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+/*************************************************************************/
+/* quat.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* http://www.godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+#include "quat.h"
+#include "print_string.h"
+
+void Quat::set_euler(const Vector3& p_euler) {
+ real_t half_yaw = p_euler.x * 0.5;
+ real_t half_pitch = p_euler.y * 0.5;
+ real_t half_roll = p_euler.z * 0.5;
+ real_t cos_yaw = Math::cos(half_yaw);
+ real_t sin_yaw = Math::sin(half_yaw);
+ real_t cos_pitch = Math::cos(half_pitch);
+ real_t sin_pitch = Math::sin(half_pitch);
+ real_t cos_roll = Math::cos(half_roll);
+ real_t sin_roll = Math::sin(half_roll);
+ set(cos_roll * sin_pitch * cos_yaw+sin_roll * cos_pitch * sin_yaw,
+ cos_roll * cos_pitch * sin_yaw - sin_roll * sin_pitch * cos_yaw,
+ sin_roll * cos_pitch * cos_yaw - cos_roll * sin_pitch * sin_yaw,
+ cos_roll * cos_pitch * cos_yaw+sin_roll * sin_pitch * sin_yaw);
+}
+
+void Quat::operator*=(const Quat& q) {
+
+ set(w * q.x+x * q.w+y * q.z - z * q.y,
+ w * q.y+y * q.w+z * q.x - x * q.z,
+ w * q.z+z * q.w+x * q.y - y * q.x,
+ w * q.w - x * q.x - y * q.y - z * q.z);
+}
+
+Quat Quat::operator*(const Quat& q) const {
+
+ Quat r=*this;
+ r*=q;
+ return r;
+}
+
+
+
+
+real_t Quat::length() const {
+
+ return Math::sqrt(length_squared());
+}
+
+void Quat::normalize() {
+ *this /= length();
+}
+
+
+Quat Quat::normalized() const {
+ return *this / length();
+}
+
+Quat Quat::inverse() const {
+ return Quat( -x, -y, -z, w );
+}
+
+
+Quat Quat::slerp(const Quat& q, const real_t& t) const {
+
+#if 0
+
+
+ Quat dst=q;
+ Quat src=*this;
+
+ src.normalize();
+ dst.normalize();
+
+ real_t cosine = dst.dot(src);
+
+ if (cosine < 0 && true) {
+ cosine = -cosine;
+ dst = -dst;
+ } else {
+ dst = dst;
+ }
+
+ if (Math::abs(cosine) < 1 - CMP_EPSILON) {
+ // Standard case (slerp)
+ real_t sine = Math::sqrt(1 - cosine*cosine);
+ real_t angle = Math::atan2(sine, cosine);
+ real_t inv_sine = 1.0f / sine;
+ real_t coeff_0 = Math::sin((1.0f - t) * angle) * inv_sine;
+ real_t coeff_1 = Math::sin(t * angle) * inv_sine;
+ Quat ret= src * coeff_0 + dst * coeff_1;
+
+ return ret;
+ } else {
+ // There are two situations:
+ // 1. "rkP" and "q" are very close (cosine ~= +1), so we can do a linear
+ // interpolation safely.
+ // 2. "rkP" and "q" are almost invedste of each other (cosine ~= -1), there
+ // are an infinite number of possibilities interpolation. but we haven't
+ // have method to fix this case, so just use linear interpolation here.
