mirror of
https://github.com/NVIDIA/cuda-samples.git
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439 lines
11 KiB
C++
439 lines
11 KiB
C++
/*
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* Copyright 1993-2015 NVIDIA Corporation. All rights reserved.
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*
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* Please refer to the NVIDIA end user license agreement (EULA) associated
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* with this source code for terms and conditions that govern your use of
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* this software. Any use, reproduction, disclosure, or distribution of
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* this software and related documentation outside the terms of the EULA
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* is strictly prohibited.
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*
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*/
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//
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// Template math library for common 3D functionality
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//
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// nvQuaterion.h - quaternion template and utility functions
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//
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// This code is in part deriver from glh, a cross platform glut helper library.
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// The copyright for glh follows this notice.
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//
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// Copyright (c) NVIDIA Corporation. All rights reserved.
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////////////////////////////////////////////////////////////////////////////////
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/*
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Copyright (c) 2000 Cass Everitt
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Copyright (c) 2000 NVIDIA Corporation
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All rights reserved.
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Redistribution and use in source and binary forms, with or
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without modification, are permitted provided that the following
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conditions are met:
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* Redistributions of source code must retain the above
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copyright notice, this list of conditions and the following
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disclaimer.
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* Redistributions in binary form must reproduce the above
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copyright notice, this list of conditions and the following
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disclaimer in the documentation and/or other materials
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provided with the distribution.
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* The names of contributors to this software may not be used
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to endorse or promote products derived from this software
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without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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Cass Everitt - cass@r3.nu
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*/
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#ifndef NV_QUATERNION_H
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#define NV_QUATERNION_H
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namespace nv {
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template <class T>
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class vec2;
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template <class T>
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class vec3;
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template <class T>
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class vec4;
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////////////////////////////////////////////////////////////////////////////////
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//
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// Quaternion
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//
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////////////////////////////////////////////////////////////////////////////////
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template <class T>
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class quaternion {
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public:
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quaternion() : x(0.0), y(0.0), z(0.0), w(0.0) {}
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quaternion(const T v[4]) { set_value(v); }
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quaternion(T q0, T q1, T q2, T q3) { set_value(q0, q1, q2, q3); }
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quaternion(const matrix4<T> &m) { set_value(m); }
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quaternion(const vec3<T> &axis, T radians) { set_value(axis, radians); }
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quaternion(const vec3<T> &rotateFrom, const vec3<T> &rotateTo) {
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set_value(rotateFrom, rotateTo);
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}
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quaternion(const vec3<T> &from_look, const vec3<T> &from_up,
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const vec3<T> &to_look, const vec3<T> &to_up) {
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set_value(from_look, from_up, to_look, to_up);
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}
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const T *get_value() const { return &_array[0]; }
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void get_value(T &q0, T &q1, T &q2, T &q3) const {
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q0 = _array[0];
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q1 = _array[1];
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q2 = _array[2];
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q3 = _array[3];
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}
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quaternion &set_value(T q0, T q1, T q2, T q3) {
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_array[0] = q0;
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_array[1] = q1;
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_array[2] = q2;
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_array[3] = q3;
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return *this;
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}
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void get_value(vec3<T> &axis, T &radians) const {
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radians = T(acos(_array[3]) * T(2.0));
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if (radians == T(0.0)) {
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axis = vec3<T>(0.0, 0.0, 1.0);
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} else {
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axis[0] = _array[0];
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axis[1] = _array[1];
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axis[2] = _array[2];
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axis = normalize(axis);
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}
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}
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void get_value(matrix4<T> &m) const {
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T s, xs, ys, zs, wx, wy, wz, xx, xy, xz, yy, yz, zz;
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T norm = _array[0] * _array[0] + _array[1] * _array[1] +
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_array[2] * _array[2] + _array[3] * _array[3];
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s = (norm == T(0.0)) ? T(0.0) : (T(2.0) / norm);
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xs = _array[0] * s;
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ys = _array[1] * s;
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zs = _array[2] * s;
