268 lines
7.3 KiB
C++
268 lines
7.3 KiB
C++
/*************************************************************************/
|
|
/* quat.cpp */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* http://www.godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2015 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));
|
|
}
|
|
}
|