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\n#include \"linMath.h\"\n\n#define FIX\n\ndouble radians(double);\nVec3 degrees(Vec3 angles);\nMat4x4 eulerAngleXYZ(double rX, double rY, double rZ);\nvoid extractEulerAngles(const Mat4x4 &mat, double &rX, double &rY, double &rZ);\nVec3 rotateX(const Vec3 &p, double angle);\nVec3 rotateY(const Vec3 &p, double angle);\nVec3 rotateZ(const Vec3 &p, double angle);\n\n// combines 2 XYZ euler angles given in degrees\nVec3 eulerCombine(const Vec3 &first, const Vec3 &second)\n{\n const Mat4x4 mat1 = eulerAngleXYZ(radians(first.x), radians(first.y), radians(first.z));\n const Mat4x4 mat2 = eulerAngleXYZ(radians(second.x), radians(second.y), radians(second.z));\n Vec3 output;\n extractEulerAngles(mat2 * mat1, output.x, output.y, output.z);\n return degrees(output);\n}\n\n// applies the XYZ euler rotation on p\nVec3 eulerRotate(const Vec3 &p, const Vec3 &euler)\n{\n#ifndef FIX // Theo:\n Vec3 output;\n output = rotateX(p, radians(euler.x));\n output = rotateY(output, radians(euler.y));\n output = rotateZ(output, radians(euler.z));\n return output;\n#else // Dirk:\n return rotateX(rotateY(rotateZ(p, radians(euler.z)), radians(euler.y)), radians(euler.x));\n#endif // FIX\n}\n\nint main()\n{\n Vec3 euler1(30, 20, 90); // euler angles in degrees\n Vec3 euler2(20, 30, 10);\n Vec3 euler3 = eulerCombine(euler1, euler2);\n Vec3 p(-10, 7, 23);\n \n Vec3 result1 = eulerRotate(eulerRotate(p, euler1), euler2);\n Vec3 result2 = eulerRotate(p, euler3);\n\n std::cout << result1.x << \" \" << result1.y << \" \" << result1.z << std::endl;\n std::cout << result2.x << \" \" << result2.y << \" \" << result2.z << std::endl;\n // done\n return 0;\n}\n\ndouble radians(double angle) { return degToRad(angle); }\n\nVec3 degrees(Vec3 angles)\n{\n return Vec3(radToDeg(angles.x), radToDeg(angles.y), radToDeg(angles.z));\n}\n\nMat4x4 eulerAngleXYZ(double rX, double rY, double rZ)\n{\n return Mat4x4(InitRotX, rX) * Mat4x4(InitRotY, rY) * Mat4x4(InitRotZ, rZ);\n}\n\nvoid extractEulerAngles(const Mat4x4 &mat, double &rX, double &rY, double &rZ)\n{\n decompose(mat, RotX, RotY, RotZ, rX, rY, rZ);\n}\n\nVec3 rotateX(const Vec3 &p, double angle)\n{\n const Vec4 p_ = Mat4x4(InitRotX, angle) * Vec4(p, 1.0);\n return Vec3(p_.x, p_.y, p_.z);\n}\n\nVec3 rotateY(const Vec3 &p, double angle)\n{\n const Vec4 p_ = Mat4x4(InitRotY, angle) * Vec4(p, 1.0);\n return Vec3(p_.x, p_.y, p_.z);\n}\n\nVec3 rotateZ(const Vec3 &p, double angle)\n{\n const Vec4 p_ = Mat4x4(InitRotZ, angle) * Vec4(p, 1.0);\n return Vec3(p_.x, p_.y, p_.z);\n}\n","codes",[3388],{"_3389":3390,"_3384":3391},"file","linMath.h","#ifndef LIN_MATH_H\n#define LIN_MATH_H\n\n#include \n#include \n#include \n\ndouble Pi = 3.1415926535897932384626433832795;\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\ntemplate \nstruct Vec2T {\n VALUE x, y;\n Vec2T() { }\n Vec2T(VALUE x, VALUE y): x(x), y(y) { }\n};\ntemplate \nVALUE length(const Vec2T &vec)\n{\n return sqrt(vec.x * vec.x + vec.y * vec.y);\n}\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec2T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \" )\";\n}\n\ntypedef Vec2T Vec2f;\ntypedef Vec2T Vec2;\n\ntemplate \nstruct Vec3T {\n VALUE x, y, z;\n Vec3T() { }\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};\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec3T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \", \" << v.z << \" )\";\n}\n\ntypedef Vec3T Vec3f;\ntypedef Vec3T Vec3;\n\ntemplate \nstruct Vec4T {\n VALUE x, y, z, w;\n Vec4T() { }\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};\ntemplate \nstd::ostream& operator<<(std::ostream &out, const Vec4T &v)\n{\n return out << \"( \" << v.x << \", \" << v.y << \", \" << v.z << \", \" << v.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 };\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 // 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 // operator to allow access with [][]\n double* operator [] (int i)\n {\n assert(i >= 0 && i < 4);\n return comp + 4 * i;\n }\n // operator to allow access with [][]\n const double* 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}\ntypedef Mat4x4T Mat4x4f;\ntypedef Mat4x4T Mat4x4;\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 = 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 = -atan2(s2, mat[i][i]);\n } else {\n const VALUE s2 = length(Vec2T(mat[j][i], mat[k][i]));\n angle2 = atan2(s2, mat[i][i]);\n }\n const VALUE s1 = sin(angle1);\n const VALUE c1 = cos(angle1);\n angle3 = 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 = atan2(-mat[i][k], -c2);\n } else angle2 = atan2(-mat[i][k], c2);\n const VALUE s1 = sin(angle1);\n const VALUE c1 = cos(angle1);\n angle3 = 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\n#endif // LIN_MATH_H","stdin","compiler","warning,optimize,boost-nothing-gcc-head,c++11,cpp-no-pedantic","createdAt",1532292737,"title","description","isPrivate","compilerInfo",{"_11":332,"_13":3402,"_15":333,"_17":18,"_19":3403,"_22":23,"_24":25,"_26":335,"_28":3404},"9.0.0 20180720 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