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\n\n#include \"linmath.h\"\n\nint main()\n{\n Vec3f posChild(0.0f, 0.0f, 1.0f);\n \n Vec3f posParent(0.0f, 0.0f, 0.0f);\n float abcParent[] = { 0.0f, 90.0f, 0.0f };\n \n // child pos as homogeneous coordinate\n Vec4f posChildH(posChild, 1.0f);\n \n // compose parent matrix of pos and ori\n Mat4x4f matParent\n = Mat4x4f(InitTrans, posParent)\n * makeEuler(RotZYX,\n degToRad(abcParent[0]),\n degToRad(abcParent[1]),\n degToRad(abcParent[2]));\n \n // make posChildH global\n Vec4f posChildHW = matParent * posChildH;\n \n // homogeneous coordinate -> pos in 3d\n Vec3f posChildW(\n posChildHW.x / posChildHW.w,\n posChildHW.y / posChildHW.w,\n posChildHW.z / posChildHW.w);\n \n // print result\n std::cout << \"posChild in WCS: \" << std::fixed << posChildW << '\\n';\n}","codes",[3428,3432],{"_3429":3430,"_3424":3431},"file","linmath.h","#ifndef LIN_MATH_H\n#define LIN_MATH_H\n\n#include \n#include \n#include \n\nextern const double Pi;\n\ntemplate \ninline VALUE degToRad(VALUE angle)\n{\n return (VALUE)Pi * angle / (VALUE)180;\n}\n\ntemplate \ninline VALUE radToDeg(VALUE angle)\n{\n return (VALUE)180 * angle / (VALUE)Pi;\n}\n\nenum ArgNull { Null };\n\ntemplate \nstruct Vec2T {\n typedef VALUE Value;\n Value x, y;\n // default constructor (leaving elements uninitialized)\n Vec2T() { }\n Vec2T(ArgNull): x((Value)0), y((Value)0) { }\n Vec2T(Value x, Value y): x(x), y(y) { }\n};\n\ntemplate \nVec2T operator+(const Vec2T &v) { return v; }\n\ntemplate \nVec2T operator-(const Vec2T &v)\n{\n return Vec2T(-v.x, -v.y);\n}\n\ntemplate \nVec2T operator+(const Vec2T &v1, const Vec2T &v2)\n{\n return Vec2T(v1.x + v2.x, v1.y + v2.y);\n}\n\ntemplate \nVec2T operator-(const Vec2T &v1, const Vec2T &v2)\n{\n return Vec2T(v1.x - v2.x, v1.y - v2.y);\n}\n\ntemplate \nVec2T operator*(const Vec2T &v, VALUE s)\n{\n return Vec2T(v.x * s, v.y * s);\n}\n\ntemplate \nVec2T operator*(VALUE s, const Vec2T &v) { return v * s; }\n\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec2T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \" )\";\n}\n\ntemplate \nVALUE manhattan(const Vec2T &vec)\n{\n return vec.x * vec.x + vec.y * vec.y;\n}\n\ntypedef Vec2T Vec2f;\ntypedef Vec2T Vec2;\n\ntemplate \nstruct Vec3T {\n typedef VALUE Value;\n Value x, y, z;\n // default constructor (leaving elements uninitialized)\n Vec3T() { }\n Vec3T(ArgNull): x((Value)0), y((Value)0), z((Value)0) { }\n Vec3T(Value x, Value y, Value z): x(x), y(y), z(z) { }\n Vec3T(const Vec2T &xy, Value z): x(xy.x), y(xy.y), z(z) { }\n explicit operator Vec2T() const { return Vec2T(x, y); }\n const Vec2f xy() const { return Vec2f(x, y); }\n const Vec2f xz() const { return Vec2f(x, z); }\n const Vec2f yz() const { return Vec2f(y, z); }\n};\n\ntemplate \nVec3T operator+(const Vec3T &v) { return v; }\n\ntemplate \nVec3T operator-(const Vec3T &v)\n{\n return Vec3T(-v.x, -v.y, -v.z);\n}\n\ntemplate \nVec3T operator+(const Vec3T &v1, const Vec3T &v2)\n{\n return Vec3T(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z);\n}\n\ntemplate \nVec3T operator-(const Vec3T &v1, const Vec3T &v2)\n{\n return Vec3T(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z);\n}\n\ntemplate \nVec3T operator*(const Vec3T &v, VALUE s)\n{\n return Vec3T(v.x * s, v.y * s, v.z * s);\n}\n\ntemplate \nVec3T operator*(VALUE s, const Vec3T &v) { return v * s; }\n\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec3T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \", \" << v.z << \" )\";\n}\n\ntemplate \nVALUE manhattan(const Vec3T &vec)\n{\n return vec.x * vec.x + vec.y * vec.y + vec.z * vec.z;\n}\n\ntemplate \nVALUE dot(const Vec3T &v1, const Vec3T &v2)\n{\n return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;\n}\n\ntemplate \nVec3T cross(const Vec3T &v1, const Vec3T &v2)\n{\n return Vec3T(\n v1.y * v2.z - v1.z * v2.y,\n v1.z * v2.x - v1.x * v2.z,\n v1.x * v2.y - v1.y * v2.x);\n}\n\ntypedef Vec3T Vec3f;\ntypedef Vec3T Vec3;\n\ntemplate \nstruct Vec4T {\n typedef VALUE Value;\n Value x, y, z, w;\n // default constructor (leaving elements uninitialized)\n Vec4T() { }\n Vec4T(ArgNull): x((Value)0), y((Value)0), z((Value)0), w((Value)0) { }\n Vec4T(Value x, Value y, Value z, Value w): x(x), y(y), z(z), w(w) { }\n Vec4T(const Vec2T &xy, Value z, Value w):\n x(xy.x), y(xy.y), z(z), w(w)\n { }\n Vec4T(const Vec3T &xyz, Value w):\n x(xyz.x), y(xyz.y), z(xyz.z), w(w)\n { }\n explicit operator Vec2T() const { return Vec2T(x, y); }\n explicit operator Vec3T() const { return Vec3T(x, y, z); }\n const Vec2f xy() const { return Vec2f(x, y); }\n const Vec2f xz() const { return Vec2f(x, z); }\n const Vec2f yz() const { return Vec2f(y, z); }\n const Vec3f xyz() const { return Vec3f(x, y, z); }\n};\n\ntemplate \nVec4T operator+(const Vec4T &v) { return v; }\n\ntemplate \nVec4T operator-(const Vec4T &v)\n{\n return Vec4T(-v.x, -v.y, -v.z, -v.w);\n}\n\ntemplate \nVec4T operator+(const Vec4T &v1, const Vec4T &v2)\n{\n return Vec4T(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z, v1.w + v2.w);\n}\n\ntemplate \nVec4T operator-(const Vec4T &v1, const Vec4T &v2)\n{\n return Vec4T(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z, v1.w - v2.w);\n}\n\ntemplate \nVec4T operator*(const Vec4T &v, VALUE s)\n{\n return Vec4T(v.x * s, v.y * s, v.z * s, v.w * s);\n}\n\ntemplate \nVec4T operator*(VALUE s, const Vec4T &v) { return v * s; }\n\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec4T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \", \" << v.z << \", \" << v.w << \" )\";\n}\n\ntemplate \nVALUE manhattan(const Vec4T &vec)\n{\n return vec.x * vec.x + vec.y * vec.y + vec.z * vec.z + vec.w * vec.w;\n}\n\ntypedef Vec4T Vec4f;\ntypedef Vec4T Vec4;\n\nenum ArgInitIdent { InitIdent };\nenum ArgInitTrans { InitTrans };\nenum ArgInitRot { InitRot };\nenum ArgInitRotX { InitRotX };\nenum ArgInitRotY { InitRotY };\nenum ArgInitRotZ { InitRotZ };\nenum ArgInitScale { InitScale };\nenum ArgInitPersp { InitPersp };\n\ntemplate \nstruct Mat4x4T {\n union {\n VALUE comp[4 * 4];\n struct {\n VALUE _00, _01, _02, _03;\n