godot-cpp/include/godot_cpp/core/Quat.cpp

278 lines
5.3 KiB
C++

#include "Quat.h"
#include <cmath>
#include "Defs.h"
#include "Vector3.h"
#include "Basis.h"
namespace godot {
real_t Quat::length() const
{
return ::sqrt(length_squared());
}
void Quat::normalize()
{
*this /= length();
}
Quat Quat::normalized() const
{
return *this / length();
}
Quat Quat::inverse() const
{
return Quat( -x, -y, -z, w );
}
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 = ::cos(half_a1);
real_t sin_a1 = ::sin(half_a1);
real_t cos_a2 = ::cos(half_a2);
real_t sin_a2 = ::sin(half_a2);
real_t cos_a3 = ::cos(half_a3);
real_t sin_a3 = ::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);
}
Quat Quat::slerp(const Quat& q, const real_t& t) const {
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 = ::acos(cosom);
sinom = ::sin(omega);
scale0 = ::sin((1.0 - t) * omega) / sinom;
scale1 = ::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 {
const Quat &from = *this;
real_t dot = from.dot(q);
if (::fabs(dot) > 0.9999) return from;
real_t theta = ::acos(dot),
sinT = 1.0 / ::sin(theta),
newFactor = ::sin(t * theta) * sinT,
invFactor = ::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
{
//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);
}
void Quat::get_axis_and_angle(Vector3& r_axis, real_t &r_angle) const {
r_angle = 2 * ::acos(w);
r_axis.x = x / ::sqrt(1-w*w);
r_axis.y = y / ::sqrt(1-w*w);
r_axis.z = z / ::sqrt(1-w*w);
}
Quat Quat::operator*(const Vector3& v) const
{
return Quat( w * v.x + y * v.z - z * v.y,
w * v.y + z * v.x - x * v.z,
w * v.z + x * v.y - y * v.x,
-x * v.x - y * v.y - z * v.z);
}
Vector3 Quat::xform(const Vector3& v) const {
Quat q = *this * v;
q *= this->inverse();
return Vector3(q.x,q.y,q.z);
}
Quat::operator String() const
{
return String(); // @Todo
}
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 = ::sin(angle * 0.5);
real_t cos_angle = ::cos(angle * 0.5);
real_t s = sin_angle / d;
set(axis.x * s, axis.y * s, axis.z * s,
cos_angle);
}
}
Quat::Quat(const Vector3& v0, const Vector3& v1) // shortest arc
{
Vector3 c = v0.cross(v1);
real_t d = v0.dot(v1);
if (d < -1.0 + CMP_EPSILON) {
x=0;
y=1;
z=0;
w=0;
} else {
real_t s = ::sqrt((1.0 + d) * 2.0);
real_t rs = 1.0 / s;
x=c.x*rs;
y=c.y*rs;
z=c.z*rs;
w=s * 0.5;
}
}
real_t Quat::dot(const Quat& q) const {
return x * q.x+y * q.y+z * q.z+w * q.w;
}
real_t Quat::length_squared() const {
return dot(*this);
}
void Quat::operator+=(const Quat& q) {
x += q.x; y += q.y; z += q.z; w += q.w;
}
void Quat::operator-=(const Quat& q) {
x -= q.x; y -= q.y; z -= q.z; w -= q.w;
}
void Quat::operator*=(const Quat& q) {
x *= q.x; y *= q.y; z *= q.z; w *= q.w;
}
void Quat::operator*=(const real_t& s) {
x *= s; y *= s; z *= s; w *= s;
}
void Quat::operator/=(const real_t& s) {
*this *= 1.0 / s;
}
Quat Quat::operator+(const Quat& q2) const {
const Quat& q1 = *this;
return Quat( q1.x+q2.x, q1.y+q2.y, q1.z+q2.z, q1.w+q2.w );
}
Quat Quat::operator-(const Quat& q2) const {
const Quat& q1 = *this;
return Quat( q1.x-q2.x, q1.y-q2.y, q1.z-q2.z, q1.w-q2.w);
}
Quat Quat::operator*(const Quat& q2) const {
Quat q1 = *this;
q1 *= q2;
return q1;
}
Quat Quat::operator-() const {
const Quat& q2 = *this;
return Quat( -q2.x, -q2.y, -q2.z, -q2.w);
}
Quat Quat::operator*(const real_t& s) const {
return Quat(x * s, y * s, z * s, w * s);
}
Quat Quat::operator/(const real_t& s) const {
return *this * (1.0 / s);
}
bool Quat::operator==(const Quat& p_quat) const {
return x==p_quat.x && y==p_quat.y && z==p_quat.z && w==p_quat.w;
}
bool Quat::operator!=(const Quat& p_quat) const {
return x!=p_quat.x || y!=p_quat.y || z!=p_quat.z || w!=p_quat.w;
}
Vector3 Quat::get_euler() const
{
Basis m(*this);
return m.get_euler();
}
}