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main.cpp
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#include <iostream>
#include <iomanip>
#include <cstdlib>
// optional overridable definitions, here overrided with what would be the defaults
#define MATHEMATICS_SIMPLE_LIBRARY_NAMESPACE Maths
#define MATHEMATICS_SIMPLE_LIBRARY_INDEX_TYPE std::size_t
#define MATHEMATICS_SIMPLE_LIBRARY_DEFAULT_COLUMN_MAJOR false
#define MATHEMATICS_SIMPLE_LIBRARY_DEFAULT_NUMERICAL_TYPE float
#define MATHEMATICS_SIMPLE_LIBRARY_DEFAULT_CONVENTION_RAY_DIRECTION Conventions::RayDirection::Outgoing
#include "mathematics_simple_library.hpp"
using namespace MATHEMATICS_SIMPLE_LIBRARY_NAMESPACE;
#define PRINT_EXEC(...) \
std::cout << "> " << #__VA_ARGS__ << std::endl;\
__VA_ARGS__\
namespace MATHEMATICS_SIMPLE_LIBRARY_NAMESPACE {
template<typename T, std::size_t N>
std::ostream &operator<<(std::ostream &os, const std::array<T, N>& arr) {
std::string out = "(";
if(!arr.empty()) {
for(std::size_t i = 0; i < arr.size() - 1; ++i)
out += std::to_string(arr[i]) + ", ";
out += std::to_string(arr.back());
}
out += ")";
return os << out;
}
template<typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T>& vec) {
std::string out = "(";
if(!vec.empty()) {
for(std::size_t i = 0; i < vec.size() - 1; ++i)
out += std::to_string(vec[i]) + ", ";
out += std::to_string(vec.back());
}
out += ")";
return os << out;
}
template <ConceptVector V>
std::ostream &operator<<(std::ostream &os, const V& vec) {
std::string out = "(";
if(vec.size().get() > 0) {
for(std::size_t i = 0; i < vec.size().get() - 1; ++i)
out += std::to_string(vec[i]) + ", ";
out += std::to_string(vec[vec.size().get()-1]);
}
out += ")";
return os << out;
}
template <ConceptMatrix M>
std::ostream &operator<<(std::ostream &os, const M& mat) {
for (IndexType row = 0; row < mat.row_count().get(); ++row) {
for (IndexType col = 0; col < mat.column_count().get(); ++col)
os << std::setw(12) << mat[row, col] << ",";
os << std::endl;
}
return os;
}
}
int main() {
std::cout << std::fixed;
std::cout << "## procedural vector ##" << std::endl;
PRINT_EXEC(print(vec_constant<4>(1)));
PRINT_EXEC(print(vec_constant(1, 4)));
PRINT_EXEC(print(vec_procedural<4>([](auto i, auto size) { return size - i; })));
PRINT_EXEC(print(vec_procedural(4, [](auto i, auto size) { return size - i; })));
std::cout << "## procedural matrix ##" << std::endl;
PRINT_EXEC(print(mat_identity<4, 5>()));
PRINT_EXEC(print(mat_zero<2, 2>()));
PRINT_EXEC(print(mat_one<2, 2>()));
PRINT_EXEC(print(mat_constant<2, 2, float>(7)));
PRINT_EXEC(print(mat_constant<float>(7, 2, 2)));
PRINT_EXEC(print(mat_DFT<4>()));
PRINT_EXEC(print(mat_DFT(4)));
PRINT_EXEC(print(mat_walsh_sylvester<int>(8)));
PRINT_EXEC(print(mat_walsh_sylvester<8, int>()));
