341 lines
13 KiB
C++
341 lines
13 KiB
C++
/**************************************************************************/
|
|
/* quaternion.cpp */
|
|
/**************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* https://godotengine.org */
|
|
/**************************************************************************/
|
|
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
|
|
/* 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 "quaternion.h"
|
|
|
|
#include "core/math/basis.h"
|
|
#include "core/string/ustring.h"
|
|
|
|
real_t Quaternion::angle_to(const Quaternion &p_to) const {
|
|
real_t d = dot(p_to);
|
|
// acos does clamping.
|
|
return Math::acos(d * d * 2 - 1);
|
|
}
|
|
|
|
Vector3 Quaternion::get_euler(EulerOrder p_order) const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion " + operator String() + " must be normalized.");
|
|
#endif
|
|
return Basis(*this).get_euler(p_order);
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
bool Quaternion::is_finite() const {
|
|
return Math::is_finite(x) && Math::is_finite(y) && Math::is_finite(z) && Math::is_finite(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 " + operator String() + " must be normalized.");
|
|
#endif
|
|
return Quaternion(-x, -y, -z, w);
|
|
}
|
|
|
|
Quaternion Quaternion::log() const {
|
|
Quaternion src = *this;
|
|
Vector3 src_v = src.get_axis() * src.get_angle();
|
|
return Quaternion(src_v.x, src_v.y, src_v.z, 0);
|
|
}
|
|
|
|
Quaternion Quaternion::exp() const {
|
|
Quaternion src = *this;
|
|
Vector3 src_v = Vector3(src.x, src.y, src.z);
|
|
real_t theta = src_v.length();
|
|
src_v = src_v.normalized();
|
|
if (theta < CMP_EPSILON || !src_v.is_normalized()) {
|
|
return Quaternion(0, 0, 0, 1);
|
|
}
|
|
return Quaternion(src_v, theta);
|
|
}
|
|
|
|
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 " + operator String() + " must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion " + p_to.operator String() + " 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 < 0.0f) {
|
|
cosom = -cosom;
|
|
to1 = -p_to;
|
|
} else {
|
|
to1 = p_to;
|
|
}
|
|
|
|
// calculate coefficients
|
|
|
|
if ((1.0f - cosom) > (real_t)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 = 1.0f - 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 " + operator String() + " must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion " + p_to.operator String() + " must be normalized.");
|
|
#endif
|
|
const Quaternion &from = *this;
|
|
|
|
real_t dot = from.dot(p_to);
|
|
|
|
if (Math::absf(dot) > 0.9999f) {
|
|
return from;
|
|
}
|
|
|
|
real_t theta = Math::acos(dot),
|
|
sinT = 1.0f / Math::sin(theta),
|
|
newFactor = Math::sin(p_weight * theta) * sinT,
|
|
invFactor = Math::sin((1.0f - 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::spherical_cubic_interpolate(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 " + operator String() + " must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion " + p_b.operator String() + " must be normalized.");
|
|
#endif
|
|
Quaternion from_q = *this;
|
|
Quaternion pre_q = p_pre_a;
|
|
Quaternion to_q = p_b;
|
|
Quaternion post_q = p_post_b;
|
|
|
|
// Align flip phases.
|
|
from_q = Basis(from_q).get_rotation_quaternion();
|
|
pre_q = Basis(pre_q).get_rotation_quaternion();
|
|
to_q = Basis(to_q).get_rotation_quaternion();
|
|
post_q = Basis(post_q).get_rotation_quaternion();
|
|
|
|
// Flip quaternions to shortest path if necessary.
|
|
bool flip1 = signbit(from_q.dot(pre_q));
|
|
pre_q = flip1 ? -pre_q : pre_q;
|
|
bool flip2 = signbit(from_q.dot(to_q));
|
|
to_q = flip2 ? -to_q : to_q;
|
|
bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
|
|
post_q = flip3 ? -post_q : post_q;
|
|
|
|
// Calc by Expmap in from_q space.
