/*************************************************************************/
/* quat.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2017 Godot Engine contributors (cf. AUTHORS.md) */
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/* The above copyright notice and this permission notice shall be */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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#include "quat.h"
#include "matrix3.h"
#include "print_string.h"
// set_euler expects a vector containing the Euler angles in the format
// (c,b,a), where a is the angle of the first rotation, and c is the last.
// The current implementation uses XYZ convention (Z is the first rotation).
void Quat::set_euler(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 returns a vector containing the Euler angles in the format
// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last.
// The current implementation uses XYZ convention (Z is the first rotation).
Vector3 Quat::get_euler() const {
Basis m(*this);
return m.get_euler();
}
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();
}
bool Quat::is_normalized() const {
return Math::is_equal_approx(length(), 1.0);
}
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 = 1.0 / sine;
real_t coeff_0 = Math::sin((1.0 - 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 * (1.0 - t) + dst *t;
// taking the complement requires renormalisation
ret.normalize();
return ret;
}
#else
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);
#endif
}
Quat Quat::slerpni(const Quat &q, const real_t &t) const {
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);
#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 :|
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);
}
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 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);
}
}