/* * Created by Brett on 28/02/23. * Licensed under GNU General Public License V3.0 * See LICENSE file for license detail */ #ifndef BLT_TESTS_MATRIX_H #define BLT_TESTS_MATRIX_H #include #include #include #ifndef M_PI // MSVC does not have M_PI # define M_PI 3.14159265358979323846 #endif namespace blt { class mat4x4 { static_assert(std::is_trivially_copyable_v && "Vector must be trivially copyable!"); protected: // 4x4 = 16 // union dataType // { // float single[16]; // float dim[4][4]; // blt::vec4 v[4]; // }; blt::vec4 data[4]; friend mat4x4 operator+(const mat4x4& left, const mat4x4& right); friend mat4x4 operator-(const mat4x4& left, const mat4x4& right); friend mat4x4 operator*(const mat4x4& left, const mat4x4& right); friend mat4x4 operator*(float c, const mat4x4& v); friend mat4x4 operator*(const mat4x4& v, float c); friend mat4x4 operator/(const mat4x4& v, float c); friend mat4x4 operator/(float c, const mat4x4& v); public: static mat4x4 make_empty() { mat4x4 ret; ret.m00(0); ret.m11(0); ret.m22(0); ret.m33(0); return ret; } mat4x4() { // for (float& i : data.single) // i = 0; // set identity matrix default m00(1); m11(1); m22(1); m33(1); } mat4x4(const blt::vec4& c1, const blt::vec4& c2, const blt::vec4& c3, const blt::vec4& c4) { // dangerous? // std::memcpy(data.dim[0], c1.data(), 4 * sizeof(float)); // std::memcpy(data.dim[1], c2.data(), 4 * sizeof(float)); // std::memcpy(data.dim[2], c3.data(), 4 * sizeof(float)); // std::memcpy(data.dim[3], c4.data(), 4 * sizeof(float)); data[0] = c1; data[1] = c2; data[2] = c3; data[3] = c4; } mat4x4(const mat4x4& mat) { for (int i = 0; i < 4; i++) { data[i] = mat.data[i]; } } mat4x4& operator=(const mat4x4& copy) { if (© == this) return *this; for (int i = 0; i < 4; i++) { data[i] = copy.data[i]; } return *this; } explicit mat4x4(const float dat[16]) { for (int i = 0; i < 4; i++) for (int j = 0; j < 4; j++) data[i][j] = dat[j + i * 4]; } explicit mat4x4(const blt::vec4 dat[4]) { for (int i = 0; i < 4; i++) data[i] = dat[i]; } inline mat4x4& translate(float x, float y, float z) { mat4x4 translation_mat{}; /** * 9.005 Are OpenGL matrices column-major or row-major? * For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out contiguously in memory. * The translation components occupy the 13th, 14th, and 15th elements of the 16-element matrix, * where indices are numbered from 1 to 16 as described in section 2.11.2 of the OpenGL 2.1 Specification. */ translation_mat.m03(x); translation_mat.m13(y); translation_mat.m23(z); *this = *this * translation_mat; return *this; } inline mat4x4& translate(const vec4& vec) { return translate(vec[0], vec[1], vec[2]); } inline mat4x4& translate(const vec3& vec) { return translate(vec[0], vec[1], vec[2]); } inline mat4x4& translate(const vec2& vec) { return translate(vec[0], vec[1], 0); } inline mat4x4& scale(float x, float y, float z) { mat4x4 scale_mat{}; m00(m00() * x); m11(m11() * y); m22(m22() * z); *this = *this * scale_mat; return *this; } inline mat4x4& scale(const vec4& vec) { return scale(vec[0], vec[1], vec[2]); } inline mat4x4& scale(const vec3& vec) { return scale(vec[0], vec[1], vec[2]); } inline mat4x4& scale(const vec2& vec) { return scale(vec[0], vec[1], 1.0f); } // angle in radians inline mat4x4& rotateX(float angle) { mat4x4 rotationMatrix{}; rotationMatrix.m(1, 1, std::cos(angle)); rotationMatrix.m(1, 2, -std::sin(angle)); rotationMatrix.m(2, 1, std::sin(angle)); rotationMatrix.m(2, 2, std::cos(angle)); *this = *this * rotationMatrix; return *this; } inline mat4x4& rotateY(float angle) { mat4x4 rotationMatrix{}; rotationMatrix.m(0, 0, std::cos(angle)); rotationMatrix.m(0, 2, std::sin(angle)); rotationMatrix.m(2, 