godot-cpp/include/godot/core/Basis.h

#ifndef BASIS_H
#define BASIS_H

#include "Vector3.h"

#include <algorithm>

typedef float real_t; // @Todo move this to a global Godot.h

#define CMP_EPSILON 0.00001 // @Todo move this somewhere more global
#define CMP_EPSILON2 (CMP_EPSILON*CMP_EPSILON) // @Todo same as above
#define Math_PI 3.14159265358979323846 // I feel like I'm talking to myself



namespace godot {

class Quat;

class Basis {
public:

	Vector3 elements[3];

	Basis(const Quat& p_quat); // euler
	Basis(const Vector3& p_euler); // euler
	Basis(const Vector3& p_axis, real_t p_phi);

	Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2)
	{
		elements[0]=row0;
		elements[1]=row1;
		elements[2]=row2;
	}

	Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {

		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
	}

	Basis() {

		elements[0][0]=1;
		elements[0][1]=0;
		elements[0][2]=0;
		elements[1][0]=0;
		elements[1][1]=1;
		elements[1][2]=0;
		elements[2][0]=0;
		elements[2][1]=0;
		elements[2][2]=1;
	}





	const Vector3& operator[](int axis) const {

		return elements[axis];
	}
	Vector3& operator[](int axis) {

		return elements[axis];
	}

#define cofac(row1,col1, row2, col2)\
	(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])

	void invert()
	{
		real_t co[3]={
			cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
		};
		real_t det =	elements[0][0] * co[0]+
				elements[0][1] * co[1]+
				elements[0][2] * co[2];

		if ( det != 0 ) {
			// WTF
			__builtin_trap(); // WTF WTF WTF

			// I shouldn't do this
			// @Todo @Fixme @Todo @Todo
		}
		real_t s = 1.0/det;

		set(  co[0]*s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
		      co[1]*s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
		      co[2]*s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s );
	}
#undef cofac

	bool isequal_approx(const Basis& a, const Basis& b) const {

		for (int i=0;i<3;i++) {
			for (int j=0;j<3;j++) {
				if ((::fabs(a.elements[i][j]-b.elements[i][j]) < CMP_EPSILON) == false)
					return false;
			}
		}

		return true;
	}


	bool is_orthogonal() const
	{
		Basis id;
		Basis m = (*this)*transposed();

		return isequal_approx(id,m);
	}

	bool is_rotation() const
	{
		return ::fabs(determinant()-1) < CMP_EPSILON && is_orthogonal();
	}

	void transpose()
	{
		std::swap(elements[0][1],elements[1][0]);
		std::swap(elements[0][2],elements[2][0]);
		std::swap(elements[1][2],elements[2][1]);
	}

	Basis inverse() const
	{
		Basis b = *this;
		b.invert();
		return b;
	}

	Basis transposed() const
	{
		Basis b = *this;
		b.transpose();
		return b;
	}

	real_t determinant() const
	{
		return elements[0][0]*(elements[1][1]*elements[2][2] - elements[2][1]*elements[1][2]) -
		       elements[1][0]*(elements[0][1]*elements[2][2] - elements[2][1]*elements[0][2]) +
		       elements[2][0]*(elements[0][1]*elements[1][2] - elements[1][1]*elements[0][2]);
	}

	Vector3 get_axis(int p_axis) const {
		// get actual basis axis (elements is transposed for performance)
		return Vector3( elements[0][p_axis], elements[1][p_axis], elements[2][p_axis] );
	}
	void set_axis(int p_axis, const Vector3& p_value) {
		// get actual basis axis (elements is transposed for performance)
		elements[0][p_axis]=p_value.x;
		elements[1][p_axis]=p_value.y;
		elements[2][p_axis]=p_value.z;
	}

	void rotate(const Vector3& p_axis, real_t p_phi)
	{
		*this = rotated(p_axis, p_phi);
	}

