.. _program_listing_file_src_o3ds_math.h: Program Listing for File math.h =============================== |exhale_lsh| :ref:`Return to documentation for file ` (``src/o3ds/math.h``) .. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS .. code-block:: cpp /* Open 3D Stream Copyright 2020 Alastair Macleod Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #ifndef O3DS_MATRIX_H #define O3DS_MATRIX_H #include namespace O3DS { double rad(double deg); template class Vector4 { public: Vector4(T x, T y, T z, T w) : v{ x, y, z, w } {} Vector4() : v{0, 0, 0, 1} {} T v[4]; T& operator[](int n) { return v[n]; } }; typedef Vector4 Vector4d; template double dist(const Vector4 a, const Vector4 b) { double x = a.v[0] - b.v[0]; double y = a.v[1] - b.v[1]; double z = a.v[2] - b.v[2]; double w = a.v[3] - b.v[3]; double r = x * x + y * y + z * z + w * w; if (r == 0) return 0; return sqrt(r); } template class Vector3 { public: Vector3(T x, T y, T z) : v{ x, y, z } {} Vector3() : v{ 0, 0, 0 } {} T v[3]; T& operator[](int n) { return v[n]; } }; typedef Vector3 Vector3d; template double dist(const Vector3 a, const Vector3 b) { double x = a.v[0] - b.v[0]; double y = a.v[1] - b.v[1]; double z = a.v[2] - b.v[2]; double r = x * x + y * y + z * z; if (r == 0) return 0; return sqrt(r); } template class Matrix { public: Matrix(T m11, T m12, T m13, T m14, T m21, T m22, T m23, T m24, T m31, T m32, T m33, T m34, T m41, T m42, T m43, T m44) { m[0][0] = m11; m[0][1] = m12; m[0][2] = m13; m[0][3] = m14; m[1][0] = m21; m[1][1] = m22; m[1][2] = m23; m[1][3] = m24; m[2][0] = m31; m[2][1] = m32; m[2][2] = m33; m[2][3] = m34; m[3][0] = m41; m[3][1] = m42; m[3][2] = m43; m[3][3] = m44; } Matrix() { m[0][0] = 1; m[0][1] = 0; m[0][2] = 0; m[0][3] = 0; m[1][0] = 0; m[1][1] = 1; m[1][2] = 0; m[1][3] = 0; m[2][0] = 0; m[2][1] = 0; m[2][2] = 1; m[2][3] = 0; m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1; } Matrix(T value[]) { for(int u=0,i=0; u < 4; u++) { for (int v = 0; v < 4; v++, i++) { m[u][v] = value[i]; } } } double& operator()(int u, int v) { return m[u][v]; } const Matrix Transpose() const { return CMatrix4x4( m[0][0], m[1][0], m[2][0], m[3][0], m[0][1], m[1][1], m[2][1], m[3][1], m[0][2], m[1][2], m[2][2], m[3][2], m[0][3], m[1][3], m[2][3], m[3][3]); } const Vector4 GetTranslation() { Vector4 v; v.v[0] = m[3][0]; v.v[1] = m[3][1]; v.v[2] = m[3][2]; v.v[3] = 0; return v; } static const Matrix TranslateXYZ(T tx, T ty, T tz) { return Matrix(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, tx, ty, tz, 1); } static Matrix TranslateXYZ(Vector3 v) { return