|
|
Quaternion ln_from = Quaternion(0, 0, 0, 0);
|
|
Quaternion ln_to = (from_q.inverse() * to_q).log();
|
|
Quaternion ln_pre = (from_q.inverse() * pre_q).log();
|
|
Quaternion ln_post = (from_q.inverse() * post_q).log();
|
|
Quaternion ln = Quaternion(0, 0, 0, 0);
|
|
ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
|
|
ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
|
|
ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
|
|
Quaternion q1 = from_q * ln.exp();
|
|
|
|
// Calc by Expmap in to_q space.
|
|
ln_from = (to_q.inverse() * from_q).log();
|
|
ln_to = Quaternion(0, 0, 0, 0);
|
|
ln_pre = (to_q.inverse() * pre_q).log();
|
|
ln_post = (to_q.inverse() * post_q).log();
|
|
ln = Quaternion(0, 0, 0, 0);
|
|
ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
|
|
ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
|
|
ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
|
|
Quaternion q2 = to_q * ln.exp();
|
|
|
|
// To cancel error made by Expmap ambiguity, do blending.
|
|
return q1.slerp(q2, p_weight);
|
|
}
|
|
|
|
Quaternion Quaternion::spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight,
|
|
const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion " + operator String() + " must be normalized.");
|
|
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion " + p_b.operator String() + " must be normalized.");
|
|
#endif
|
|
Quaternion from_q = *this;
|
|
Quaternion pre_q = p_pre_a;
|
|
Quaternion to_q = p_b;
|
|
Quaternion post_q = p_post_b;
|
|
|
|
// Align flip phases.
|
|
from_q = Basis(from_q).get_rotation_quaternion();
|
|
pre_q = Basis(pre_q).get_rotation_quaternion();
|
|
to_q = Basis(to_q).get_rotation_quaternion();
|
|
post_q = Basis(post_q).get_rotation_quaternion();
|
|
|
|
// Flip quaternions to shortest path if necessary.
|
|
bool flip1 = signbit(from_q.dot(pre_q));
|
|
pre_q = flip1 ? -pre_q : pre_q;
|
|
bool flip2 = signbit(from_q.dot(to_q));
|
|
to_q = flip2 ? -to_q : to_q;
|
|
bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
|
|
post_q = flip3 ? -post_q : post_q;
|
|
|
|
// Calc by Expmap in from_q space.
|
|
Quaternion ln_from = Quaternion(0, 0, 0, 0);
|
|
Quaternion ln_to = (from_q.inverse() * to_q).log();
|
|
Quaternion ln_pre = (from_q.inverse() * pre_q).log();
|
|
Quaternion ln_post = (from_q.inverse() * post_q).log();
|
|
Quaternion ln = Quaternion(0, 0, 0, 0);
|
|
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
Quaternion q1 = from_q * ln.exp();
|
|
|
|
// Calc by Expmap in to_q space.
|
|
ln_from = (to_q.inverse() * from_q).log();
|
|
ln_to = Quaternion(0, 0, 0, 0);
|
|
ln_pre = (to_q.inverse() * pre_q).log();
|
|
ln_post = (to_q.inverse() * post_q).log();
|
|
ln = Quaternion(0, 0, 0, 0);
|
|
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
|
|
Quaternion q2 = to_q * ln.exp();
|
|
|
|
// To cancel error made by Expmap ambiguity, do blending.
|
|
return q1.slerp(q2, p_weight);
|
|
}
|
|
|
|
Quaternion::operator String() const {
|
|
return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
|
|
}
|
|
|
|
Vector3 Quaternion::get_axis() const {
|
|
if (Math::abs(w) > 1 - CMP_EPSILON) {
|
|
return Vector3(x, y, z);
|
|
}
|
|
real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
|
|
return Vector3(x * r, y * r, z * r);
|
|
}
|
|
|
|
real_t Quaternion::get_angle() const {
|
|
return 2 * Math::acos(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 " + p_axis.operator String() + " 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 * 0.5f);
|
|
real_t cos_angle = Math::cos(p_angle * 0.5f);
|
|
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::from_euler(const Vector3 &p_euler) {
|
|
real_t half_a1 = p_euler.y * 0.5f;
|
|
real_t half_a2 = p_euler.x * 0.5f;
|
|
real_t half_a3 = p_euler.z * 0.5f;
|
|
|
|
// 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);
|
|
|
|
return Quaternion(
|
|
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);
|
|
}
|