	Basis rotated(const Vector3& p_axis, real_t p_phi) const
	{
		return Basis(p_axis, p_phi) * (*this);
	}

	void scale( const Vector3& p_scale )
	{
		elements[0][0]*=p_scale.x;
		elements[0][1]*=p_scale.x;
		elements[0][2]*=p_scale.x;
		elements[1][0]*=p_scale.y;
		elements[1][1]*=p_scale.y;
		elements[1][2]*=p_scale.y;
		elements[2][0]*=p_scale.z;
		elements[2][1]*=p_scale.z;
		elements[2][2]*=p_scale.z;
	}

	Basis scaled( const Vector3& p_scale ) const
	{
		Basis b = *this;
		b.scale(p_scale);
		return b;
	}

	Vector3 get_scale() const
	{
		// We are assuming M = R.S, and performing a polar decomposition to extract R and S.
		// FIXME: We eventually need a proper polar decomposition.
		// As a cheap workaround until then, to ensure that R is a proper rotation matrix with determinant +1
		// (such that it can be represented by a Quat or Euler angles), we absorb the sign flip into the scaling matrix.
		// As such, it works in conjuction with get_rotation().
		real_t det_sign = determinant() > 0 ? 1 : -1;
		return det_sign*Vector3(
			Vector3(elements[0][0],elements[1][0],elements[2][0]).length(),
			Vector3(elements[0][1],elements[1][1],elements[2][1]).length(),
			Vector3(elements[0][2],elements[1][2],elements[2][2]).length()
		);
	}

	Vector3 get_euler() const
	{
		// Euler angles in XYZ convention.
		// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
		//
		// rot =  cy*cz          -cy*sz           sy
		//        cz*sx*sy+cx*sz  cx*cz-sx*sy*sz -cy*sx
		//       -cx*cz*sy+sx*sz  cz*sx+cx*sy*sz  cx*cy

		Vector3 euler;

		if (is_rotation() == false)
			return euler;

		euler.y = ::asin(elements[0][2]);
		if ( euler.y < Math_PI*0.5) {
			if ( euler.y > -Math_PI*0.5) {
				euler.x = ::atan2(-elements[1][2],elements[2][2]);
				euler.z = ::atan2(-elements[0][1],elements[0][0]);

			} else {
				real_t r = ::atan2(elements[1][0],elements[1][1]);
				euler.z = 0.0;
				euler.x = euler.z - r;

			}
		} else {
			real_t r = ::atan2(elements[0][1],elements[1][1]);
			euler.z = 0;
			euler.x = r - euler.z;
		}

		return euler;
	}

	void set_euler(const Vector3& p_euler)
	{
		real_t c, s;

		c = ::cos(p_euler.x);
		s = ::sin(p_euler.x);
		Basis xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c);

		c = ::cos(p_euler.y);
		s = ::sin(p_euler.y);
		Basis ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c);

		c = ::cos(p_euler.z);
		s = ::sin(p_euler.z);
		Basis zmat(c,-s,0.0,s,c,0.0,0.0,0.0,1.0);

		//optimizer will optimize away all this anyway
		*this = xmat*(ymat*zmat);
	}

	// transposed dot products
	real_t tdotx(const Vector3& v) const  {
		return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
	}
	real_t tdoty(const Vector3& v) const {
		return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
	}
	real_t tdotz(const Vector3& v) const {
		return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
	}

	bool operator==(const Basis& p_matrix) const
	{
		for (int i=0;i<3;i++) {
			for (int j=0;j<3;j++) {
				if (elements[i][j] != p_matrix.elements[i][j])
					return false;
			}
		}

		return true;
	}

	bool operator!=(const Basis& p_matrix) const
	{
		return (!(*this==p_matrix));
	}

	Vector3 xform(const Vector3& p_vector) const {

		return Vector3(
			elements[0].dot(p_vector),
			elements[1].dot(p_vector),
			elements[2].dot(p_vector)
		);
	}