0, -std::sin(angle)); rotationMatrix.m(2, 2, std::cos(angle)); *this = *this * rotationMatrix; return *this; } inline mat4x4& rotateZ(float angle) { mat4x4 rotationMatrix{}; rotationMatrix.m(0, 0, std::cos(angle)); rotationMatrix.m(0, 1, -std::sin(angle)); rotationMatrix.m(1, 0, std::sin(angle)); rotationMatrix.m(1, 1, std::cos(angle)); *this = *this * rotationMatrix; return *this; } [[nodiscard]] mat4x4 transpose() const { mat4x4 copy{*this}; for (int i = 0; i < 4; i++) { for (int j = 0; j < 4; j++) { copy.m(j, i, m(i, j)); } } return copy; } [[nodiscard]] float determinant() const { return m00() * (m11() * m22() * m33() + m12() * m23() * m31() + m13() * m21() * m32() - m31() * m22() * m13() - m32() * m23() * m11() - m33() * m21() * m12()) - m10() * (m01() * m22() * m33() + m02() * m23() * m31() + m03() * m21() * m32() - m31() * m32() * m03() - m32() * m23() * m01() - m33() * m21() * m02()) + m20() * (m01() * m12() * m33() + m02() * m13() * m31() + m03() * m11() * m32() - m31() * m12() * m03() - m32() * m13() * m01() - m33() * m11() * m02()) - m30() * (m01() * m12() * m23() + m02() * m13() * m21() + m03() * m11() * m22() - m21() * m12() * m03() - m22() * m13() * m01() - m23() * m11() * m02()); } [[nodiscard]] mat4x4 adjugate() const { auto& m = *this; auto Coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3]; auto Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3]; auto Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3]; auto Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3]; auto Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3]; auto Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3]; auto Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2]; auto Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2]; auto Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2]; auto Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3]; auto Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3]; auto Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3]; auto Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2]; auto Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2]; auto Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2]; auto Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1]; auto Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1]; auto Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1]; blt::vec4 Fac0(Coef00, Coef00, Coef02, Coef03); blt::vec4 Fac1(Coef04, Coef04, Coef06, Coef07); blt::vec4 Fac2(Coef08, Coef08, Coef10, Coef11); blt::vec4 Fac3(Coef12, Coef12, Coef14, Coef15); blt::vec4 Fac4(Coef16, Coef16, Coef18, Coef19); blt::vec4 Fac5(Coef20, Coef20, Coef22, Coef23); blt::vec4 Vec0(m[1][0], m[0][0], m[0][0], m[0][0]); blt::vec4 Vec1(m[1][1], m[0][1], m[0][1], m[0][1]); blt::vec4 Vec2(m[1][2], m[0][2], m[0][2], m[0][2]); blt::vec4 Vec3(m[1][3], m[0][3], m[0][3], m[0][3]); blt::vec4 Inv0(Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2); blt::vec4 Inv1(Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4); blt::vec4 Inv2(Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5); blt::vec4 Inv3(Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5); blt::vec4 SignA(+1, -1, +1, -1); blt::vec4 SignB(-1, +1, -1, +1); return mat4x4(Inv0 * SignA, Inv1 * SignB, Inv2 * SignA, Inv3 * SignB); } [[nodiscard]] mat4x4 inverse() const { auto& m = *this; auto Inverse = adjugate(); blt::vec4 Row0(Inverse[0][0], Inverse[1][0], Inverse[2][0], Inverse[3][0]); blt::vec4 Dot0(m[0] * Row0); auto Dot1 = (Dot0.x() + Dot0.y()) + (Dot0.z() + Dot0.w()); auto OneOverDeterminant = 1.0f / Dot1; return Inverse * OneOverDeterminant; } inline const blt::vec4& operator[](int column) const { return