0be6d925dc
Which means that reduz' beloved style which we all became used to will now be changed automatically to remove the first empty line. This makes us lean closer to 1TBS (the one true brace style) instead of hybridating it with some Allman-inspired spacing. There's still the case of braces around single-statement blocks that needs to be addressed (but clang-format can't help with that, but clang-tidy may if we agree about it). Part of #33027.
250 lines
8.9 KiB
C++
250 lines
8.9 KiB
C++
/*************************************************************************/
|
|
/* quat.cpp */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* https://godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
|
|
/* Copyright (c) 2014-2020 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 "quat.h"
|
|
|
|
#include "core/math/basis.h"
|
|
#include "core/print_string.h"
|
|
|
|
// set_euler_xyz 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 XYZ convention (Z is the first rotation).
|
|
void Quat::set_euler_xyz(const Vector3 &p_euler) {
|
|
real_t half_a1 = p_euler.x * 0.5;
|
|
real_t half_a2 = p_euler.y * 0.5;
|
|
real_t half_a3 = p_euler.z * 0.5;
|
|
|
|
// R = X(a1).Y(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-2)
|
|
// 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);
|
|
|
|
set(sin_a1 * cos_a2 * cos_a3 + sin_a2 * sin_a3 * cos_a1,
|
|
-sin_a1 * sin_a3 * cos_a2 + sin_a2 * cos_a1 * cos_a3,
|
|
sin_a1 * sin_a2 * cos_a3 + sin_a3 * cos_a1 * cos_a2,
|
|
-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
|
|
}
|
|
|
|
// 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 Quat::get_euler_xyz() const {
|
|
Basis m(*this);
|
|
return m.get_euler_xyz();
|
|
}
|
|
|
|
// set_euler_yxz 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).
|
|
void Quat::set_euler_yxz(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);
|
|
|
|
set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
|
|
sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
|
|
-sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3,
|
|
sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
|
|
}
|
|
|
|
// 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 Quat::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 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;
|
|
}
|
|
|
|
bool Quat::is_equal_approx(const Quat &p_quat) const {
|
|
return Math::is_equal_approx(x, p_quat.x) && Math::is_equal_approx(y, p_quat.y) && Math::is_equal_approx(z, p_quat.z) && Math::is_equal_approx(w, p_quat.w);
|
|
}
|
|
|
|
real_t Quat::length() const {
|
|
return Math::sqrt(length_squared());
|
|
}
|
|
|
|
void Quat::normalize() {
|
|
*this /= length();
|
|
}
|
|
|
|
Quat Quat::normalized() const {
|
|
return *this / length();
|
|
}
|
|
|
|
bool Quat::is_normalized() const {
|
|
return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon
|
|
}
|
|
|
|
Quat Quat::inverse() const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The quaternion must be normalized.");
|
|
#endif
|
|
return Quat(-x, -y, -z, w);
|
|
}
|
|
|
|
Quat Quat::slerp(const Quat &q, const real_t &t) const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
|
|
#endif
|
|
Quat to1;
|
|
real_t omega, cosom, sinom, scale0, scale1;
|
|
|
|
// calc cosine
|
|
cosom = dot(q);
|
|
|
|
// adjust signs (if necessary)
|
|
if (cosom < 0.0) {
|
|
cosom = -cosom;
|
|
to1.x = -q.x;
|
|
to1.y = -q.y;
|
|
to1.z = -q.z;
|
|
to1.w = -q.w;
|
|
} else {
|
|
to1.x = q.x;
|
|
to1.y = q.y;
|
|
to1.z = q.z;
|
|
to1.w = 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.x,
|
|
scale0 * y + scale1 * to1.y,
|
|
scale0 * z + scale1 * to1.z,
|
|
scale0 * w + scale1 * to1.w);
|
|
}
|
|
|
|
Quat Quat::slerpni(const Quat &q, const real_t &t) const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
|
|
#endif
|
|
const Quat &from = *this;
|
|
|
|
real_t dot = from.dot(q);
|
|
|
|
if (Math::absf(dot) > 0.9999)
|
|
return from;
|
|
|
|
real_t theta = Math::acos(dot),
|
|
sinT = 1.0 / Math::sin(theta),
|
|
newFactor = Math::sin(t * theta) * sinT,
|
|
invFactor = Math::sin((1.0 - 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);
|
|
}
|
|
|
|
Quat Quat::cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
|
|
#endif
|
|
//the only way to do slerp :|
|
|
real_t 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);
|
|
}
|
|
|
|
void Quat::set_axis_angle(const Vector3 &axis, const real_t &angle) {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_MSG(!axis.is_normalized(), "The axis Vector3 must be normalized.");
|
|
#endif
|
|
real_t d = axis.length();
|
|
if (d == 0)
|
|
set(0, 0, 0, 0);
|
|
else {
|
|
real_t sin_angle = Math::sin(angle * 0.5);
|
|
real_t cos_angle = Math::cos(angle * 0.5);
|
|
real_t s = sin_angle / d;
|
|
set(axis.x * s, axis.y * s, axis.z * s,
|
|
cos_angle);
|
|
}
|
|
}
|