VALUE _10, _11, _12, _13;\n VALUE _20, _21, _22, _23;\n VALUE _30, _31, _32, _33;\n };\n };\n\n // default constructor (leaving elements uninitialized)\n Mat4x4T() { }\n // constructor to build a matrix by elements\n Mat4x4T(\n VALUE _00, VALUE _01, VALUE _02, VALUE _03,\n VALUE _10, VALUE _11, VALUE _12, VALUE _13,\n VALUE _20, VALUE _21, VALUE _22, VALUE _23,\n VALUE _30, VALUE _31, VALUE _32, VALUE _33):\n _00(_00), _01(_01), _02(_02), _03(_03),\n _10(_10), _11(_11), _12(_12), _13(_13),\n _20(_20), _21(_21), _22(_22), _23(_23),\n _30(_30), _31(_31), _32(_32), _33(_33)\n { }\n // constructor to build an identity matrix\n Mat4x4T(ArgInitIdent):\n _00((VALUE)1), _01((VALUE)0), _02((VALUE)0), _03((VALUE)0),\n _10((VALUE)0), _11((VALUE)1), _12((VALUE)0), _13((VALUE)0),\n _20((VALUE)0), _21((VALUE)0), _22((VALUE)1), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n // constructor to build a matrix for translation\n Mat4x4T(ArgInitTrans, const Vec3T &t):\n _00((VALUE)1), _01((VALUE)0), _02((VALUE)0), _03((VALUE)t.x),\n _10((VALUE)0), _11((VALUE)1), _12((VALUE)0), _13((VALUE)t.y),\n _20((VALUE)0), _21((VALUE)0), _22((VALUE)1), _23((VALUE)t.z),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n // constructor to build a matrix for rotation about axis\n Mat4x4T(ArgInitRot, const Vec3T &axis, VALUE angle):\n _03((VALUE)0), _13((VALUE)0), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n {\n //axis.normalize();\n const VALUE sinAngle = sin(angle), cosAngle = cos(angle);\n const VALUE xx = axis.x * axis.x, xy = axis.x * axis.y;\n const VALUE xz = axis.x * axis.z, yy = axis.y * axis.y;\n const VALUE yz = axis.y * axis.z, zz = axis.z * axis.z;\n _00 = xx + cosAngle * ((VALUE)1 - xx) /* + sinAngle * 0 */;\n _01 = xy - cosAngle * xy - sinAngle * axis.z;\n _02 = xz - cosAngle * xz + sinAngle * axis.y;\n _10 = xy - cosAngle * xy + sinAngle * axis.z;\n _11 = yy + cosAngle * ((VALUE)1 - yy) /* + sinAngle * 0 */;\n _12 = yz - cosAngle * yz - sinAngle * axis.x;\n _20 = xz - cosAngle * xz - sinAngle * axis.y;\n _21 = yz - cosAngle * yz + sinAngle * axis.x;\n _22 = zz + cosAngle * ((VALUE)1 - zz) /* + sinAngle * 0 */;\n }\n // constructor to build a matrix for rotation about x axis\n Mat4x4T(ArgInitRotX, VALUE angle):\n _00((VALUE)1), _01((VALUE)0), _02((VALUE)0), _03((VALUE)0),\n _10((VALUE)0), _11(cos(angle)), _12(-sin(angle)), _13((VALUE)0),\n _20((VALUE)0), _21(sin(angle)), _22(cos(angle)), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n // constructor to build a matrix for rotation about y axis\n Mat4x4T(ArgInitRotY, VALUE angle):\n _00(cos(angle)), _01((VALUE)0), _02(sin(angle)), _03((VALUE)0),\n _10((VALUE)0), _11((VALUE)1), _12((VALUE)0), _13((VALUE)0),\n _20(-sin(angle)), _21((VALUE)0), _22(cos(angle)), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n // constructor to build a matrix for rotation about z axis\n Mat4x4T(ArgInitRotZ, VALUE angle):\n _00(cos(angle)), _01(-sin(angle)), _02((VALUE)0), _03((VALUE)0),\n _10(sin(angle)), _11(cos(angle)), _12((VALUE)0), _13((VALUE)0),\n _20((VALUE)0), _21((VALUE)0), _22((VALUE)1), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n // constructor to build a matrix for scaling\n Mat4x4T(ArgInitScale, VALUE sx, VALUE sy, VALUE sz):\n _00((VALUE)sx), _01((VALUE)0), _02((VALUE)0), _03((VALUE)0),\n _10((VALUE)0), _11((VALUE)sy), _12((VALUE)0), _13((VALUE)0),\n _20((VALUE)0), _21((VALUE)0), _22((VALUE)sz), _23((VALUE)0),\n _30((VALUE)0), _31((VALUE)0), _32((VALUE)0), _33((VALUE)1)\n { }\n /* constructor to build a matrix for perspective view.\n *\n * l ... left border\n * r ... right border\n * t ... top border\n * b ... bottom border\n * n ... near clip distance\n * f ... far clip distance\n */\n Mat4x4T(\n ArgInitPersp, VALUE l, VALUE r, VALUE b, VALUE t, VALUE n, VALUE f):\n _00(((VALUE)2 * n) / (r - l)),\n _01((VALUE)0),\n _02((r + l) / (r - l)),\n _03((VALUE)0),\n _10((VALUE)0),\n _11(((VALUE)2 * n) / (t - b)),\n _12((t + b) / (t - b)),\n _13((VALUE)0),\n _20((VALUE)0),\n _21((VALUE)0),\n _22(-(f + n) / (f - n)),\n _23(((VALUE)-2 * f * n) / (f - n)),\n _30((VALUE)0),\n _31((VALUE)0),\n _32((VALUE)-1),\n _33((VALUE)0)\n { }\n // operator to allow access with [][]\n VALUE* operator [] (int i)\n {\n assert(i >= 0 && i < 4);\n return comp + 4 * i;\n }\n // operator to allow access with [][]\n const VALUE* operator [] (int i) const\n {\n assert(i >= 0 && i < 4);\n return comp + 4 * i;\n }\n // multiply matrix with matrix -> matrix\n Mat4x4T operator * (const Mat4x4T &mat) const\n {\n return Mat4x4T(\n _00 * mat._00 + _01 * mat._10 + _02 * mat._20 + _03 * mat._30,\n _00 * mat._01 + _01 * mat._11 + _02 * mat._21 + _03 * mat._31,\n _00 * mat._02 + _01 * mat._12 + _02 * mat._22 + _03 * mat._32,\n _00 * mat._03 + _01 * mat._13 + _02 * mat._23 + _03 * mat._33,\n _10 * mat._00 + _11 * mat._10 + _12 * mat._20 + _13 * mat._30,\n _10 * mat._01 + _11 * mat._11 + _12 * mat._21 + _13 * mat._31,\n _10 * mat._02 + _11 * mat._12 + _12 * mat._22 + _13 * mat._32,\n _10 * mat._03 + _11 * mat._13 + _12 * mat._23 + _13 * mat._33,\n _20 * mat._00 + _21 * mat._10 + _22 * mat._20 + _23 * mat._30,\n _20 * mat._01 + _21 * mat._11 + _22 * mat._21 + _23 * mat._31,\n _20 * mat._02 + _21 * mat._12 + _22 * mat._22 + _23 * mat._32,\n _20 * mat._03 + _21 * mat._13 + _22 * mat._23 + _23 * mat._33,\n _30 * mat._00 + _31 * mat._10 + _32 * mat._20 + _33 * mat._30,\n _30 * mat._01 + _31 * mat._11 + _32 * mat._21 + _33 * mat._31,\n _30 * mat._02 + _31 * mat._12 + _32 * mat._22 + _33 * mat._32,\n _30 * mat._03 + _31 * mat._13 + _32 * mat._23 + _33 * mat._33);\n }\n // multiply matrix with vector -> vector\n Vec4T operator * (const Vec4T &vec) const\n {\n return Vec4T(\n _00 * vec.x + _01 * vec.y + _02 * vec.z + _03 * vec.w,\n _10 * vec.x + _11 * vec.y + _12 * vec.z + _13 * vec.w,\n _20 * vec.x + _21 * vec.y + _22 * vec.z + _23 * vec.w,\n _30 * vec.x + _31 * vec.y + _32 * vec.z + _33 * vec.w);\n }\n};\n\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Mat4x4T &m)\n{\n return out\n << m._00 << '\\t' << m._01 << '\\t' << m._02 << '\\t' << m._03 << '\\n'\n << m._10 << '\\t' << m._11 << '\\t' << m._12 << '\\t' << m._13 << '\\n'\n << m._20 << '\\t' << m._21 << '\\t' << m._22 << '\\t' << m._23 << '\\n'\n << m._30 << '\\t' << m._31 << '\\t' << m._32 << '\\t' << m._33 << '\\n';\n}\n\n/* computes determinant of a matrix.