324 lines
6.4 KiB
C++
324 lines
6.4 KiB
C++
#ifndef QUAT_H
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#define QUAT_H
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#include <cmath>
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#include "Vector3.h"
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// #include "Basis.h"
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namespace godot {
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#define CMP_EPSILON 0.00001
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typedef float real_t;
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class Quat{
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public:
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real_t x,y,z,w;
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real_t length_squared() const; // down below
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real_t length() const
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{
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return ::sqrt(length_squared());
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}
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void normalize()
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{
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*this /= length();
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}
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Quat normalized() const
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{
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return *this / length();
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}
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Quat inverse() const
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{
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return Quat( -x, -y, -z, w );
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}
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real_t dot(const Quat& q) const; // down below
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void set_euler(const Vector3& p_euler)
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{
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real_t half_a1 = p_euler.x * 0.5;
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real_t half_a2 = p_euler.y * 0.5;
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real_t half_a3 = p_euler.z * 0.5;
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// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = ::cos(half_a1);
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real_t sin_a1 = ::sin(half_a1);
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real_t cos_a2 = ::cos(half_a2);
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real_t sin_a2 = ::sin(half_a2);
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real_t cos_a3 = ::cos(half_a3);
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real_t sin_a3 = ::sin(half_a3);
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set(sin_a1*cos_a2*cos_a3 + sin_a2*sin_a3*cos_a1,
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-sin_a1*sin_a3*cos_a2 + sin_a2*cos_a1*cos_a3,
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sin_a1*sin_a2*cos_a3 + sin_a3*cos_a1*cos_a2,
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-sin_a1*sin_a2*sin_a3 + cos_a1*cos_a2*cos_a3);
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}
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Vector3 get_euler() const; // down below
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Quat slerp(const Quat& q, const real_t& t) const {
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Quat to1;
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real_t omega, cosom, sinom, scale0, scale1;
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// calc cosine
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cosom = dot(q);
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// adjust signs (if necessary)
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if ( cosom <0.0 ) {
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cosom = -cosom;
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to1.x = - q.x;
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to1.y = - q.y;
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to1.z = - q.z;
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to1.w = - q.w;
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} else {
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to1.x = q.x;
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to1.y = q.y;
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to1.z = q.z;
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to1.w = q.w;
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}
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// calculate coefficients
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if ( (1.0 - cosom) > CMP_EPSILON ) {
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// standard case (slerp)
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omega = ::acos(cosom);
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sinom = ::sin(omega);
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scale0 = ::sin((1.0 - t) * omega) / sinom;
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scale1 = ::sin(t * omega) / sinom;
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} else {
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// "from" and "to" quaternions are very close
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// ... so we can do a linear interpolation
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scale0 = 1.0 - t;
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scale1 = t;
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}
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// calculate final values
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return Quat(
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scale0 * x + scale1 * to1.x,
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scale0 * y + scale1 * to1.y,
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scale0 * z + scale1 * to1.z,
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scale0 * w + scale1 * to1.w
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);
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}
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Quat slerpni(const Quat& q, const real_t& t) const {
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const Quat &from = *this;
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real_t dot = from.dot(q);
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if (::fabs(dot) > 0.9999) return from;
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real_t theta = ::acos(dot),
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sinT = 1.0 / ::sin(theta),
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newFactor = ::sin(t * theta) * sinT,
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invFactor = ::sin((1.0 - t) * theta) * sinT;
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return Quat(invFactor * from.x + newFactor * q.x,
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invFactor * from.y + newFactor * q.y,
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invFactor * from.z + newFactor * q.z,
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invFactor * from.w + newFactor * q.w);
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}
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Quat cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const
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{
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//the only way to do slerp :|
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real_t t2 = (1.0-t)*t*2;
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Quat sp = this->slerp(q,t);
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Quat sq = prep.slerpni(postq,t);
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return sp.slerpni(sq,t2);
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}
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void get_axis_and_angle(Vector3& r_axis, real_t &r_angle) const {
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r_angle = 2 * ::acos(w);
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r_axis.x = x / ::sqrt(1-w*w);
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r_axis.y = y / ::sqrt(1-w*w);
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r_axis.z = z / ::sqrt(1-w*w);
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}
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void operator*=(const Quat& q); // down below
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Quat operator*(const Quat& q) const; // down below
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Quat operator*(const Vector3& v) const
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{
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return Quat( w * v.x + y * v.z - z * v.y,
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w * v.y + z * v.x - x * v.z,
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w * v.z + x * v.y - y * v.x,
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-x * v.x - y * v.y - z * v.z);
