References

Zonotopes

• Computing Reachable Sets of Hybrid Systems Using a Combination of Zonotopes and Polytopes. Matthias Althoff, Olaf Stursberg, and Martin Buss

• Le Guernic Thesis.

• EFFICIENT CONVERSION OF GEOMETRIC STATE SET REPRESENTATIONS FOR HYBRID SYSTEMS

• https://mediatum.ub.tum.de/doc/1285848/805972.pdf

• Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars, M. Althoff's PhD thesis.

• Zonotopes as Bounding Volumes

• An Efficient Algorithm for Vertex Enumeration of Two-Dimensional Projection of Polytopes Amit Gurung and Rajarshi Ray

• http://www.lsv.fr/~fribourg/MPRI_2019_Girard_Zonotopes.pdf

Minkowski sum

• https://hal.archives-ouvertes.fr/hal-01092060/document
• https://pdfs.semanticscholar.org/7492/2769a31a4d6695f3ada51b05134f77b4fe5b.pdf
• https://arxiv.org/pdf/1810.01587.pdf

Minkowski difference

• https://en.wikipedia.org/wiki/Minkowski_addition
• On Computing the Minkowski Difference of Zonotopes. Matthias Althoff.
• Theory and computation of disturbance invariant sets for discrete-time linear systems. Ilya Kolmanovsky and Elmer G. Gilbert.
• The Minkowski Difference for Convex Polyhedra and Some its Applications. Z. R. Gabidullina.

Triangulations

• https://github.com/JuliaGeometry/TetGen.jl
• https://github.com/gridap/MiniQhull.jl
  • https://apps.fedoraproject.org/packages/s/libqhull
• https://github.com/JuliaGeometry/VoronoiDelaunay.jl/issues/8
• https://github.com/JuliaPDE/SurveyofPDEPackages
• http://www.personal.psu.edu/cxc11/AERSP560/DELAUNEY/13_Two_algorithms_Delauney.pdf
• https://www.codeproject.com/Articles/587629/A-Delaunay-triangulation-function-in-C
• https://github.com/esimov/triangle
• http://algorist.com/problems/Triangulation.html
• http://algorist.com/sections/Computational_Geometry.html
• http://www.qhull.org/
• http://www.cs.cmu.edu/~quake/triangle.research.html
• Walking through triangulation: https://hal.inria.fr/inria-00102194/document

Polygon intersection

• https://www.sciencedirect.com/science/article/abs/pii/0146664X82900235?via%3Dihub
• https://www.geeksforgeeks.org/geometric-algorithms/
• https://github.com/w8r/orourke-compc/blob/master/convconv/convconv.c
• http://cs.smith.edu/~jorourke/books/compgeom.html
• http://www.geom.uiuc.edu/software/qhull/html/qhalf.htm
• https://www.sciencedirect.com/science/article/abs/pii/0146664X82900235
• https://stackoverflow.com/questions/13101288/intersection-of-two-convex-polygons
• https://link.springer.com/article/10.1007/BF01898355
• https://www.swtestacademy.com/intersection-convex-polygons-algorithm/
• https://www.bowdoin.edu/~ltoma/teaching/cs3250-CompGeom/spring17/Lectures/cg-convexintersection.pdf
• https://rosettacode.org/wiki/Sutherland-Hodgman_polygon_clipping#Julia
• https://github.com/JuliaGeometry/PolygonClipping.jl/blob/master/src/PolygonClipping.jl

More on intersections

• https://apps.dtic.mil/dtic/tr/fulltext/u2/a057560.pdf
• http://www-ljk.imag.fr/membres/Antoine.Girard/Publications/hscc2008b.pdf << Zonotope - HalfSpace intersections

Disjointness check

• Chazelle, B., & Dobkin, D. P. (1980, April). Detection is easier than computation. In Proceedings of the twelfth annual ACM symposium on Theory of computing (pp. 146-153).

Enumerations

• Löhne, A. (2020). Approximate Vertex Enumeration. arXiv preprint arXiv:2007.06325.

• Awasthi, P., Kalantari, B., & Zhang, Y. (2018, March). Robust vertex enumeration for convex hulls in high dimensions. In International Conference on Artificial Intelligence and Statistics (pp. 1387-1396).