\n *\n * det = |M|\n *\n * mat ... the matrix\n */\ntemplate \nVALUE determinant(const Mat4x4T &mat)\n{\n /* determinant of 4x4 matrix is computed from\n * sum of m00 * M00 - m01 * M01 + m02 * M02 - m03 * M03\n * M00 ... M03 are the minors of the elements m00 ... m03\n */\n return\n mat._00\n * (mat._11 * (mat._22 * mat._33 - mat._23 * mat._32)\n + mat._12 * (mat._23 * mat._31 - mat._21 * mat._33)\n + mat._13 * (mat._21 * mat._32 - mat._22 * mat._31))\n - mat._01\n * (mat._10 * (mat._22 * mat._33 - mat._23 * mat._32)\n + mat._12 * (mat._23 * mat._30 - mat._20 * mat._33)\n + mat._13 * (mat._20 * mat._32 - mat._22 * mat._30))\n + mat._02\n * (mat._10 * (mat._21 * mat._33 - mat._23 * mat._31)\n + mat._11 * (mat._23 * mat._30 - mat._20 * mat._33)\n + mat._13 * (mat._20 * mat._31 - mat._21 * mat._30))\n - mat._03\n * (mat._10 * (mat._21 * mat._32 - mat._22 * mat._31)\n + mat._11 * (mat._22 * mat._30 - mat._20 * mat._32)\n + mat._12 * (mat._20 * mat._31 - mat._21 * mat._30));\n}\n\n/* returns the inverse of a regular matrix.\n *\n * mat matrix to invert\n * eps epsilon for regularity of matrix\n */\ntemplate \nMat4x4T invert(\n const Mat4x4T &mat, VALUE eps = (VALUE)1E-10)\n{\n assert(eps >= (VALUE)0);\n // compute determinant and check that it its unequal to 0\n // (Otherwise, matrix is singular!)\n const VALUE det = determinant(mat);\n if (abs(det) < eps) throw std::domain_error(\"Singular matrix!\");\n // reciproke of determinant\n const VALUE detInvPos = (VALUE)1 / det, detInvNeg = -detInvPos;\n // compute each element by determinant of sub-matrix which is build\n // striking out row and column of pivot element itself\n // BTW, the determinant is multiplied with -1 when sum of row and column\n // index is odd (chess board rule)\n // (This is usually called cofactor of related element.)\n // transpose matrix and multiply with 1/determinant of original matrix\n return Mat4x4T(\n detInvPos\n * (mat._11 * mat._22 * mat._33\n + mat._12 * mat._23 * mat._31\n + mat._13 * mat._21 * mat._32\n - mat._13 * mat._22 * mat._31\n - mat._11 * mat._23 * mat._32\n - mat._12 * mat._21 * mat._33),\n detInvNeg\n * (mat._01 * mat._22 * mat._33\n + mat._02 * mat._23 * mat._31\n + mat._03 * mat._21 * mat._32\n - mat._03 * mat._22 * mat._31\n - mat._01 * mat._23 * mat._32\n - mat._02 * mat._21 * mat._33),\n detInvPos\n * (mat._01 * mat._12 * mat._33\n + mat._02 * mat._13 * mat._31\n + mat._03 * mat._11 * mat._32\n - mat._03 * mat._12 * mat._31\n - mat._01 * mat._13 * mat._32\n - mat._02 * mat._11 * mat._33),\n detInvNeg\n * (mat._01 * mat._12 * mat._23\n + mat._02 * mat._13 * mat._21\n + mat._03 * mat._11 * mat._22\n - mat._03 * mat._12 * mat._21\n - mat._01 * mat._13 * mat._22\n - mat._02 * mat._11 * mat._23),\n detInvNeg\n * (mat._10 * mat._22 * mat._33\n + mat._12 * mat._23 * mat._30\n + mat._13 * mat._20 * mat._32\n - mat._13 * mat._22 * mat._30\n - mat._10 * mat._23 * mat._32\n - mat._12 * mat._20 * mat._33),\n detInvPos\n * (mat._00 * mat._22 * mat._33\n + mat._02 * mat._23 * mat._30\n + mat._03 * mat._20 * mat._32\n - mat._03 * mat._22 * mat._30\n - mat._00 * mat._23 * mat._32\n - mat._02 * mat._20 * mat._33),\n detInvNeg\n * (mat._00 * mat._12 * mat._33\n + mat._02 * mat._13 * mat._30\n + mat._03 * mat._10 * mat._32\n - mat._03 * mat._12 * mat._30\n - mat._00 * mat._13 * mat._32\n - mat._02 * mat._10 * mat._33),\n detInvPos\n * (mat._00 * mat._12 * mat._23\n + mat._02 * mat._13 * mat._20\n + mat._03 * mat._10 * mat._22\n - mat._03 * mat._12 * mat._20\n - mat._00 * mat._13 * mat._22\n - mat._02 * mat._10 * mat._23),\n detInvPos\n * (mat._10 * mat._21 * mat._33\n + mat._11 * mat._23 * mat._30\n + mat._13 * mat._20 * mat._31\n - mat._13 * mat._21 * mat._30\n - mat._10 * mat._23 * mat._31\n - mat._11 * mat._20 * mat._33),\n detInvNeg\n * (mat._00 * mat._21 * mat._33\n + mat._01 * mat._23 * mat._30\n + mat._03 * mat._20 * mat._31\n - mat._03 * mat._21 * mat._30\n - mat._00 * mat._23 * mat._31\n - mat._01 * mat._20 * mat._33),\n detInvPos\n * (mat._00 * mat._11 * mat._33\n + mat._01 * mat._13 * mat._30\n + mat._03 * mat._10 * mat._31\n - mat._03 * mat._11 * mat._30\n - mat._00 * mat._13 * mat._31\n - mat._01 * mat._10 * mat._33),\n detInvNeg\n * (mat._00 * mat._11 * mat._23\n + mat._01 * mat._13 * mat._20\n + mat._03 * mat._10 * mat._21\n - mat._03 * mat._11 * mat._20\n - mat._00 * mat._13 * mat._21\n - mat._01 * mat._10 * mat._23),\n detInvNeg\n * (mat._10 * mat._21 * mat._32\n + mat._11 * mat._22 * mat._30\n + mat._12 * mat._20 * mat._31\n - mat._12 * mat._21 * mat._30\n - mat._10 * mat._22 * mat._31\n - mat._11 * mat._20 * mat._32),\n detInvPos\n * (mat._00 * mat._21 * mat._32\n + mat._01 * mat._22 * mat._30\n + mat._02 * mat._20 * mat._31\n - mat._02 * mat._21 * mat._30\n - mat._00 * mat._22 * mat._31\n - mat._01 * mat._20 * mat._32),\n detInvNeg\n * (mat._00 * mat._11 * mat._32\n + mat._01 * mat._12 * mat._30\n + mat._02 * mat._10 * mat._31\n - mat._02 * mat._11 * mat._30\n - mat._00 * mat._12 * mat._31\n - mat._01 * mat._10 * mat._32),\n detInvPos\n * (mat._00 * mat._11 * mat._22\n + mat._01 * mat._12 * mat._20\n + mat._02 * mat._10 * mat._21\n - mat._02 * mat._11 * mat._20\n - mat._00 * mat._12 * mat._21\n - mat._01 * mat._10 * mat._22));\n}\n\ntypedef Mat4x4T Mat4x4f;\ntypedef Mat4x4T Mat4x4;\n\ntemplate \ntypename VECTOR::Value length(const VECTOR &vec)\n{\n return std::sqrt(manhattan(vec));\n}\n\nenum ArgNoThrow { NoThrow };\n\ntemplate \nVECTOR normalize(const VECTOR &vec)\n{\n typedef typename VECTOR::Value Value;\n const Value len = length(vec);\n if (len < (Value)1E-10) throw std::domain_error(\"Null vector!