500 lines
14 KiB
C++
500 lines
14 KiB
C++
#include <stdbool.h>
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#include <stdio.h>
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#include "runner.hpp"
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#include "math/vec2.hpp"
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#include "math/vec3.hpp"
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#include "math/vec4.hpp"
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#include "math/mat2x2.hpp"
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#include "math/mat3x3.hpp"
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#include "math/mat4x4.hpp"
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using vec2 = vec<2, float>;
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using vec3 = vec<3, float>;
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using vec4 = vec<4, float>;
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using mat2x2 = mat<2, 2, float>;
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using mat3x3 = mat<3, 3, float>;
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using mat4x4 = mat<4, 4, float>;
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static const float epsilon = 0.00001;
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#define fabsf __builtin_fabsf
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inline static bool float_equal(float a, float b)
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{
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return fabsf(a - b) < epsilon;
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}
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inline static bool vec4_equal(vec4 a, vec4 b)
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{
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return
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float_equal(a.x, b.x) &&
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float_equal(a.y, b.y) &&
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float_equal(a.z, b.z) &&
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float_equal(a.w, b.w);
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}
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inline static bool mat2x2_equal(mat2x2 a,
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mat2x2 b)
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{
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return
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float_equal(a[0][0], b[0][0]) &&
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float_equal(a[0][1], b[0][1]) &&
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float_equal(a[1][0], b[1][0]) &&
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float_equal(a[1][1], b[1][1]);
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}
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inline static bool mat3x3_equal(mat3x3 a,
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mat3x3 b)
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{
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return
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float_equal(a[0][0], b[0][0]) &&
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float_equal(a[0][1], b[0][1]) &&
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float_equal(a[0][2], b[0][2]) &&
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float_equal(a[1][0], b[1][0]) &&
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float_equal(a[1][1], b[1][1]) &&
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float_equal(a[1][2], b[1][2]) &&
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float_equal(a[2][0], b[2][0]) &&
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float_equal(a[2][1], b[2][1]) &&
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float_equal(a[2][2], b[2][2]);
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}
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inline static bool mat4x4_equal(mat4x4 a,
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mat4x4 b)
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{
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return
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float_equal(a[0][0], b[0][0]) &&
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float_equal(a[0][1], b[0][1]) &&
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float_equal(a[0][2], b[0][2]) &&
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float_equal(a[0][3], b[0][3]) &&
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float_equal(a[1][0], b[1][0]) &&
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float_equal(a[1][1], b[1][1]) &&
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float_equal(a[1][2], b[1][2]) &&
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float_equal(a[1][3], b[1][3]) &&
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float_equal(a[2][0], b[2][0]) &&
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float_equal(a[2][1], b[2][1]) &&
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float_equal(a[2][2], b[2][2]) &&
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float_equal(a[2][3], b[2][3]) &&
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float_equal(a[3][0], b[3][0]) &&
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float_equal(a[3][1], b[3][1]) &&
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float_equal(a[3][2], b[3][2]) &&
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float_equal(a[3][3], b[3][3]);
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}
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inline static bool mat4x4_is_invertible(mat4x4 a)
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{
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return !float_equal(determinant(a), 0.f);
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}
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static bool matrices_test_0(const char ** scenario)
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{
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*scenario = "A 4x4 matrix ought to be representable";