PRINT_EXEC(print(mat_procedural<4, 5>([](auto m, auto n, auto rows, auto columns)->int { return m*columns + n; })));
std::cout << std::endl;
std::cout << "## vector or matrix reference (user-defined storage) ##" << std::endl;
PRINT_EXEC(print(vec_ref({1, 2, 3})));
PRINT_EXEC(print(mat_ref<2,3>({1, 2, 3, 4, 5, 6,})));
PRINT_EXEC(std::array a = {1, 2, 3, 4});
PRINT_EXEC(std::vector b = {4, 3, 2, 1});
PRINT_EXEC(print(vec_ref(a)));
PRINT_EXEC(print(vec_ref<2>(a.data())));
PRINT_EXEC(print(vec_ref(a.data(), 2)));
PRINT_EXEC(print(vec_ref(b)));
PRINT_EXEC(print(vec_ref(b.data(), 2)));
PRINT_EXEC(print(mat_ref<4,1>(a)));
PRINT_EXEC(print(mat_ref<1,4>(b)));
PRINT_EXEC(print(mat_ref<4,1>(a)*mat_ref<1,4>(b)));
std::cout << std::endl;
std::cout << "## vector or matrix object (embedded storage: std::array or std::vector) ##" << std::endl;
PRINT_EXEC(print(vec_static_t<4, float>(1, 2, 3, 4)));
PRINT_EXEC(auto vobj_static = vec(1, 2));
PRINT_EXEC(auto vobj_dynamic = vec<float>({1, 2, 3, 4}));
PRINT_EXEC(print(vobj_static));
PRINT_EXEC(print(vobj_dynamic));
PRINT_EXEC(vobj_dynamic.resize(2));
PRINT_EXEC(print(vobj_dynamic));
PRINT_EXEC(auto joined_vec = vec(vobj_dynamic, vobj_static));
PRINT_EXEC(print(joined_vec));
PRINT_EXEC(auto joined_vec2 = vec(vobj_static, vobj_dynamic));
PRINT_EXEC(print(joined_vec2));
PRINT_EXEC(auto joined_vec3 = vec(vec_ref({0, 1, 2}), vec_ref({3, 4})));
PRINT_EXEC(print(joined_vec3));
PRINT_EXEC(auto joined_vec4 = vec(joined_vec3, 5));
PRINT_EXEC(print(joined_vec4));
PRINT_EXEC(auto truncated_vec = vec<2>(joined_vec4));
PRINT_EXEC(print(truncated_vec));
PRINT_EXEC(auto mobj_static = mat<2, 2>({1, 2, 3, 4}));
PRINT_EXEC(auto mobj_dynamic = mat<float>({1, 2, 3, 4}, 2, 2));
PRINT_EXEC(print(mobj_static));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(mobj_dynamic.resize(1, 2));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(mobj_dynamic.resize(2, 2));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(mobj_dynamic = mat_ref<4,1>(a));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(mobj_dynamic = scaling(vec_ref({1, 2, 3})));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(mobj_dynamic = translation(vec_ref({4, 5, 6})) * scaling(vec_ref({1, 2, 3, 1})));
PRINT_EXEC(print(mobj_dynamic));
std::cout << std::endl;
std::cout << "## temporary objects in expressions and underlying type casting via object constructor ##" << std::endl;
PRINT_EXEC(auto vector_int = vec<int>(1, 2));
PRINT_EXEC(print(vector_int));
PRINT_EXEC(print(vec<float>(vector_int)));
PRINT_EXEC(auto vector_of_vectors = vec<2, vec_static_t<2, int>>(vec(-1, 0), vec(1, 2)));
PRINT_EXEC(print(vector_of_vectors));
PRINT_EXEC(auto vector_of_float_vectors = vec<vec_static_t<2, float>>(vector_of_vectors));