data[column]; } inline blt::vec4& operator[](int column) { return data[column]; } [[nodiscard]] inline float m(int row, int column) const { return data[column][row]; }; [[nodiscard]] inline float m00() const { return m(0, 0); } [[nodiscard]] inline float m10() const { return m(1, 0); } [[nodiscard]] inline float m20() const { return m(2, 0); } [[nodiscard]] inline float m30() const { return m(3, 0); } [[nodiscard]] inline float m01() const { return m(0, 1); } [[nodiscard]] inline float m11() const { return m(1, 1); } [[nodiscard]] inline float m21() const { return m(2, 1); } [[nodiscard]] inline float m31() const { return m(3, 1); } [[nodiscard]] inline float m02() const { return m(0, 2); } [[nodiscard]] inline float m12() const { return m(1, 2); } [[nodiscard]] inline float m22() const { return m(2, 2); } [[nodiscard]] inline float m32() const { return m(3, 2); } [[nodiscard]] inline float m03() const { return m(0, 3); } [[nodiscard]] inline float m13() const { return m(1, 3); } [[nodiscard]] inline float m23() const { return m(2, 3); } [[nodiscard]] inline float m33() const { return m(3, 3); } inline float m(int row, int column, float value) { return data[column][row] = value; }; inline float m00(float d) { return m(0, 0, d); } inline float m10(float d) { return m(1, 0, d); } inline float m20(float d) { return m(2, 0, d); } inline float m30(float d) { return m(3, 0, d); } inline float m01(float d) { return m(0, 1, d); } inline float m11(float d) { return m(1, 1, d); } inline float m21(float d) { return m(2, 1, d); } inline float m31(float d) { return m(3, 1, d); } inline float m02(float d) { return m(0, 2, d); } inline float m12(float d) { return m(1, 2, d); } inline float m22(float d) { return m(2, 2, d); } inline float m32(float d) { return m(3, 2, d); } inline float m03(float d) { return m(0, 3, d); } inline float m13(float d) { return m(1, 3, d); } inline float m23(float d) { return m(2, 3, d); } inline float m33(float d) { return m(3, 3, d); } [[nodiscard]] inline float w(int row, int column) const { return data[column - 1][row - 1]; }; [[nodiscard]] inline float w11() const { return m(0, 0); } [[nodiscard]] inline float w21() const { return m(1, 0); } [[nodiscard]] inline float w31() const { return m(2, 0); } [[nodiscard]] inline float w41() const { return m(3, 0); } [[nodiscard]] inline float w12() const { return m(0, 1); } [[nodiscard]] inline float w22() const { return m(1, 1); } [[nodiscard]] inline float w32() const { return m(2, 1); } [[nodiscard]] inline float w42() const { return m(3, 1); } [[nodiscard]] inline float w13() const { return m(0, 2); } [[nodiscard]] inline float w23() const { return m(1, 2); } [[nodiscard]] inline float w33() const { return m(2, 2); } [[nodiscard]] inline float w43() const { return m(3, 2); } [[nodiscard]] inline float w14() const { return m(0, 3); } [[nodiscard]] inline float w24() const { return m(1, 3); } [[nodiscard]] inline float w34() const { return m(2, 3); } [[nodiscard]] inline float w44() const { return m(3, 3); } inline float w(int row, int column, float value) { return data[column - 1][row - 1] = value; }; inline float w11(float d) { return m(0, 0, d); } inline float w21(float d) { return m(1, 0, d); } inline float w31(float d) { return m(2, 0, d); } inline float w41(float d) { return m(3, 0, d); } inline float w12(float d) { return m(0, 1, d); } inline float w22(float d) { return m(1, 1, d); } inline float w32(float d) { return m(2, 1, d); } inline float w42(float d) { return m(3, 1, d); } inline float w13(float d) { return m(0, 2, d); } inline float w23(float d) { return m(1, 2, d); } inline float w33(float d) { return m(2, 2, d); } inline float w43(float d) { return