/* Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * Neither the name of NVIDIA CORPORATION nor the names of its * contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ // // Template math library for common 3D functionality // // nvQuaterion.h - quaternion template and utility functions // // This code is in part deriver from glh, a cross platform glut helper library. // The copyright for glh follows this notice. // // Copyright (c) NVIDIA Corporation. All rights reserved. //////////////////////////////////////////////////////////////////////////////// /* Copyright (c) 2000 Cass Everitt Copyright (c) 2000 NVIDIA Corporation All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * The names of contributors to this software may not be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. Cass Everitt - cass@r3.nu */ #ifndef NV_QUATERNION_H #define NV_QUATERNION_H namespace nv { template class vec2; template class vec3; template class vec4; //////////////////////////////////////////////////////////////////////////////// // // Quaternion // //////////////////////////////////////////////////////////////////////////////// template< class T> class quaternion { public: quaternion() : x(0.0), y(0.0), z(0.0), w(0.0) { } quaternion(const T v[4]) { set_value(v); } quaternion(T q0, T q1, T q2, T q3) { set_value(q0, q1, q2, q3); } quaternion(const matrix4 &m) { set_value(m); } quaternion(const vec3 &axis, T radians) { set_value(axis, radians); } quaternion(const vec3 &rotateFrom, const vec3 &rotateTo) { set_value(rotateFrom, rotateTo); } quaternion(const vec3 &from_look, const vec3 &from_up, const vec3 &to_look, const vec3 &to_up) { set_value(from_look, from_up, to_look, to_up); } const T *get_value() const { return &_array[0]; } void get_value(T &q0, T &q1, T &q2, T &q3) const { q0 = _array[0]; q1 = _array[1]; q2 = _array[2]; q3 = _array[3]; } quaternion &set_value(T q0, T q1, T q2, T q3) { _array[0] = q0; _array[1] = q1; _array[2] = q2; _array[3] = q3; return *this; } void get_value(vec3 &axis, T &radians) const { radians = T(acos(_array[3]) * T(2.0)); if (radians == T(0.0)) { axis = vec3(0.0, 0.0, 1.0); } else { axis[0] = _array[0]; axis[1] = _array[1]; axis[2] = _array[2]; axis = normalize(axis); } } void get_value(matrix4 &m) const { T s, xs, ys, zs, wx, wy, wz, xx, xy, xz, yy, yz, zz; T norm = _array[0] * _array[0] + _array[1] * _array[1] + _array[2] * _array[2] + _array[3] * _array[3]; s = (norm == T(0.0)) ? T(0.0) : (T(2.0) / norm); xs = _array[0] * s; ys = _array[1] * s; zs = _array[2] * s; wx = _array[3] * xs; wy = _array[3] * ys; wz = _array[3] * zs; xx = _array[0] * xs; xy = _array[0] * ys; xz = _array[0] * zs; yy = _array[1] * ys; yz = _array[1] * zs; zz = _array[2] * zs; m(0,0) = T(T(1.0) - (yy + zz)); m(1,0) = T(xy + wz); m(2,0) = T(xz - wy); m(0,1) = T(xy - wz); m(1,1) = T(T(1.0) - (xx + zz)); m(2,1) = T(yz + wx); m(0,2) = T(xz + wy); m(1,2) = T(yz - wx); m(2,2) = T(T(1.0) - (xx + yy)); m(3,0) = m(3,1) = m(3,2) = m(0,3) = m(1,3) = m(2,3) = T(0.0); m(3,3) = T(1.0); } quaternion &set_value(const T *qp) { for (int i = 0; i < 4; i++) { _array[i] = qp[i]; } return *this; } quaternion &set_value(const matrix4 &m) { T tr, s; int i, j, k; const int nxt[3] = { 1, 2, 0 }; tr = m(0,0) + m(1,1) + m(2,2); if (tr > T(0)) { s = T(sqrt(tr + m(3,3))); _array[3] = T(s * 0.5); s = T(0.5) / s; _array[0] = T((m(1,2) - m(2,1)) * s); _array[1] = T((m(2,0) - m(0,2)) * s); _array[2] = T((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 = T(sqrt((m(i,j) - (m(j,j) + m(k,k))) + T(1.0))); _array[i] = T(s * 0.5); s = T(0.5 / s); _array[3] = T((m(j,k) - m(k,j)) * s); _array[j] = T((m(i,j) + m(j,i)) * s); _array[k] = T((m(i,k) + m(k,i)) * s); } return *this; } quaternion &set_value(const vec3 &axis, T theta) { T sqnorm = square_norm(axis); if (sqnorm == T(0.0)) { // axis too small. x = y = z = T(0.0); w = T(1.0); } else { theta *= T(0.5); T sin_theta = T(sin(theta)); if (sqnorm != T(1)) { sin_theta /= T(sqrt(sqnorm)); } x = sin_theta * axis[0]; y = sin_theta * axis[1]; z = sin_theta * axis[2]; w = T(cos(theta)); } return *this; } quaternion &set_value(const vec3 &rotateFrom, const vec3 &rotateTo) { vec3 p1, p2; T alpha; p1 = normalize(rotateFrom); p2 = normalize(rotateTo); alpha = dot(p1, p2); if (alpha == T(1.0)) { *this = quaternion(); return *this; } // ensures that the anti-parallel case leads to a positive dot if (alpha == T(-1.0)) { vec3 v; if (p1[0] != p1[1] || p1[0] != p1[2]) { v = vec3(p1[1], p1[2], p1[0]); } else { v = vec3(-p1[0], p1[1], p1[2]); } v -= p1 * dot(p1, v); v = normalize(v); set_value(v, T(3.1415926)); return *this; } p1 = normalize(cross(p1, p2)); set_value(p1,T(acos(alpha))); return *this; } quaternion &set_value(const vec3 &from_look, const vec3 &from_up, const vec3 &to_look, const vec3 &to_up) { quaternion r_look = quaternion(from_look, to_look); vec3 rotated_from_up(from_up); r_look.mult_vec(rotated_from_up); quaternion r_twist = quaternion(rotated_from_up, to_up); *this = r_twist; *this *= r_look; return *this; } quaternion &operator *= (const quaternion &qr) { quaternion ql(*this); w = ql.w * qr.w - ql.x * qr.x - ql.y * qr.y - ql.z * qr.z; x = ql.w * qr.x + ql.x * qr.w + ql.y * qr.z - ql.z * qr.y; y = ql.w * qr.y + ql.y * qr.w + ql.z * qr.x - ql.x * qr.z; z = ql.w * qr.z + ql.z * qr.w + ql.x * qr.y - ql.y * qr.x; return *this; } friend quaternion normalize(const quaternion &q) { quaternion r(q); T rnorm = T(1.0) / T(sqrt(q.w * q.w + q.x * q.x + q.y * q.y + q.z * q.z)); r.x *= rnorm; r.y *= rnorm; r.z *= rnorm; r.w *= rnorm; } friend quaternion conjugate(const quaternion &q) { quaternion r(q); r._array[0] *= T(-1.0); r._array[1] *= T(-1.0); r._array[2] *= T(-1.0); return r; } friend quaternion inverse(const quaternion &q) { return conjugate(q); } // // Quaternion multiplication with cartesian vector // v' = q*v*q(star) // void mult_vec(const vec3 &src, vec3 &dst) const { T v_coef = w * w - x * x - y * y - z * z; T u_coef = T(2.0) * (src[0] * x + src[1] * y + src[2] * z); T c_coef = T(2.0) * w; dst.v[0] = v_coef * src.v[0] + u_coef * x + c_coef * (y * src.v[2] - z * src.v[1]); dst.v[1] = v_coef * src.v[1] + u_coef * y + c_coef * (z * src.v[0] - x * src.v[2]); dst.v[2] = v_coef * src.v[2] + u_coef * z + c_coef * (x * src.v[1] - y * src.v[0]); } void mult_vec(vec3 &src_and_dst) const { mult_vec(vec3(src_and_dst), src_and_dst); } void scale_angle(T scaleFactor) { vec3 axis; T radians; get_value(axis, radians); radians *= scaleFactor; set_value(axis, radians); } friend quaternion slerp(const quaternion &p, const quaternion &q, T alpha) { quaternion r; T cos_omega = p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w; // if B is on opposite hemisphere from A, use -B instead int bflip; if ((bflip = (cos_omega < T(0)))) { cos_omega = -cos_omega; } // complementary interpolation parameter T beta = T(1) - alpha; if (cos_omega >= T(1)) { return p; } T omega = T(acos(cos_omega)); T one_over_sin_omega = T(1.0) / T(sin(omega)); beta = T(sin(omega*beta) * one_over_sin_omega); alpha = T(sin(omega*alpha) * one_over_sin_omega); if (bflip) { alpha = -alpha; } r.x = beta * p._array[0]+ alpha * q._array[0]; r.y = beta * p._array[1]+ alpha * q._array[1]; r.z = beta * p._array[2]+ alpha * q._array[2]; r.w = beta * p._array[3]+ alpha * q._array[3]; return r; } T &operator [](int i) { return _array[i]; } const T &operator [](int i) const { return _array[i]; } friend bool operator == (const quaternion &lhs, const quaternion &rhs) { bool r = true; for (int i = 0; i < 4; i++) { r &= lhs._array[i] == rhs._array[i]; } return r; } friend bool operator != (const quaternion &lhs, const quaternion &rhs) { bool r = true; for (int i = 0; i < 4; i++) { r &= lhs._array[i] == rhs._array[i]; } return r; } friend quaternion operator * (const quaternion &lhs, const quaternion &rhs) { quaternion r(lhs); r *= rhs; return r; } union { struct { T x; T y; T z; T w; }; T _array[4]; }; }; }; #endif