godot/core/math/quat.cpp

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/*  quat.cpp                                                             */
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#include "quat.h"

#include "core/math/basis.h"
#include "core/print_string.h"

real_t Quat::angle_to(const Quat &p_to) const {
	real_t d = dot(p_to);
	return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
}

// 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 * 0.5f;
	real_t half_a2 = p_euler.y * 0.5f;
	real_t half_a3 = p_euler.z * 0.5f;

	// 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 * 0.5f;
	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);

	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 &p_q) {
	set(w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y,
			w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z,
			w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x,
			w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z);
}

Quat Quat::operator*(const Quat &p_q) const {
	Quat r = *this;
	r *= p_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, (real_t)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 &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
	ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
	ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");
#endif
	Quat to1;
	real_t omega, cosom, sinom, scale0, scale1;

	// calc cosine
	cosom = dot(p_to);

	// adjust signs (if necessary)
	if (cosom < 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 - cosom) > (real_t)CMP_EPSILON) {
		// standard case (slerp)
		omega = Math::acos(cosom);
		sinom = Math::sin(omega);
		scale0 = Math::sin((1 - 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 - p_weight;
		scale1 = p_weight;
	}
	// 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 &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
	ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
	ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");
#endif
	const Quat &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 / Math::sin(theta),
		   newFactor = Math::sin(p_weight * theta) * sinT,
		   invFactor = Math::sin((1 - p_weight) * theta) * sinT;

	return Quat(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);
}

Quat Quat::cubic_slerp(const Quat &p_b, const Quat &p_pre_a, const Quat &p_post_b, const real_t &p_weight) const {
#ifdef MATH_CHECKS
	ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
	ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quat(), "The end quaternion must be normalized.");
#endif
	//the only way to do slerp :|
	real_t t2 = (1 - p_weight) * p_weight * 2;
	Quat sp = this->slerp(p_b, p_weight);
	Quat sq = p_pre_a.slerpni(p_post_b, p_weight);
	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 * 0.5f);
		real_t cos_angle = Math::cos(angle * 0.5f);
		real_t s = sin_angle / d;
		set(axis.x * s, axis.y * s, axis.z * s,
				cos_angle);
	}
}