\");\n return vec * ((Value)1 / len);\n}\n\ntemplate \nVECTOR normalize(const VECTOR &vec, ArgNoThrow)\n{\n typedef typename VECTOR::Value Value;\n const Value len = length(vec);\n return len < (Value)1E-10 ? VECTOR(Null) : vec * ((Value)1 / len);\n}\n\ntemplate \nVec3T transformPoint(\n const Mat4x4T &mat, const Vec3T &pt)\n{\n Vec4T pt_ = mat * Vec4T(pt.x, pt.y, pt.z, (VALUE)1);\n return pt_.w != (VALUE)0\n ? Vec3T(pt_.x / pt_.w, pt_.y / pt_.w, pt_.z / pt_.w)\n : Vec3T(pt_.x, pt_.y, pt_.z);\n}\n\ntemplate \nVec3T transformVec(\n const Mat4x4T &mat, const Vec3T &v)\n{\n Vec4T vec = mat * Vec4T(v.x, v.y, v.z, (VALUE)0);\n return Vec3T(vec.x, vec.y, vec.z);\n}\n\n/* builds a symmetrical perspective view matrix.\n *\n * fov ... vertical field of view (in rad.)\n * ar ... aspect ratio (view width / view height)\n * dNear ... distance of near clip plane\n * dFar ... distance of far clip plane\n */\ntemplate \ninline Mat4x4T makePersp(\n VALUE fov, VALUE ar, VALUE dNear, VALUE dFar)\n{\n const VALUE d = std::tan(fov / 2.0) * 2.0 * dNear;\n return Mat4x4T(InitPersp, -d * ar, d * ar, -d, d, dNear, dFar);\n}\n\n// enumeration of rotation axes\nenum RotAxis {\n RotX, // rotation about x axis\n RotY, // rotation about y axis\n RotZ // rotation about z axis\n};\n\n// enumeration of possible Euler angles\nenum EulerAngle {\n RotXYX = RotX + 3 * RotY + 9 * RotX, // 0 + 3 + 0 = 3\n RotXYZ = RotX + 3 * RotY + 9 * RotZ, // 0 + 3 + 18 = 21\n RotXZX = RotX + 3 * RotZ + 9 * RotX, // 0 + 6 + 0 = 6\n RotXZY = RotX + 3 * RotZ + 9 * RotY, // 0 + 6 + 9 = 15\n RotYXY = RotY + 3 * RotX + 9 * RotY, // 1 + 0 + 9 = 10\n RotYXZ = RotY + 3 * RotX + 9 * RotZ, // 1 + 0 + 18 = 19\n RotYZX = RotY + 3 * RotZ + 9 * RotX, // 1 + 6 + 0 = 7\n RotYZY = RotY + 3 * RotZ + 9 * RotY, // 1 + 6 + 9 = 16\n RotZXY = RotZ + 3 * RotX + 9 * RotY, // 2 + 0 + 9 = 11\n RotZXZ = RotZ + 3 * RotX + 9 * RotZ, // 2 + 0 + 18 = 20\n RotZYX = RotZ + 3 * RotY + 9 * RotX, // 2 + 3 + 0 = 5\n RotZYZ = RotZ + 3 * RotY + 9 * RotZ, // 2 + 3 + 18 = 23\n RotHPR = RotZXY, // used in OpenGL Performer\n RotABC = RotZYX // used in German engineering\n};\n\n/* decomposes the combined EULER angle type into the corresponding\n * individual EULER angle axis types.\n */\ninline void decompose(\n EulerAngle type, RotAxis &axis1, RotAxis &axis2, RotAxis &axis3)\n{\n unsigned type_ = (unsigned)type;\n axis1 = (RotAxis)(type_ % 3); type_ /= 3;\n axis2 = (RotAxis)(type_ % 3); type_ /= 3;\n axis3 = (RotAxis)type_;\n}\n\ntemplate \nMat4x4T makeEuler(\n EulerAngle mode, VALUE rot1, VALUE rot2, VALUE rot3)\n{\n RotAxis axis1, axis2, axis3;\n decompose(mode, axis1, axis2, axis3);\n const static VALUE axes[3][3] = {\n { (VALUE)1, (VALUE)0, (VALUE)0 },\n { (VALUE)0, (VALUE)1, (VALUE)0 },\n { (VALUE)0, (VALUE)0, (VALUE)1 }\n };\n return\n Mat4x4T(InitRot,\n Vec3T(axes[axis1][0], axes[axis1][1], axes[axis1][2]),\n rot1)\n * Mat4x4T(InitRot,\n Vec3T(axes[axis2][0], axes[axis2][1], axes[axis2][2]),\n rot2)\n * Mat4x4T(InitRot,\n Vec3T(axes[axis3][0], axes[axis3][1], axes[axis3][2]),\n rot3);\n}\n\n/* decomposes a rotation matrix into EULER angles.\n *\n * It is necessary that the upper left 3x3 matrix is composed of rotations\n * only. Translational parts are not considered.