+++ /dev/null
-/*
- * Copyright 1993-2014 NVIDIA Corporation. All rights reserved.
- *
- * Please refer to the NVIDIA end user license agreement (EULA) associated
- * with this source code for terms and conditions that govern your use of
- * this software. Any use, reproduction, disclosure, or distribution of
- * this software and related documentation outside the terms of the EULA
- * is strictly prohibited.
- *
- */
-
-//
-// 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 T> class vec2;
- template <class T> class vec3;
- template <class T> 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<T> &m)
- {
- set_value(m);
- }
-
-
- quaternion(const vec3<T> &axis, T radians)
- {
- set_value(axis, radians);
- }
-
-
- quaternion(const vec3<T> &rotateFrom, const vec3<T> &rotateTo)
- {
- set_value(rotateFrom, rotateTo);
- }
-
- quaternion(const vec3<T> &from_look, const vec3<T> &from_up,
- const vec3<T> &to_look, const vec3<T> &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<T> &axis, T &radians) const
- {
- radians = T(acos(_array[3]) * T(2.0));
-
- if (radians == T(0.0))
- {
- axis = vec3<T>(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<T> &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<T> &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<T> &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<T> &rotateFrom, const vec3<T> &rotateTo)
- {
- vec3<T> 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<T> v;
-
- if (p1[0] != p1[1] || p1[0] != p1[2])
- {
- v = vec3<T>(p1[1], p1[2], p1[0]);
- }
- else
- {
- v = vec3<T>(-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<T> &from_look, const vec3<T> &from_up,
- const vec3<T> &to_look, const vec3<T> &to_up)
- {
- quaternion r_look = quaternion(from_look, to_look);
-
- vec3<T> 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<T> &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<T> &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<T> conjugate(const quaternion<T> &q)
- {
- quaternion<T> r(q);
- r._array[0] *= T(-1.0);
- r._array[1] *= T(-1.0);
- r._array[2] *= T(-1.0);
- return r;
- }
-
- friend quaternion<T> inverse(const quaternion<T> &q)
- {
- return conjugate(q);
- }
-
- //
- // Quaternion multiplication with cartesian vector
- // v' = q*v*q(star)
- //
- void mult_vec(const vec3<T> &src, vec3<T> &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<T> &src_and_dst) const
- {
- mult_vec(vec3<T>(src_and_dst), src_and_dst);
- }
-
- void scale_angle(T scaleFactor)
- {
- vec3<T> axis;
- T radians;
-
- get_value(axis, radians);
- radians *= scaleFactor;
- set_value(axis, radians);
- }
-
- friend quaternion<T> slerp(const quaternion<T> &p, const quaternion<T> &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<T> &lhs, const quaternion<T> &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<T> &lhs, const quaternion<T> &rhs)
- {
- bool r = true;
-
- for (int i = 0; i < 4; i++)
- {
- r &= lhs._array[i] == rhs._array[i];
- }
-
- return r;
- }
-
- friend quaternion<T> operator * (const quaternion<T> &lhs, const quaternion<T> &rhs)
- {
- quaternion r(lhs);
- r *= rhs;
- return r;
- }
-
-
- union
- {
- struct
- {
- T x;
- T y;
- T z;
- T w;
- };
- T _array[4];
- };
-
- };
-
-
-
-};
-
-#endif
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