PRINT_EXEC(print(vector_of_float_vectors));
PRINT_EXEC(auto matrix_int = mat<2, 2>({1, 2, 3, 4}));
PRINT_EXEC(print(matrix_int));
PRINT_EXEC(print(mat<float>(matrix_int)));
PRINT_EXEC(matrix_int = mat(matrix_int * matrix_int)); // a temporary is actually required here to avoid simultaneous read and write
PRINT_EXEC(print(matrix_int));
PRINT_EXEC(auto matrix_of_vectors = mat<2, 2, vec_static_t<2, int>>({{-3, -2}, {-1, 0}, {1, 2}, {3, 4}}));
PRINT_EXEC(print(matrix_of_vectors));
PRINT_EXEC(auto matrix_of_float_vectors = mat<vec_static_t<2, float>>(matrix_of_vectors));
PRINT_EXEC(print(matrix_of_float_vectors));
std::cout << std::endl;
std::cout << "## unary operators ##" << std::endl;
PRINT_EXEC(print(-(vec_ref({4, 5, 6}))));
PRINT_EXEC(print(-translation(vec_ref({4, 5, 6}))));
PRINT_EXEC(print(unary_operation(vec_ref({1, 2, 3, 4, 5}), [](auto x) { return x*x; })));
PRINT_EXEC(print(unary_operation(-translation(vec_ref({4, 5, 6})), [](auto x) { return x*x; })));
std::cout << std::endl;
std::cout << "## binary operators ##" << std::endl;
PRINT_EXEC(print(translation(vec_ref({4, 5, 6})) * as_column(vec_ref({1, 2, 3, 1}))));
PRINT_EXEC(print(translation(vec_ref({4, 5, 6})) * vec_ref({1, 2, 3, 1})));
PRINT_EXEC(print(as_row(vec_ref({1, 2, 3, 1})) * translation(vec_ref({4, 5, 6}))));
PRINT_EXEC(print(vec_ref({1, 2, 3, 1}) * transpose(translation(vec_ref({4, 5, 6})))));
PRINT_EXEC(print(vec_ref({1, 2, 3}) * vec_ref({4, 5, 6})));
PRINT_EXEC(print(vec_ref({1, 2, 3}) + vec_ref({4, 5, 6})));
PRINT_EXEC(print(vec_ref({1, 2, 3}) - vec_ref({4, 5, 6})));
PRINT_EXEC(print(vec_ref({1, 2, 3}) / vec_ref({4, 5, 6})));
PRINT_EXEC(print(vec_ref({1, 2, 3}) * 2));
PRINT_EXEC(print(2 * vec_ref({1, 2, 3})));
PRINT_EXEC(print(vec_ref({1, 2, 3}) / 2));
PRINT_EXEC(print(vec_ref({1, 2, 3}) + 2));
PRINT_EXEC(print(vec_ref({1, 2, 3}) - 2));
PRINT_EXEC(std::cout << dot(vec_ref({1, 2, 3}), vec_ref({4, 5, 6})) << std::endl);
PRINT_EXEC(print(cross(vec_ref({1, 0, 0}), vec_ref({0, 1, 0}))));
PRINT_EXEC(print(outer_product(vec_ref({1, 2, 3}), vec_ref({4, 5}))));
PRINT_EXEC(print(kronecker_product(vec_ref({1, 2, 3}), vec_ref({4, 5}))));
PRINT_EXEC(print(translation(vec_ref({4, 5, 6})) * 2.0f));
PRINT_EXEC(print(mat_identity(4,4)/translation(vec_ref({4, 5, 6}))));
PRINT_EXEC(mat_dynamic_t<float> mat_kp_left = mat({1, 2, 3, 4, 5, 6, 7, 8}, 2, 4));
PRINT_EXEC(mat_static_t<2,2,float> mat_kp_right = mat<2,2>({10, 20, 30, 40}));
PRINT_EXEC(print(mat_kp_left));
PRINT_EXEC(print(mat_kp_right));
PRINT_EXEC(print(kronecker_product(mat_kp_left, mat_kp_right)));
PRINT_EXEC(print(hadamard_product(mat({1, 2, 3, 4}, 2, 2), mat({2, 5, 10, 100}, 2, 2))));
PRINT_EXEC(std::cout << mat(matrix_of_vectors * matrix_of_vectors) << std::endl);
