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godot/core/math/quaternion.cpp

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/*************************************************************************/
/* quaternion.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* 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 "quaternion.h"
#include "core/math/basis.h"
#include "core/string/print_string.h"
// get_euler_xyz returns a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses XYZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_xyz() const {
Basis m(*this);
return m.get_euler_xyz();
}
// get_euler_yxz returns a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_yxz() const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
#endif
Basis m(*this);
return m.get_euler_yxz();
}
void Quaternion::operator*=(const Quaternion &p_q) {
real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
x = xx;
y = yy;
z = zz;
}
Quaternion Quaternion::operator*(const Quaternion &p_q) const {
Quaternion r = *this;
r *= p_q;
return r;
}
bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
return Math::is_equal_approx(x, p_quaternion.x) && Math::is_equal_approx(y, p_quaternion.y) && Math::is_equal_approx(z, p_quaternion.z) && Math::is_equal_approx(w, p_quaternion.w);
}
real_t Quaternion::length() const {
return Math::sqrt(length_squared());
}
void Quaternion::normalize() {
*this /= length();
}
Quaternion Quaternion::normalized() const {
return *this / length();
}
bool Quaternion::is_normalized() const {
return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); //use less epsilon
}
Quaternion Quaternion::inverse() const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
#endif
return Quaternion(-x, -y, -z, w);
}
Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
Quaternion to1;
real_t omega, cosom, sinom, scale0, scale1;
// calc cosine
cosom = dot(p_to);
// adjust signs (if necessary)
if (cosom < 0.0) {
cosom = -cosom;
to1.x = -p_to.x;
to1.y = -p_to.y;
to1.z = -p_to.z;
to1.w = -p_to.w;
} else {
to1.x = p_to.x;
to1.y = p_to.y;
to1.z = p_to.z;
to1.w = p_to.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 - p_weight) * omega) / sinom;
scale1 = Math::sin(p_weight * omega) / sinom;
} else {
// "from" and "to" quaternions are very close
// ... so we can do a linear interpolation
scale0 = 1.0 - p_weight;
scale1 = p_weight;
}
// calculate final values
return Quaternion(
scale0 * x + scale1 * to1.x,
scale0 * y + scale1 * to1.y,
scale0 * z + scale1 * to1.z,
scale0 * w + scale1 * to1.w);
}
Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
const Quaternion &from = *this;
real_t dot = from.dot(p_to);
if (Math::absf(dot) > 0.9999) {
return from;
}
real_t theta = Math::acos(dot),
sinT = 1.0 / Math::sin(theta),
newFactor = Math::sin(p_weight * theta) * sinT,
invFactor = Math::sin((1.0 - p_weight) * theta) * sinT;
return Quaternion(invFactor * from.x + newFactor * p_to.x,
invFactor * from.y + newFactor * p_to.y,
invFactor * from.z + newFactor * p_to.z,
invFactor * from.w + newFactor * p_to.w);
}
Quaternion Quaternion::cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
//the only way to do slerp :|
real_t t2 = (1.0 - p_weight) * p_weight * 2;
Quaternion sp = this->slerp(p_b, p_weight);
Quaternion sq = p_pre_a.slerpni(p_post_b, p_weight);
return sp.slerpni(sq, t2);
}
Quaternion::operator String() const {
return String::num(x) + ", " + String::num(y) + ", " + String::num(z) + ", " + String::num(w);
}
Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
#ifdef MATH_CHECKS
ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
#endif
real_t d = p_axis.length();
if (d == 0) {
x = 0;
y = 0;
z = 0;
w = 0;
} else {
real_t sin_angle = Math::sin(p_angle * 0.5);
real_t cos_angle = Math::cos(p_angle * 0.5);
real_t s = sin_angle / d;
x = p_axis.x * s;
y = p_axis.y * s;
z = p_axis.z * s;
w = cos_angle;
}
}
// Euler constructor expects a vector containing the Euler angles in the format
// (ax, ay, az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
Quaternion::Quaternion(const Vector3 &p_euler) {
real_t half_a1 = p_euler.y * 0.5;
real_t half_a2 = p_euler.x * 0.5;
real_t half_a3 = p_euler.z * 0.5;
// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
// a3 is the angle of the first rotation, following the notation in this reference.
real_t cos_a1 = Math::cos(half_a1);
real_t sin_a1 = Math::sin(half_a1);
real_t cos_a2 = Math::cos(half_a2);
real_t sin_a2 = Math::sin(half_a2);
real_t cos_a3 = Math::cos(half_a3);
real_t sin_a3 = Math::sin(half_a3);
x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
z = -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3;
w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
}
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