:length(modIn[2])]) + EulerChar = length(modOut[1])-edges+length(modOut[2]) # V - E + F + @test EulerChar == 1 + end +end