PRINT_EXEC(std::cout << binary_operation(matrix_of_vectors, vec_static_t<2, int>({1, 2}), [](auto a, auto b) { return dot(a, b); }) << std::endl);
std::cout << std::endl;
std::cout << "## ternary operators ##" << std::endl;
PRINT_EXEC(print(clamp(vec({1, 2, 3}), 0, 2)));
PRINT_EXEC(std::cout << matrix_of_float_vectors);
PRINT_EXEC(std::cout << clamp(matrix_of_float_vectors, -1.0f, 1.0f));
PRINT_EXEC(std::cout << mat<vec_static_t<2, uint8_t>>(clamp(matrix_of_float_vectors, 0.0f, 1.0f) * 255.0f));
PRINT_EXEC(std::cout << matrix_int);
PRINT_EXEC(std::cout << ternary_operation(matrix_int, 10, 12345, [](const auto& a, auto b, auto c) { return a > b? a : c; }));
std::cout << std::endl;
std::cout << "## transformation matrices ##" << std::endl;
PRINT_EXEC(print(scaling(vec_ref({1, 2, 3}))));
PRINT_EXEC(print(rotation(vec_ref({1, 0, 0}), vec_ref({0, 1, 0}), std::numbers::pi_v<float>)));
PRINT_EXEC(print(translation(vec_ref({4, 5, 6}))));
PRINT_EXEC(mat_static_t<4,4,float> transform = mat_identity<4, 4>());
PRINT_EXEC(print(transform));
PRINT_EXEC(mat_dynamic_t<float> transform_dynamic = mat_identity<4, 4>());
PRINT_EXEC(print(transform));
PRINT_EXEC(mat_static_t<4,4,float> m_translation = translation(vec_ref<float>({1, 2, 3})));
PRINT_EXEC(print(m_translation));
PRINT_EXEC(mat_static_t<4,4,float> m_rotation = rotation(vec_ref<float>({1, 0, 0, 0}), vec_ref<float>({0, 1, 0, 0}), std::numbers::pi_v<float>));
PRINT_EXEC(print(m_rotation));
PRINT_EXEC(mat_static_t<4,4,float> m_scaling = scaling(vec_ref<float>({1, 2, 3, 1})));
PRINT_EXEC(print(m_scaling));
PRINT_EXEC(transform = m_translation * m_rotation * m_scaling);
PRINT_EXEC(print(transform));
PRINT_EXEC(transform_dynamic = m_translation * m_rotation * m_scaling);
PRINT_EXEC(print(transform_dynamic));
//left handed +X right +Y up +Z forward to OpenGL's right handed +X right +Y up -Z forward
PRINT_EXEC(using mat3 = mat_static_t<3,3,float>);
PRINT_EXEC(using vec3 = vec_static_t<3,float>);
PRINT_EXEC(vec3 src_right{1, 0, 0});
PRINT_EXEC(vec3 src_up{0, 1, 0});
PRINT_EXEC(vec3 src_fwd{0, 0, 1});
PRINT_EXEC(vec3 ogl_right{1, 0, 0});
PRINT_EXEC(vec3 ogl_up{0, 1, 0});
PRINT_EXEC(vec3 ogl_fwd{0, 0, -1});
PRINT_EXEC(mat3 m_basis_opengl_3x3 = mat_change_of_basis(mat_columns(src_right, src_up, src_fwd), mat_columns(ogl_right, ogl_up, ogl_fwd)));
PRINT_EXEC(mat_static_t<4,4,float> m_basis_opengl = extend_identity<4,4>(m_basis_opengl_3x3));
PRINT_EXEC(print(m_basis_opengl));
PRINT_EXEC(mat_static_t<4,4,float> m_perspective = mat_projection_perspective(std::numbers::pi_v<float>/2, 1.0f, 0.1f, 1.0f, -1.0f, 1.0f));
PRINT_EXEC(print(m_perspective));
PRINT_EXEC(mat_static_t<4,4,float> m_perspective_opengl = m_basis_opengl * m_perspective);
PRINT_EXEC(print(m_perspective_opengl));