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}
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Vector3 xform(const Vector3& v) const {
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Quat q = *this * v;
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q *= this->inverse();
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return Vector3(q.x,q.y,q.z);
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}
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// everything's down
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void operator+=(const Quat& q);
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void operator-=(const Quat& q);
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void operator*=(const real_t& s);
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void operator/=(const real_t& s);
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Quat operator+(const Quat& q2) const;
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Quat operator-(const Quat& q2) const;
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Quat operator-() const;
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Quat operator*(const real_t& s) const;
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Quat operator/(const real_t& s) const;
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bool operator==(const Quat& p_quat) const;
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bool operator!=(const Quat& p_quat) const;
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operator String() const
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{
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return String(); // @Todo
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}
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inline void set( real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
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x=p_x; y=p_y; z=p_z; w=p_w;
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}
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inline Quat(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
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x=p_x; y=p_y; z=p_z; w=p_w;
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}
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Quat(const Vector3& axis, const real_t& angle)
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{
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real_t d = axis.length();
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if (d==0)
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set(0,0,0,0);
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else {
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real_t sin_angle = ::sin(angle * 0.5);
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real_t cos_angle = ::cos(angle * 0.5);
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real_t s = sin_angle / d;
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set(axis.x * s, axis.y * s, axis.z * s,
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cos_angle);
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}
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}
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Quat(const Vector3& v0, const Vector3& v1) // shortest arc
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{
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Vector3 c = v0.cross(v1);
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real_t d = v0.dot(v1);
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if (d < -1.0 + CMP_EPSILON) {
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x=0;
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y=1;
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z=0;
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w=0;
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} else {
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real_t s = ::sqrt((1.0 + d) * 2.0);
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real_t rs = 1.0 / s;
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x=c.x*rs;
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y=c.y*rs;
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z=c.z*rs;
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w=s * 0.5;
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}
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}
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Quat() {x=y=z=0; w=1; }
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};
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real_t Quat::dot(const Quat& q) const {
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return x * q.x+y * q.y+z * q.z+w * q.w;
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}
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real_t Quat::length_squared() const {
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return dot(*this);
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}
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void Quat::operator+=(const Quat& q) {
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x += q.x; y += q.y; z += q.z; w += q.w;
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}
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void Quat::operator-=(const Quat& q) {
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x -= q.x; y -= q.y; z -= q.z; w -= q.w;
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}
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void Quat::operator*=(const Quat& q) {
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x *= q.x; y *= q.y; z *= q.z; w *= q.w;
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}
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void Quat::operator*=(const real_t& s) {
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x *= s; y *= s; z *= s; w *= s;
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}
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void Quat::operator/=(const real_t& s) {
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*this *= 1.0 / s;
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}
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Quat Quat::operator+(const Quat& q2) const {
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const Quat& q1 = *this;
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return Quat( q1.x+q2.x, q1.y+q2.y, q1.z+q2.z, q1.w+q2.w );
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}
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Quat Quat::operator-(const Quat& q2) const {
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const Quat& q1 = *this;
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return Quat( q1.x-q2.x, q1.y-q2.y, q1.z-q2.z, q1.w-q2.w);
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}
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Quat Quat::operator*(const Quat& q2) const {
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Quat q1 = *this;
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q1 *= q2;
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return q1;
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}
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Quat Quat::operator-() const {
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const Quat& q2 = *this;
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return Quat( -q2.x, -q2.y, -q2.z, -q2.w);
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}
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Quat Quat::operator*(const real_t& s) const {
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return Quat(x * s, y * s, z * s, w * s);
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}
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Quat Quat::operator/(const real_t& s) const {
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return *this * (1.0 / s);
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}
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bool Quat::operator==(const Quat& p_quat) const {
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return x==p_quat.x && y==p_quat.y && z==p_quat.z && w==p_quat.w;
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}
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bool Quat::operator!=(const Quat& p_quat) const {
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return x!=p_quat.x || y!=p_quat.y || z!=p_quat.z || w!=p_quat.w;
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}
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}
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#include "Basis.h"
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namespace godot {
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Vector3 Quat::get_euler() const
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{
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Basis m(*this);
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return m.get_euler();
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}
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}
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#endif // QUAT_H
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