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wx = _array[3] * xs;
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wy = _array[3] * ys;
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wz = _array[3] * zs;
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xx = _array[0] * xs;
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xy = _array[0] * ys;
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xz = _array[0] * zs;
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yy = _array[1] * ys;
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yz = _array[1] * zs;
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zz = _array[2] * zs;
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m(0, 0) = T(T(1.0) - (yy + zz));
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m(1, 0) = T(xy + wz);
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m(2, 0) = T(xz - wy);
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m(0, 1) = T(xy - wz);
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m(1, 1) = T(T(1.0) - (xx + zz));
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m(2, 1) = T(yz + wx);
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m(0, 2) = T(xz + wy);
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m(1, 2) = T(yz - wx);
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m(2, 2) = T(T(1.0) - (xx + yy));
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m(3, 0) = m(3, 1) = m(3, 2) = m(0, 3) = m(1, 3) = m(2, 3) = T(0.0);
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m(3, 3) = T(1.0);
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}
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quaternion &set_value(const T *qp) {
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for (int i = 0; i < 4; i++) {
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_array[i] = qp[i];
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}
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return *this;
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}
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quaternion &set_value(const matrix4<T> &m) {
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T tr, s;
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int i, j, k;
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const int nxt[3] = {1, 2, 0};
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tr = m(0, 0) + m(1, 1) + m(2, 2);
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if (tr > T(0)) {
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s = T(sqrt(tr + m(3, 3)));
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_array[3] = T(s * 0.5);
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s = T(0.5) / s;
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_array[0] = T((m(1, 2) - m(2, 1)) * s);
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_array[1] = T((m(2, 0) - m(0, 2)) * s);
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_array[2] = T((m(0, 1) - m(1, 0)) * s);
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} else {
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i = 0;
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if (m(1, 1) > m(0, 0)) {
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i = 1;
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}
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if (m(2, 2) > m(i, i)) {
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i = 2;
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}
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j = nxt[i];
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k = nxt[j];
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s = T(sqrt((m(i, j) - (m(j, j) + m(k, k))) + T(1.0)));
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_array[i] = T(s * 0.5);
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s = T(0.5 / s);
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_array[3] = T((m(j, k) - m(k, j)) * s);
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_array[j] = T((m(i, j) + m(j, i)) * s);
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_array[k] = T((m(i, k) + m(k, i)) * s);
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}
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return *this;
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}
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quaternion &set_value(const vec3<T> &axis, T theta) {
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T sqnorm = square_norm(axis);
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if (sqnorm == T(0.0)) {
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// axis too small.
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x = y = z = T(0.0);
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w = T(1.0);
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} else {
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theta *= T(0.5);
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T sin_theta = T(sin(theta));
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if (sqnorm != T(1)) {
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sin_theta /= T(sqrt(sqnorm));
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}
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x = sin_theta * axis[0];
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y = sin_theta * axis[1];
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z = sin_theta * axis[2];
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w = T(cos(theta));
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}
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return *this;
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}
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quaternion &set_value(const vec3<T> &rotateFrom, const vec3<T> &rotateTo) {
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vec3<T> p1, p2;
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T alpha;
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p1 = normalize(rotateFrom);
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p2 = normalize(rotateTo);
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alpha = dot(p1, p2);
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if (alpha == T(1.0)) {
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*this = quaternion();
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return *this;
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}
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// ensures that the anti-parallel case leads to a positive dot
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if (alpha == T(-1.0)) {
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vec3<T> v;
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if (p1[0] != p1[1] || p1[0] != p1[2]) {
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v = vec3<T>(p1[1], p1[2], p1[0]);
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} else {
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v = vec3<T>(-p1[0], p1[1], p1[2]);
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}
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v -= p1 * dot(p1, v);
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v = normalize(v);
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set_value(v, T(3.1415926));
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return *this;
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}
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p1 = normalize(cross(p1, p2));
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set_value(p1, T(acos(alpha)));
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return *this;
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}
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quaternion &set_value(const vec3<T> &from_look, const vec3<T> &from_up,
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const vec3<T> &to_look, const vec3<T> &to_up) {
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quaternion r_look = quaternion(from_look, to_look);
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vec3<T> rotated_from_up(from_up);
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r_look.mult_vec(rotated_from_up);
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quaternion r_twist = quaternion(rotated_from_up, to_up);
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*this = r_twist;
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*this *= r_look;
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return *this;
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}
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quaternion &operator*=(const quaternion<T> &qr) {