PRINT_EXEC(mat_static_t<4,4,float> m_ortho = mat_projection_orthographic(-1.0f, 1.0f, -1.0f, 1.0f, 0.1f, 1.0f, -1.0f, 1.0f));
PRINT_EXEC(print(m_ortho));
PRINT_EXEC(mat_static_t<4,4,float> m_ortho_opengl = m_basis_opengl * m_ortho);
PRINT_EXEC(print(m_ortho_opengl));
PRINT_EXEC(vec3 a_right{1, 0, 0});
PRINT_EXEC(vec3 a_up{0, 0, 1});
PRINT_EXEC(vec3 a_fwd{0, 1, 0});
PRINT_EXEC(vec3 b_right{1, 0, 0});
PRINT_EXEC(vec3 b_up{0, -1, 0});
PRINT_EXEC(vec3 b_fwd{0, 0, -1});
PRINT_EXEC(print(extend_identity<4,4>(mat_change_of_basis(mat_columns(a_right, a_up, a_fwd), mat_columns(b_right, b_up, b_fwd)))));
std::cout << std::endl;
std::cout << "## rectangular matrix partition access (block matrices) ##" << std::endl;
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(print(rectangular_partition<2, 2, 2, 2>(mobj_dynamic)));
PRINT_EXEC(print(rectangular_partition<2, 4, 2, 4>(mobj_dynamic)));
PRINT_EXEC(print(rectangular_partition<1, 1, 2, 4>(mobj_dynamic)));
PRINT_EXEC(print(rectangular_partition(mobj_dynamic, 2, 2, 2, 2)));
PRINT_EXEC(print(rectangular_partition(mobj_dynamic, 2, 4, 2, 4)));
PRINT_EXEC(print(rectangular_partition(mobj_dynamic, 1, 1, 2, 4)));
PRINT_EXEC(print(rectangular_partition(mobj_dynamic, 3, 3, 1, 1)));
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(rectangular_partition(mobj_dynamic, 3, 3, 1, 1)[0,0] = 5);
PRINT_EXEC(print(mobj_dynamic));
PRINT_EXEC(print(mobj_static));
PRINT_EXEC(print(rectangular_partition<1, 1, 1, 1>(mobj_static)));
PRINT_EXEC(print(rectangular_partition<1, 4, 1, 4>(mobj_static)));
PRINT_EXEC(print(rectangular_partition<1, 1, 0, 4>(mobj_static)));
PRINT_EXEC(print(rectangular_partition(mobj_static, 1, 1, 1, 1)));
PRINT_EXEC(print(rectangular_partition(mobj_static, 1, 4, 1, 4)));
PRINT_EXEC(print(rectangular_partition(mobj_static, 1, 1, 0, 4)));
PRINT_EXEC(print(rectangular_partition(mobj_static, 1, 1, 0, 4)));
PRINT_EXEC(print(rectangular_partition(mobj_static, 1, 1, 1, 1)));
PRINT_EXEC(print(mobj_static));
PRINT_EXEC(rectangular_partition(mobj_static, 1, 1, 1, 1)[0,0] = 5);
PRINT_EXEC(print(mobj_static));
std::cout << std::endl;
std::cout << "## quaternion ##" << std::endl;
PRINT_EXEC(print(quat_ref(vec_ref<float>({1, 0, 0, 0}))));
PRINT_EXEC(auto qaa = quat_axis_angle(vec_ref<float>({0, 1, 0}), std::numbers::pi_v<float>));
PRINT_EXEC(print(qaa));
PRINT_EXEC(print(as_matrix(qaa)));
PRINT_EXEC(auto q = quat(vec_ref<float>({5, 6, 0, 0})));
PRINT_EXEC(mat_static_t<3,3,double> qm3x3 = as_matrix<3, 3>(q));
PRINT_EXEC(print(qm3x3));
PRINT_EXEC(print(as_quat(qm3x3)));
PRINT_EXEC(print(as_matrix<4, 4>(q)));
PRINT_EXEC(auto qnorm = quat_ref(normalize(q)));
PRINT_EXEC(auto qmat = mat(as_matrix(q)));
PRINT_EXEC(print(qmat));
PRINT_EXEC(auto qnormmat = mat(as_matrix(qnorm)));
PRINT_EXEC(print(qnormmat));