Matrix(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, v.v[0], v.v[1], v.v[2], 1); } static const Matrix RotateX(T a) { return Matrix( 1, 0, 0, 0, 0, cos(a), sin(a), 0, 0, -sin(a), cos(a), 0, 0, 0, 0, 1); } static const Matrix RotateY(T a) { return Matrix( cos(a), 0, -sin(a), 0, 0, 1, 0, 0, sin(a), 0, cos(a), 0, 0, 0, 0, 1); } static const Matrix RotateZ(T a) { return Matrix( cos(a), sin(a), 0, 0, -sin(a), cos(a), 0, 0, 0, 0, 1, 0, 0, 0, 0, 1); } static const Matrix Quaternion(Vector4 q) { T x2 = q.v[0] + q.v[0]; T y2 = q.v[1] + q.v[1]; T z2 = q.v[2] + q.v[2]; T xx = q.v[0] * x2; T xy = q.v[0] * y2; T xz = q.v[0] * z2; T yy = q.v[1] * y2; T yz = q.v[1] * z2; T zz = q.v[2] * z2; T wx = q.v[3] * x2; T wy = q.v[3] * y2; T wz = q.v[3] * z2; return Matrix( 1.0 - (yy + zz), xy + wz, xz - wy, 0.0, xy - wz, 1.0 - (xx + zz), yz + wx, 0.0, xz + wy, yz - wx, 1.0 - (xx + yy), 0.0, 0, 0, 0, 1); } static const Matrix Scale(Vector3 s) { return Matrix( s[0], 0, 0, 0, 0, s[1], 0, 0, 0, 0, s[2], 0, 0, 0, 0, 1); } const Matrix Inverse() { T m22_33_23_32 = m[2][2] * m[3][3] - m[2][3] * m[3][2]; T m23_30_20_33 = m[2][3] * m[3][0] - m[2][0] * m[3][3]; T m20_31_21_30 = m[2][0] * m[3][1] - m[2][1] * m[3][0]; T m21_32_22_31 = m[2][1] * m[3][2] - m[2][2] * m[3][1]; T m23_31_21_33 = m[2][3] * m[3][1] - m[2][1] * m[3][3]; T m20_32_22_30 = m[2][0] * m[3][2] - m[2][2] * m[3][0]; T d00 = m[1][1] * m22_33_23_32 + m[1][2] * m23_31_21_33 + m[1][3] * m21_32_22_31; T d01 = m[1][0] * m22_33_23_32 + m[1][2] * m23_30_20_33 + m[1][3] * m20_32_22_30; T d02 = m[1][0] * -m23_31_21_33 + m[1][1] * m23_30_20_33 + m[1][3] * m20_31_21_30; T d03 = m[1][0] * m21_32_22_31 + m[1][1] * -m20_32_22_30 + m[1][2] * m20_31_21_30; T d10 = m[0][1] * m22_33_23_32 + m[0][2] * m23_31_21_33 + m[0][3] * m21_32_22_31; T d11 = m[0][0] * m22_33_23_32 + m[0][2] * m23_30_20_33 + m[0][3] * m20_32_22_30; T d12 = m[0][0] *-m23_31_21_33 + m[0][1] * m23_30_20_33 + m[0][3] * m20_31_21_30; T d13 = m[0][0] * m21_32_22_31 + m[0][1] * -m20_32_22_30 + m[0][2] * m20_31_21_30; T m02_13_03_12 = m[0][2] * m[1][3] - m[0][3] * m[1][2]; T m03_10_00_13 = m[0][3] * m[1][0] - m[0][0] * m[1][3]; T m00_11_01_10 = m[0][0] * m[1][1] - m[0][1] * m[1][0]; T m01_12_02_11 = m[0][1] * m[1][2] - m[0][2] * m[1][1]; T m03_11_01_13 = m[0][3] * m[1][1] - m[0][1] * m[1][3]; T m00_12_02_10 = m[0][0] * m[1][2] - m[0][2] * m[1][0]; T d20 = m[3][1] * m02_13_03_12 + m[3][2] * m03_11_01_13 + m[3][3] * m01_12_02_11; T d21 = m[3][0] * m02_13_03_12 + m[3][2] * m03_10_00_13 + m[3][3] * m00_12_02_10; T d22 = m[3][0] *-m03_11_01_13 + m[3][1] * m03_10_00_13 + m[3][3] * m00_11_01_10; T d23 = m[3][0] * m01_12_02_11 + m[3][1] *-m00_12_02_10 + m[3][2] * m00_11_01_10; T d30 = m[2][1] * m02_13_03_12 + m[2][2] * m03_11_01_13 + m[2][3] * m01_12_02_11; T d31 = m[2][0] * m02_13_03_12 + m[2][2] * m03_10_00_13 + m[2][3] * m00_12_02_10; T d32 = m[2][0] *-m03_11_01_13 + m[2][1] * m03_10_00_13 + m[2][3] * m00_11_01_10; T d33 = m[2][0] * m01_12_02_11 + m[2][1] *-m00_12_02_10 + m[2][2] * m00_11_01_10; T D = m[0][0] *d00 - m[0][1] *d01 + m[0][2] *d02 - m[0][3] *d03; return Matrix( d00 / D, -d10 / D, d20 / D, -d30 / D, -d01 / D, d11 / D, -d21 / D, d31 / D, d02 / D, -d12 / D, d22 / D, -d32 / D, -d03 / D, d13 / D, -d23 / D, d33 / D); } Vector4 GetQuaternion() { T qx, qy, qz, qw; T tr = m[0][0] + m[1][1] + m[2][2]; T q[4], s; int i, j, k; const int nxt[3] = { 1, 2, 0 }; if (tr > 0.0) { s = sqrt(tr + 1.0); qw = s / 2.0; s = 0.5 / s; qx = (m[1][2] - m[2][1]) * s; qy = (m[2][0] - m[0][2]) * s; qz = (m[0][1] - m[1][0]) * s; } else { i = 0; if (m[1][1] > m[0][0]) i = 1; if (m[2][2] > m[i][i]) i = 2; j = nxt[i]; k = nxt[j]; s = sqrt((m[i][i] - (m[j][j] + m[k][k])) + 1.0); q[i] = s * 0.5; if (s != 0.0) s = 0.5 / s; q[3] = (m[j][k] - m[k][j]) * s; q[j] = (m[i][j] + m[j][i]) * s; q[k] = (m[i][k] + m[k][i]) * s; qx = q[0]; qy = q[1]; qz = q[2]; qw = q[3]; } // Normalize T denom = sqrt(qx*qx + qy*qy + qz*qz + qw*qw); if (denom > 1.0e-7) { qx /= denom; qy /= denom; qz /= denom; qw /= denom; } else { qx = qy = qz = 0; qw = 1; } Vector4 ret; ret.v[0] = qx; ret.v[1] = qy; ret.v[2] = qz; ret.v[3] = qw; return ret; } #if 0 void pr(const char *lbl) { printf("==== %s ====\n", this->lbl); for (int u = 0; u < 4; u++) { for (int v = 0; v < 4; v++) { printf("%f ", this->m[u][v]); } printf("\n"); } } #endif T m[4][4]; }; // Matrix typedef Matrix Matrixd; #define CALC(i, j) lhs.m[i][0] * rhs.m[0][j] + lhs.m[i][1] * rhs.m[1][j] + \ lhs.m[i][2] * rhs.m[2][j] + lhs.m[i][3] * rhs.m[3][j] template const Matrix operator *(const Matrix &lhs, const Matrix &rhs) { return Matrix( CALC(0, 0), CALC(0, 1), CALC(0, 2), CALC(0, 3), CALC(1, 0), CALC(1, 1), CALC(1, 2), CALC(1, 3), CALC(2, 0), CALC(2, 1), CALC(2, 2), CALC(2, 3), CALC(3, 0), CALC(3, 1), CALC(3, 2), CALC(3, 3)); } template const Vector4 operator *(const Matrix &m, const Vector4 &v) { Vector4 res; res.v[0] = v.v[0] * m.m[0][0] + v.v[1] * m.m[1][0] + v.v[2] * m.m[2][0] + m.m[3][0]; res.v[1] = v.v[0] * m.m[0][1] + v.v[1] * m.m[1][1] + v.v[2] * m.m[2][1] + m.m[3][1]; res.v[2] = v.v[0] * m.m[0][2] + v.v[1] * m.m[1][2] + v.v[2] * m.m[2][2] + m.m[3][2]; res.v[3] = v.v[0] * m.m[0][3] + v.v[1] * m.m[1][3] + v.v[2] * m.m[2][3] + m.m[3][3]; return res; } } // O3DS #endif // O3DS_MATRIX_H