\n * Other transformations (e.g. scaling, shearing, projection) may cause\n * wrong results.\n */\ntemplate \nvoid decompose(\n const Mat4x4T &mat,\n RotAxis axis1, RotAxis axis2, RotAxis axis3,\n VALUE &angle1, VALUE &angle2, VALUE &angle3)\n{\n assert(axis1 != axis2 && axis2 != axis3);\n /* This is ported from EulerAngles.h of the Eigen library. */\n const int odd = (axis1 + 1) % 3 == axis2 ? 0 : 1;\n const int i = axis1;\n const int j = (axis1 + 1 + odd) % 3;\n const int k = (axis1 + 2 - odd) % 3;\n if (axis1 == axis3) {\n angle1 = std::atan2(mat[j][i], mat[k][i]);\n if ((odd && angle1 < (VALUE)0) || (!odd && angle1 > (VALUE)0)) {\n angle1 = angle1 > (VALUE)0 ? angle1 - (VALUE)Pi : angle1 + (VALUE)Pi;\n const VALUE s2 = length(Vec2T(mat[j][i], mat[k][i]));\n angle2 = -std::atan2(s2, mat[i][i]);\n } else {\n const VALUE s2 = length(Vec2T(mat[j][i], mat[k][i]));\n angle2 = std::atan2(s2, mat[i][i]);\n }\n const VALUE s1 = sin(angle1);\n const VALUE c1 = cos(angle1);\n angle3 = std::atan2(c1 * mat[j][k] - s1 * mat[k][k],\n c1 * mat[j][j] - s1 * mat[k][j]);\n } else {\n angle1 = atan2(mat[j][k], mat[k][k]);\n const VALUE c2 = length(Vec2T(mat[i][i], mat[i][j]));\n if ((odd && angle1<(VALUE)0) || (!odd && angle1 > (VALUE)0)) {\n angle1 = (angle1 > (VALUE)0)\n ? angle1 - (VALUE)Pi : angle1 + (VALUE)Pi;\n angle2 = std::atan2(-mat[i][k], -c2);\n } else angle2 = std::atan2(-mat[i][k], c2);\n const VALUE s1 = std::sin(angle1);\n const VALUE c1 = std::cos(angle1);\n angle3 = std::atan2(s1 * mat[k][i] - c1 * mat[j][i],\n c1 * mat[j][j] - s1 * mat[k][j]);\n }\n if (!odd) {\n angle1 = -angle1; angle2 = -angle2; angle3 = -angle3;\n }\n}\n\ntemplate \nvoid decompose(\n const Mat4x4T &mat,\n EulerAngle modeEuler, VALUE &angle1, VALUE &angle2, VALUE &angle3)\n{\n RotAxis axis1, axis2, axis3;\n decompose(modeEuler, axis1, axis2, axis3);\n decompose(mat, axis1, axis2, axis3, angle1, angle2, angle3);\n}\n\n#endif // 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C++17.","",{"_3557":3600,"_3559":3601},"v3.4.0","2023-10-13T13:45:17Z",{"_3557":3600,"_3559":3601},{"_11":3604,"_3550":3605,"_3443":3606,"_3553":3607,"_3555":3608,"_3561":3611},"rapidjson","Tencent/rapidjson","A fast JSON parser/generator for C++ with both SAX/DOM style API","",{"_3557":3609,"_3559":3610},"v1.1.0","2016-08-25T08:01:22Z",{"_3557":3609,"_3559":3610},{"_11":3613,"_3550":3614,"_3443":3615,"_3553":3616,"_3555":3617,"_3561":3620},"picojson","kazuho/picojson","a header-file-only, JSON parser serializer in C++","",{"_3557":3618,"_3559":3619},"v1.3.0","2015-02-25T04:12:53Z",{"_3557":3618,"_3559":3619},{"_11":3622,"_3550":3622,"_3443":3623,"_3553":3624,"_3555":3625,"_3561":3628},"nlohmann/json","JSON for Modern C++","",{"_3557":3626,"_3559":3627},"v3.12.0","2025-04-11T08:43:39Z",{"_3557":3629,"_3559":3630},"v3.11.3","2023-11-28T21:38:09Z",{"_11":3632,"_3550":3633,"_3443":3634,"_3553":3635,"_3555":3636,"_3561":3639},"csv-parser","vincentlaucsb/csv-parser","A high-performance, 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