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mat4x4 m = mat4x4( 1.0f, 2.0f, 3.0f, 4.0f,
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5.5f, 6.5f, 7.5f, 8.5f,
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9.0f, 10.0f, 11.0f, 12.0f,
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13.5f, 14.5f, 15.5f, 16.5f);
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return
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m[0][0] == 1.0f &&
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m[0][3] == 4.0f &&
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m[1][0] == 5.5f &&
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m[1][2] == 7.5f &&
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m[2][2] == 11.0f &&
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m[3][0] == 13.5f &&
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m[3][2] == 15.5f;
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}
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static bool matrices_test_1(const char ** scenario)
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{
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*scenario = "A 2x2 matrix ought to be representable";
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mat2x2 m = mat2x2(-3.0f, 5.0f,
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1.0f, -2.0f);
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return
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m[0][0] == -3.0f &&
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m[0][1] == 5.0f &&
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m[1][0] == 1.0f &&
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m[1][1] == -2.0f;
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}
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static bool matrices_test_2(const char ** scenario)
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{
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*scenario = "A 3x3 matrix ought to be representable";
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mat3x3 m = mat3x3(-3.0f, 5.0f, 0.0f,
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1.0f, -2.0f, -7.0f,
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0.0f, 1.0f, 1.0f);
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return
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m[0][0] == -3.0f &&
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m[1][1] == -2.0f &&
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m[2][2] == 1.0f;
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}
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static bool matrices_test_3(const char ** scenario)
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{
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*scenario = "Matrix equality with identical matrices";
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mat4x4 a = mat4x4(1.0f, 2.0f, 3.0f, 4.0f,
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5.0f, 6.0f, 7.0f, 8.0f,
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9.0f, 8.0f, 7.0f, 6.0f,
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5.0f, 4.0f, 3.0f, 2.0f);
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mat4x4 b = mat4x4(1.0f, 2.0f, 3.0f, 4.0f,
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5.0f, 6.0f, 7.0f, 8.0f,
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9.0f, 8.0f, 7.0f, 6.0f,
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5.0f, 4.0f, 3.0f, 2.0f);
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return mat4x4_equal(a, b);
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}
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static bool matrices_test_4(const char ** scenario)
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{
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*scenario = "Matrix equality with different matrices";
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mat4x4 a = mat4x4(1.0f, 2.0f, 3.0f, 4.0f,
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5.0f, 6.0f, 7.0f, 8.0f,
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9.0f, 8.0f, 7.0f, 6.0f,
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5.0f, 4.0f, 3.0f, 2.0f);
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mat4x4 b = mat4x4(2.0f, 3.0f, 4.0f, 5.0f,
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6.0f, 7.0f, 8.0f, 9.0f,
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8.0f, 7.0f, 6.0f, 5.0f,
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4.0f, 3.0f, 2.0f, 1.0f);
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return !mat4x4_equal(a, b);
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}
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static bool matrices_test_5(const char ** scenario)
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{
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*scenario = "Multiplying two matrices";
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mat4x4 a = mat4x4(1.0f, 2.0f, 3.0f, 4.0f,
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5.0f, 6.0f, 7.0f, 8.0f,
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9.0f, 8.0f, 7.0f, 6.0f,
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5.0f, 4.0f, 3.0f, 2.0f);
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mat4x4 b = mat4x4(-2.0f, 1.0f, 2.0f, 3.0f,
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3.0f, 2.0f, 1.0f, -1.0f,
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4.0f, 3.0f, 6.0f, 5.0f,
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1.0f, 2.0f, 7.0f, 8.0f);
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mat4x4 m1 = a * b;
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mat4x4 m2 = mat4x4(20.0f, 22.0f, 50.0f, 48.0f,
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44.0f, 54.0f, 114.0f, 108.0f,
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40.0f, 58.0f, 110.0f, 102.0f,
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16.0f, 26.0f, 46.0f, 42.0f);
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return mat4x4_equal(m1, m2);
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}