PRINT_EXEC(auto vqtr = vec<float>({1, 1, 0}));
PRINT_EXEC(print(vqtr));
PRINT_EXEC(print(qnormmat * vqtr));
PRINT_EXEC(print(qnorm * vqtr));
PRINT_EXEC(print(qnorm * quat(vec<float>({float{0}, vqtr[0], vqtr[1], vqtr[2]})) * inverse(qnorm)));
PRINT_EXEC(print(qmat * vqtr));
PRINT_EXEC(print(q * vqtr));
PRINT_EXEC(print(vqtr * q));
PRINT_EXEC(print(q * vqtr * q));
PRINT_EXEC(print(q * quat(vec<float>({float{0}, vqtr[0], vqtr[1], vqtr[2]})) * inverse(q)));
PRINT_EXEC(print(q * quat(vec<float>({float{0}, vqtr[0], vqtr[1], vqtr[2]})) * conjugate(q)));
std::cout << std::endl;
std::cout << "## function library ##" << std::endl;
std::cout << " - matrix -" << std::endl;
PRINT_EXEC(std::cout << trace(transform) << std::endl);
PRINT_EXEC(std::cout << determinant(transform) << std::endl);
PRINT_EXEC(std::cout << determinant(mat_identity<4, 4>()) << std::endl);
PRINT_EXEC(std::cout << det(mobj_static) << std::endl);
PRINT_EXEC(std::cout << det(mobj_dynamic) << std::endl);
PRINT_EXEC(print(inverse(transform)));
PRINT_EXEC(print(inv(transform)*transform));
PRINT_EXEC(print(inverse_gauss_jordan(transform)));
PRINT_EXEC(print(inverse_gauss_jordan(transform_dynamic)));
PRINT_EXEC(auto dftmat = mat_DFT<4>());
PRINT_EXEC(print(transpose(dftmat)));
PRINT_EXEC(print(transpose_hermitian(dftmat)));
PRINT_EXEC(print(transpose_hermitian(dftmat)*dftmat));
PRINT_EXEC(print(join(vec_ref({0, 1, 2}), vec_ref({3, 4}))));
PRINT_EXEC(print(augment(mat_multiplicative_identity(4, 4), mat_hadamard_identity(4, 2))));
PRINT_EXEC(print(split_right(transform, 2)));
PRINT_EXEC(print(normalize(transform)));
PRINT_EXEC(print(normalize_max(transform)));
PRINT_EXEC(print(normalize_minmax(transform)));
PRINT_EXEC(print(submatrix(transform, 0, 0)));
PRINT_EXEC(print(adjugate(transform)));
PRINT_EXEC(print(cofactor(transform)));
PRINT_EXEC(print(gramian(transform)));
std::cout << " - decomposition -" << std::endl;
PRINT_EXEC(auto [c_perspective, c_translation, c_scaling, c_shear, c_rotation] = decompose_mat4x4(transform));
PRINT_EXEC(print(c_perspective));
PRINT_EXEC(print(c_translation));
PRINT_EXEC(print(c_scaling));
PRINT_EXEC(print(c_shear));
PRINT_EXEC(print(c_rotation));
PRINT_EXEC(transform = m_rotation * scaling(vec(0, 2, 1, 1)));
PRINT_EXEC(std::tie(c_perspective, c_translation, c_scaling, c_shear, c_rotation) = decompose_mat4x4(transform));
PRINT_EXEC(print(c_perspective));
PRINT_EXEC(print(c_translation));
PRINT_EXEC(print(c_scaling));
PRINT_EXEC(print(c_shear));
PRINT_EXEC(print(c_rotation));
std::cout << " - vector/ray -" << std::endl;
PRINT_EXEC(print(normalize(vec<float>(1,1,1))));
PRINT_EXEC(print(normalize_max(vec<float>(1,5,10))));
PRINT_EXEC(print(normalize_minmax(vec<float>(-10,5,10))));
PRINT_EXEC(auto incident_ray = normalize(vec<float>(-1,1,0)));