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quaternion ql(*this);
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w = ql.w * qr.w - ql.x * qr.x - ql.y * qr.y - ql.z * qr.z;
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x = ql.w * qr.x + ql.x * qr.w + ql.y * qr.z - ql.z * qr.y;
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y = ql.w * qr.y + ql.y * qr.w + ql.z * qr.x - ql.x * qr.z;
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z = ql.w * qr.z + ql.z * qr.w + ql.x * qr.y - ql.y * qr.x;
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return *this;
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}
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friend quaternion normalize(const quaternion<T> &q) {
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quaternion r(q);
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T rnorm = T(1.0) / T(sqrt(q.w * q.w + q.x * q.x + q.y * q.y + q.z * q.z));
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r.x *= rnorm;
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r.y *= rnorm;
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r.z *= rnorm;
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r.w *= rnorm;
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}
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friend quaternion<T> conjugate(const quaternion<T> &q) {
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quaternion<T> r(q);
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r._array[0] *= T(-1.0);
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r._array[1] *= T(-1.0);
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r._array[2] *= T(-1.0);
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return r;
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}
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friend quaternion<T> inverse(const quaternion<T> &q) { return conjugate(q); }
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//
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// Quaternion multiplication with cartesian vector
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// v' = q*v*q(star)
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//
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void mult_vec(const vec3<T> &src, vec3<T> &dst) const {
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T v_coef = w * w - x * x - y * y - z * z;
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T u_coef = T(2.0) * (src[0] * x + src[1] * y + src[2] * z);
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T c_coef = T(2.0) * w;
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dst.v[0] =
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v_coef * src.v[0] + u_coef * x + c_coef * (y * src.v[2] - z * src.v[1]);
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dst.v[1] =
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v_coef * src.v[1] + u_coef * y + c_coef * (z * src.v[0] - x * src.v[2]);
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dst.v[2] =
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v_coef * src.v[2] + u_coef * z + c_coef * (x * src.v[1] - y * src.v[0]);
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}
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void mult_vec(vec3<T> &src_and_dst) const {
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mult_vec(vec3<T>(src_and_dst), src_and_dst);
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}
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void scale_angle(T scaleFactor) {
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vec3<T> axis;
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T radians;
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get_value(axis, radians);
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radians *= scaleFactor;
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set_value(axis, radians);
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}
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friend quaternion<T> slerp(const quaternion<T> &p, const quaternion<T> &q,
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T alpha) {
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quaternion r;
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T cos_omega = p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w;
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// if B is on opposite hemisphere from A, use -B instead
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int bflip;
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if ((bflip = (cos_omega < T(0)))) {
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cos_omega = -cos_omega;
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}
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// complementary interpolation parameter
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T beta = T(1) - alpha;
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if (cos_omega >= T(1)) {
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return p;
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}
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T omega = T(acos(cos_omega));
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T one_over_sin_omega = T(1.0) / T(sin(omega));
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beta = T(sin(omega * beta) * one_over_sin_omega);
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alpha = T(sin(omega * alpha) * one_over_sin_omega);
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if (bflip) {
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alpha = -alpha;
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}
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r.x = beta * p._array[0] + alpha * q._array[0];
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r.y = beta * p._array[1] + alpha * q._array[1];
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r.z = beta * p._array[2] + alpha * q._array[2];
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r.w = beta * p._array[3] + alpha * q._array[3];
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return r;
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}
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T &operator[](int i) { return _array[i]; }
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const T &operator[](int i) const { return _array[i]; }
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friend bool operator==(const quaternion<T> &lhs, const quaternion<T> &rhs) {
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bool r = true;
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for (int i = 0; i < 4; i++) {
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r &= lhs._array[i] == rhs._array[i];
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}
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return r;
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}
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friend bool operator!=(const quaternion<T> &lhs, const quaternion<T> &rhs) {
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bool r = true;
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for (int i = 0; i < 4; i++) {
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r &= lhs._array[i] == rhs._array[i];
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}
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return r;
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}
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friend quaternion<T> operator*(const quaternion<T> &lhs,
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const quaternion<T> &rhs) {
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quaternion r(lhs);
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r *= rhs;
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return r;
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}
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union {
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struct {
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T x;
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T y;
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T z;
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T w;
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};
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T _array[4];
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};
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};
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};
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#endif
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