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static bool matrices_test_6(const char ** scenario)
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{
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*scenario = "A matrix multiplied by a vec4";
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mat4x4 a = mat4x4(1.0f, 2.0f, 3.0f, 4.0f,
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2.0f, 4.0f, 4.0f, 2.0f,
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8.0f, 6.0f, 4.0f, 1.0f,
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0.0f, 0.0f, 0.0f, 1.0f);
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vec4 b = vec4(1.0f, 2.0f, 3.0f, 1.0f);
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vec4 c = a * b;
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return vec4_equal(c, vec4(18, 24, 33, 1));
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}
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static bool matrices_test_7(const char ** scenario)
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{
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*scenario = "Multiplying a matrix by the identity matrix";
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mat4x4 a = mat4x4(0.0f, 1.0f, 2.0f, 4.0f,
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1.0f, 2.0f, 4.0f, 8.0f,
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2.0f, 4.0f, 8.0f, 16.0f,
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4.0f, 8.0f, 16.0f, 32.0f);
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mat4x4 id = identity<float>();
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mat4x4 c = a * id;
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return mat4x4_equal(a, c);
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}
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static bool matrices_test_8(const char ** scenario)
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{
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*scenario = "Multiplying a the identity matrix by a vec4";
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vec4 a = vec4(1.0f, 2.0f, 3.0f, 4.0f);
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mat4x4 id = identity<float>();
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vec4 c = id * a;
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return vec4_equal(a, c);
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}
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static bool matrices_test_9(const char ** scenario)
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{
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*scenario = "Transposing a matrix";
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mat4x4 a = mat4x4(0.0f, 9.0f, 3.0f, 0.0f,
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9.0f, 8.0f, 0.0f, 8.0f,
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1.0f, 8.0f, 5.0f, 3.0f,
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0.0f, 0.0f, 5.0f, 8.0f);
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mat4x4 b = mat4x4(0.0f, 9.0f, 1.0f, 0.0f,
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9.0f, 8.0f, 8.0f, 0.0f,
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3.0f, 0.0f, 5.0f, 5.0f,
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0.0f, 8.0f, 3.0f, 8.0f);
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mat4x4 c = transpose(a);
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return mat4x4_equal(c, b);
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}
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static bool matrices_test_10(const char ** scenario)
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{
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*scenario = "Transposing the identity matrix";
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mat4x4 a = identity<float>();
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mat4x4 c = transpose(a);
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return mat4x4_equal(a, c);
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}
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static bool matrices_test_11(const char ** scenario)
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{
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*scenario = "Calculating the determinant of a 2x2 matrix";
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mat2x2 a = mat2x2( 1.0f, 5.0f,
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-3.0f, 2.0f);
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return float_equal(determinant(a), 17);
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}
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static bool matrices_test_12(const char ** scenario)
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{
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*scenario = "A submatrix of a 3x3 matrix is a 2x2 matrix";
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mat3x3 a = mat3x3( 1.0f, 5.0f, 0.0f,
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-3.0f, 2.0f, 7.0f,
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0.0f, 6.0f, -3.0f);
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mat2x2 b = submatrix(a, 0, 2);
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mat2x2 c = mat2x2(-3.0f, 2.0f,
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0.0f, 6.0f);
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return mat2x2_equal(b, c);
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}
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static bool matrices_test_13(const char ** scenario)
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{
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*scenario = "A submatrix of a 4x4 matrix is a 3x3 matrix";
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mat4x4 a = mat4x4(-6.0f, 1.0f, 1.0f, 6.0f,
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-8.0f, 5.0f, 8.0f, 6.0f,
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-1.0f, 0.0f, 8.0f, 2.0f,
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-7.0f, 1.0f, -1.0f, 1.0f);
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mat3x3 b = submatrix(a, 2, 1);