m(3, 2, d); } inline float w14(float d) { return m(0, 3, d); } inline float w24(float d) { return m(1, 3, d); } inline float w34(float d) { return m(2, 3, d); } inline float w44(float d) { return m(3, 3, d); } inline float* ptr() { return data[0].data(); } }; // adds the two mat4x4 left and right inline mat4x4 operator+(const mat4x4& left, const mat4x4& right) { mat4x4 ret = left; for (int i = 0; i < 4; i++) ret[i] += right.data[i]; return ret; } // subtracts the right mat4x4 from the left. inline mat4x4 operator-(const mat4x4& left, const mat4x4& right) { mat4x4 ret = left; for (int i = 0; i < 4; i++) ret[i] -= right.data[i]; return ret; } // since matrices are made identity by default, we need to create the result collector matrix without identity // otherwise the diagonal will be 1 off and cause weird results (see black screen issue) constexpr float emptyMatrix[16] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; // multiples the left with the right inline mat4x4 operator*(const mat4x4& left, const mat4x4& right) { mat4x4 mat = mat4x4::make_empty(); // TODO: check avx with this?? for (int i = 0; i < 4; i++) { for (int j = 0; j < 4; j++) { for (int k = 0; k < 4; k++) { mat.m(i, j, mat.m(i, j) + left.m(i, k) * right.m(k, j)); } } } return mat; } inline vec4 operator*(const mat4x4& left, const vec4& right) { vec4 ret{0, 0, 0, 0}; for (int m = 0; m < 4; m++) { for (int n = 0; n < 4; n++) { ret[m] = ret[m] + left.m(m, n) * right[n]; } } return ret; } template inline vec4 operator*(const mat4x4& left, const vec& right) { vec4 ret{0, 0, 0, 0}; for (int i = 0; i < size; i++) ret[i] = (float) right[i]; return left * ret; } // multiplies the const c with each element in the mat4x4 v inline mat4x4 operator*(float c, const mat4x4& v) { mat4x4 mat{}; for (int i = 0; i < 4; i++) { mat.data[i] = c * v.data[i]; } return mat; } // same as above but for right sided constants inline mat4x4 operator*(const mat4x4& v, float c) { mat4x4 mat{}; for (int i = 0; i < 4; i++) { mat.data[i] = v.data[i] * c; } return mat; } // divides the mat4x4 by the constant c inline mat4x4 operator/(const mat4x4& v, float c) { mat4x4 mat{}; for (int i = 0; i < 4; i++) { mat.data[i] = v.data[i] / c; } return mat; } // divides each element in the mat4x4 by over the constant inline mat4x4 operator/(float c, const mat4x4& v) { mat4x4 mat{}; for (int i = 0; i < 4; i++) { for (int j = 0; j < 4; j++) mat.data[i][j] = c / v.data[i][j]; } return mat; } // https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/building-basic-perspective-projection-matrix.html // https://ogldev.org/www/tutorial12/tutorial12.html // http://www.songho.ca/opengl/gl_projectionmatrix.html static inline mat4x4 perspective(float fov, float aspect_ratio, float near, float far) { mat4x4 perspectiveMat4x4 = mat4x4::make_empty(); float halfTan = tanf(fov * 0.5f * (float) M_PI / 180.0f); perspectiveMat4x4.m00(float(1.0 / (aspect_ratio * halfTan))); perspectiveMat4x4.m11(float(1.0 / halfTan)); perspectiveMat4x4.m22(float(-((far + near) / (far - near)))); perspectiveMat4x4.m32(-1); perspectiveMat4x4.m23(float(-((2 * near * far) / (far - near)))); return perspectiveMat4x4; } static inline mat4x4 ortho(float left, float right, float top, float bottom, float near, float far) { mat4x4 perspectiveMat4x4 = mat4x4::make_empty(); perspectiveMat4x4.m00(2 / (right - left)); perspectiveMat4x4.m11(2 / (top - bottom)); perspectiveMat4x4.m22(2 / (far - near)); perspectiveMat4x4.m33(1); perspectiveMat4x4.m03(-(right + left) / (right - left)); perspectiveMat4x4.m13(-(top + bottom) / (top - bottom)); perspectiveMat4x4.m23(-(far + near) / (far - near)); return perspectiveMat4x4; } } #endif //BLT_TESTS_MATRIX_H