PRINT_EXEC(auto normal = normalize(vec<float>(0,1,0)));
PRINT_EXEC(print(incident_ray));
PRINT_EXEC(print(normal));
PRINT_EXEC(print(reflect(incident_ray, normal)));
PRINT_EXEC(print(reflect<Conventions::RayDirection::Outgoing>(incident_ray, normal)));
PRINT_EXEC(print(reflect<Conventions::RayDirection::Incoming>(-incident_ray, normal)));
PRINT_EXEC(print(reflect(vec<float>(-1,1,0), vec<float>(0,1,0))));
PRINT_EXEC(decltype(normal)::value_type ior_src = 1.0);
PRINT_EXEC(decltype(normal)::value_type ior_dest = 1.6);
PRINT_EXEC(auto eta = ior_src/ior_dest);
PRINT_EXEC(constexpr bool total_internal_reflection = true);
PRINT_EXEC(print(refract(incident_ray, normal, eta)));
PRINT_EXEC(print(refract<Conventions::RayDirection::Outgoing, total_internal_reflection>(incident_ray, normal, eta)));
PRINT_EXEC(print(refract<Conventions::RayDirection::Incoming, total_internal_reflection>(-incident_ray, normal, eta)));
PRINT_EXEC(print(refract(incident_ray, normal, ior_src, ior_dest)));
PRINT_EXEC(print(refract<Conventions::RayDirection::Outgoing, total_internal_reflection>(incident_ray, normal, ior_dest, ior_src)));
PRINT_EXEC(print(refract<Conventions::RayDirection::Outgoing, !total_internal_reflection>(incident_ray, normal, ior_dest, ior_src)));
PRINT_EXEC(std::cout << scalar_projection(incident_ray, normal) << std::endl);
PRINT_EXEC(print(vector_projection(incident_ray, normal)));
PRINT_EXEC(print(vector_rejection(incident_ray, normal)));
PRINT_EXEC(print(orthonormalize(incident_ray, normal)));
std::cout << " - Euler angles -" << std::endl;
PRINT_EXEC(auto ea_quat = quat_euler_angles<EulerAnglesOrder::ZYXr>(vec<float>(9, 10, 21)));
PRINT_EXEC(print(ea_quat));
PRINT_EXEC(auto ea = euler_angles(ea_quat, EulerAnglesOrder::ZYXr));
PRINT_EXEC(print(ea));
PRINT_EXEC(print(slerp_flip(quat_euler_angles(ea, EulerAnglesOrder::ZYXr), ea_quat)));
std::cout << " - hyperspherical coordinates -" << std::endl;
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1}))));
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1, 2}))));
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3}))));
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4}))));
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4, 5}))));
PRINT_EXEC(print(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4, 5, 6}))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1})))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1, 2})))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3})))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4})))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4, 5})))));
PRINT_EXEC(print(hyperspherical_to_cartesian(cartesian_to_hyperspherical(vec_ref<float>({1, 2, 3, 4, 5, 6})))));
std::cout << std::endl;
return EXIT_SUCCESS;
}