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mat3x3 c = mat3x3(-6.0f, 1.0f, 6.0f,
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-8.0f, 8.0f, 6.0f,
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-7.0f, -1.0f, 1.0f);
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return mat3x3_equal(b, c);
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}
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static bool matrices_test_14(const char ** scenario)
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{
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*scenario = "Calculating a minor of a 3x3 matrix";
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mat3x3 a = mat3x3(3, 5, 0,
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2, -1, -7,
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6, -1, 5);
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mat2x2 b = submatrix(a, 1, 0);
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return
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float_equal(determinant(b), 25.0f) &&
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float_equal(minor(a, 1, 0), 25.0f);
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}
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static bool matrices_test_15(const char ** scenario)
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{
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*scenario = "Calculating a cofactor of a 3x3 matrix";
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mat3x3 a = mat3x3(3, 5, 0,
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2, -1, -7,
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6, -1, 5);
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return
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float_equal(minor(a, 0, 0), -12.0f) &&
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float_equal(cofactor(a, 0, 0), -12.0f) &&
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float_equal(minor(a, 1, 0), 25.0f) &&
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float_equal(cofactor(a, 1, 0), -25.0f) &&
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float_equal(cofactor(a, 2, 1), 21.0f);
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}
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static bool matrices_test_16(const char ** scenario)
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{
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*scenario = "Calculating the determinant of a 3x3 matrix";
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mat3x3 a = mat3x3( 1.0f, 2.0f, 6.0f,
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-5.0f, 8.0f, -4.0f,
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2.0f, 6.0f, 4.0f);
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return
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float_equal(cofactor(a, 0, 0), 56.0f) &&
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float_equal(cofactor(a, 0, 1), 12.0f) &&
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float_equal(cofactor(a, 0, 2), -46.0f) &&
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float_equal(determinant(a), -196.0f);
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}
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static bool matrices_test_17(const char ** scenario)
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{
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*scenario = "Calculating the determinant of a 4x4 matrix";
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mat4x4 a = mat4x4(-2.0f, -8.0f, 3.0f, 5.0f,
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-3.0f, 1.0f, 7.0f, 3.0f,
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1.0f, 2.0f, -9.0f, 6.0f,
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-6.0f, 7.0f, 7.0f, -9.0f);
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return
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float_equal(cofactor(a, 0, 0), 690.0f) &&
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float_equal(cofactor(a, 0, 1), 447.0f) &&
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float_equal(cofactor(a, 0, 2), 210.0f) &&
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float_equal(cofactor(a, 0, 3), 51.0f) &&
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float_equal(determinant(a), -4071.0f);
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}
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static bool matrices_test_18(const char ** scenario)
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{
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*scenario = "Testing an invertible matrix for invertibility";
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mat4x4 a = mat4x4(6.0f, 4.0f, 4.0f, 4.0f,
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5.0f, 5.0f, 7.0f, 6.0f,
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4.0f, -9.0f, 3.0f, -7.0f,
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9.0f, 1.0f, 7.0f, -6.0f);
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return
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float_equal(determinant(a), -2120.0f) &&
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mat4x4_is_invertible(a);
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}
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static bool matrices_test_19(const char ** scenario)
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{
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*scenario = "Testing a noninvertible matrix for invertibility";
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mat4x4 a = mat4x4(-4.0f, 2.0f, -2.0f, -3.0f,
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9.0f, 6.0f, 2.0f, 6.0f,
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0.0f, -5.0f, 1.0f, -5.0f,
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0.0f, 0.0f, 0.0f, 0.0f);
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return
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float_equal(determinant(a), 0.0f) &&
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!mat4x4_is_invertible(a);