+ Quat ret = src * (1.0f - t) + dst *t;
+ // taking the complement requires renormalisation
+ ret.normalize();
+ return ret;
+ }
+#else
+
+ real_t to1[4];
+ real_t omega, cosom, sinom, scale0, scale1;
+
+
+ // calc cosine
+ cosom = x * q.x + y * q.y + z * q.z
+ + w * q.w;
+
+
+ // adjust signs (if necessary)
+ if ( cosom <0.0 ) {
+ cosom = -cosom; to1[0] = - q.x;
+ to1[1] = - q.y;
+ to1[2] = - q.z;
+ to1[3] = - q.w;
+ } else {
+ to1[0] = q.x;
+ to1[1] = q.y;
+ to1[2] = q.z;
+ to1[3] = q.w;
+ }
+
+
+ // calculate coefficients
+
+ if ( (1.0 - cosom) > CMP_EPSILON ) {
+ // standard case (slerp)
+ omega = Math::acos(cosom);
+ sinom = Math::sin(omega);
+ scale0 = Math::sin((1.0 - t) * omega) / sinom;
+ scale1 = Math::sin(t * omega) / sinom;
+ } else {
+ // "from" and "to" quaternions are very close
+ // ... so we can do a linear interpolation
+ scale0 = 1.0 - t;
+ scale1 = t;
+ }
+ // calculate final values
+ return Quat(
+ scale0 * x + scale1 * to1[0],
+ scale0 * y + scale1 * to1[1],
+ scale0 * z + scale1 * to1[2],
+ scale0 * w + scale1 * to1[3]
+ );
+#endif
+}
+
+Quat Quat::slerpni(const Quat& q, const real_t& t) const {
+
+ const Quat &from = *this;
+
+ float dot = from.dot(q);
+
+ if (Math::absf(dot) > 0.9999f) return from;
+
+ float theta = Math::acos(dot),
+ sinT = 1.0f / Math::sin(theta),
+ newFactor = Math::sin(t * theta) * sinT,
+ invFactor = Math::sin((1.0f - t) * theta) * sinT;
+
+ return Quat( invFactor * from.x + newFactor * q.x,
+ invFactor * from.y + newFactor * q.y,
+ invFactor * from.z + newFactor * q.z,
+ invFactor * from.w + newFactor * q.w );
+
+#if 0
+ real_t to1[4];
+ real_t omega, cosom, sinom, scale0, scale1;
+
+
+ // calc cosine
+ cosom = x * q.x + y * q.y + z * q.z
+ + w * q.w;
+
+
+ // adjust signs (if necessary)
+ if ( cosom <0.0 && false) {
+ cosom = -cosom; to1[0] = - q.x;
+ to1[1] = - q.y;
+ to1[2] = - q.z;
+ to1[3] = - q.w;
+ } else {
+ to1[0] = q.x;
+ to1[1] = q.y;
+ to1[2] = q.z;
+ to1[3] = q.w;
+ }
+
+
+ // calculate coefficients
+
+ if ( (1.0 - cosom) > CMP_EPSILON ) {
+ // standard case (slerp)
+ omega = Math::acos(cosom);
+ sinom = Math::sin(omega);
+ scale0 = Math::sin((1.0 - t) * omega) / sinom;
+ scale1 = Math::sin(t * omega) / sinom;
+ } else {
+ // "from" and "to" quaternions are very close
+ // ... so we can do a linear interpolation
+ scale0 = 1.0 - t;
+ scale1 = t;
+ }
+ // calculate final values
+ return Quat(
+ scale0 * x + scale1 * to1[0],
+ scale0 * y + scale1 * to1[1],
+ scale0 * z + scale1 * to1[2],
+ scale0 * w + scale1 * to1[3]
+ );
+#endif
+}
+
+Quat Quat::cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const {
+
+ //the only way to do slerp :|
+ float t2 = (1.0-t)*t*2;
+ Quat sp = this->slerp(q,t);
+ Quat sq = prep.slerpni(postq,t);
+ return sp.slerpni(sq,t2);
+
+}
+
+
+Quat::operator String() const {
+
+ return String::num(x)+","+String::num(y)+","+ String::num(z)+","+ String::num(w);
+}
+
+Quat::Quat(const Vector3& axis, const real_t& angle) {
+ real_t d = axis.length();
+ if (d==0)
+ set(0,0,0,0);
+ else {
+ real_t s = Math::sin(-angle * 0.5) / d;
+ set(axis.x * s, axis.y * s, axis.z * s,
+ Math::cos(-angle * 0.5));
+ }
+}
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