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}
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static bool matrices_test_20(const char ** scenario)
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{
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*scenario = "Calculating the inverse of a matrix";
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mat4x4 a = mat4x4(-5.0, 2.0, 6.0, -8.0,
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1.0, -5.0, 1.0, 8.0,
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7.0, 7.0, -6.0, -7.0,
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1.0, -3.0, 7.0, 4.0);
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mat4x4 b = inverse(a);
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mat4x4 c = mat4x4( 0.218045f, 0.451128f, 0.240602f, -0.045113f,
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-0.808271f, -1.456767f, -0.443609f, 0.520677f,
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-0.078947f, -0.223684f, -0.052632f, 0.197368f,
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-0.522564f, -0.813910f, -0.300752f, 0.306391f);
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return
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float_equal(determinant(a), 532.0f) &&
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float_equal(cofactor(a, 2, 3), -160.0f) &&
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float_equal(b[3][2], -160.0f/532.0f) &&
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float_equal(cofactor(a, 3, 2), 105.0f) &&
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float_equal(b[2][3], 105.0f/532.0f) &&
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mat4x4_equal(b, c);
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}
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static bool matrices_test_21(const char ** scenario)
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{
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*scenario = "Calculating the inverse of a second matrix";
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mat4x4 a = mat4x4( 8.0f, -5.0f, 9.0f, 2.0f,
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7.0f, 5.0f, 6.0f, 1.0f,
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-6.0f, 0.0f, 9.0f, 6.0f,
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-3.0f, 0.0f, -9.0f, -4.0f);
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mat4x4 b = inverse(a);
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mat4x4 c = mat4x4(-0.15385f, -0.15385f, -0.28205f, -0.53846f,
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-0.07692f, 0.12308f, 0.02564f, 0.03077f,
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0.35897f, 0.35897f, 0.43590f, 0.92308f,
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-0.69231f, -0.69231f, -0.76923f, -1.92308f);
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return mat4x4_equal(b, c);
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}
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static bool matrices_test_22(const char ** scenario)
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{
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*scenario = "Calculating the inverse of a third matrix";
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|
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mat4x4 a = mat4x4( 9.0f, 3.0f, 0.0f, 9.0f,
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-5.0f, -2.0f, -6.0f, -3.0f,
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-4.0f, 9.0f, 6.0f, 4.0f,
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-7.0f, 6.0f, 6.0f, 2.0f);
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|
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mat4x4 b = inverse(a);
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|
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mat4x4 c = mat4x4(-0.04074f, -0.07778f, 0.14444f, -0.22222f,
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-0.07778f, 0.03333f, 0.36667f, -0.33333f,
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-0.02901f, -0.14630f, -0.10926f, 0.12963f,
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0.17778f, 0.06667f, -0.26667f, 0.33333f);
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|
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return mat4x4_equal(b, c);
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|
}
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|
|
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static bool matrices_test_23(const char ** scenario)
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{
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*scenario = "Multiplying a product by its inverse";
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|
|
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mat4x4 a = mat4x4( 3.0f, -9.0f, 7.0f, 3.0f,
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3.0f, -8.0f, 2.0f, -9.0f,
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|
-4.0f, 4.0f, 4.0f, 1.0f,
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|
-6.0f, 5.0f, -1.0f, 1.0f);
|
|
|
|
mat4x4 b = mat4x4( 8.0f, 2.0f, 2.0f, 2.0f,
|
|
3.0f, -1.0f, 7.0f, 0.0f,
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|
7.0f, 0.0f, 5.0f, 4.0f,
|
|
6.0f, -2.0f, 0.0f, 5.0f);
|
|
|
|
mat4x4 c = a * b;
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|
|
|
mat4x4 b_i = inverse(b);
|
|
mat4x4 d = c * b_i;
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|
|
|
return mat4x4_equal(d, a);
|
|
}
|
|
|
|
test_t matrices_tests[] = {
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|
matrices_test_0,
|
|
matrices_test_1,
|
|
matrices_test_2,
|
|
matrices_test_3,
|
|
matrices_test_4,
|
|
matrices_test_5,
|
|
matrices_test_6,
|
|
matrices_test_7,
|
|
matrices_test_8,
|
|
matrices_test_9,
|
|
matrices_test_10,
|
|
matrices_test_11,
|
|
matrices_test_12,
|
|
matrices_test_13,
|
|
matrices_test_14,
|
|
matrices_test_15,
|
|
matrices_test_16,
|
|
matrices_test_17,
|
|
matrices_test_18,
|
|
matrices_test_19,
|
|
matrices_test_20,
|
|
matrices_test_21,
|
|
matrices_test_22,
|
|
matrices_test_23,
|
|
};
|
|
|
|
RUNNER(matrices_tests)
|