	Vector3 xform_inv(const Vector3& p_vector) const {

		return Vector3(
			(elements[0][0]*p_vector.x ) + ( elements[1][0]*p_vector.y ) + ( elements[2][0]*p_vector.z ),
			(elements[0][1]*p_vector.x ) + ( elements[1][1]*p_vector.y ) + ( elements[2][1]*p_vector.z ),
			(elements[0][2]*p_vector.x ) + ( elements[1][2]*p_vector.y ) + ( elements[2][2]*p_vector.z )
		);
	}
	void operator*=(const Basis& p_matrix)
	{
		set(
			p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
			p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
			p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));

	}

	Basis operator*(const Basis& p_matrix) const
	{
		return Basis(
			p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
			p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
			p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]) );

	}


	void operator+=(const Basis& p_matrix) {

		elements[0] += p_matrix.elements[0];
		elements[1] += p_matrix.elements[1];
		elements[2] += p_matrix.elements[2];
	}

	Basis operator+(const Basis& p_matrix) const {

		Basis ret(*this);
		ret += p_matrix;
		return ret;
	}

	void operator-=(const Basis& p_matrix) {

		elements[0] -= p_matrix.elements[0];
		elements[1] -= p_matrix.elements[1];
		elements[2] -= p_matrix.elements[2];
	}

	Basis operator-(const Basis& p_matrix) const {

		Basis ret(*this);
		ret -= p_matrix;
		return ret;
	}

	void operator*=(real_t p_val) {

		elements[0]*=p_val;
		elements[1]*=p_val;
		elements[2]*=p_val;
	}

	Basis operator*(real_t p_val) const {

			Basis ret(*this);
			ret *= p_val;
			return ret;
	}

	int get_orthogonal_index() const; // down below

	void set_orthogonal_index(int p_index); // down below


	operator String() const
	{
		String s;
		// @Todo
		return s;
	}

	void get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const;

	/* create / set */


	void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {

		elements[0][0]=xx;
		elements[0][1]=xy;
		elements[0][2]=xz;
		elements[1][0]=yx;
		elements[1][1]=yy;
		elements[1][2]=yz;
		elements[2][0]=zx;
		elements[2][1]=zy;
		elements[2][2]=zz;
	}
	Vector3 get_column(int i) const {

		return Vector3(elements[0][i],elements[1][i],elements[2][i]);
	}

	Vector3 get_row(int i) const {

		return Vector3(elements[i][0],elements[i][1],elements[i][2]);
	}
	Vector3 get_main_diagonal() const {
		return Vector3(elements[0][0],elements[1][1],elements[2][2]);
	}

	void set_row(int i, const Vector3& p_row) {
		elements[i][0]=p_row.x;
		elements[i][1]=p_row.y;
		elements[i][2]=p_row.z;
	}

	Basis transpose_xform(const Basis& m) const
	{
		return Basis(
			elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
			elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
			elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
			elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
			elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
			elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
			elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
			elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
			elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
	}

	void orthonormalize()
	{
		if (determinant() != 0) {
			// not this crap again
			__builtin_trap(); // WTF WTF WTF
			// somebody please complain some day
			// so I can fix this

			// need propert error reporting here.
		}

		// Gram-Schmidt Process

		Vector3 x=get_axis(0);
		Vector3 y=get_axis(1);
		Vector3 z=get_axis(2);

		x.normalize();
		y = (y-x*(x.dot(y)));
		y.normalize();
		z = (z-x*(x.dot(z))-y*(y.dot(z)));
		z.normalize();

		set_axis(0,x);
		set_axis(1,y);
		set_axis(2,z);
	}

	Basis orthonormalized() const
	{
		Basis b = *this;
		b.orthonormalize();
		return b;
	}

	bool is_symmetric() const
	{
		if (::fabs(elements[0][1] - elements[1][0]) > CMP_EPSILON)
			return false;
		if (::fabs(elements[0][2] - elements[2][0]) > CMP_EPSILON)
			return false;
		if (::fabs(elements[1][2] - elements[2][1]) > CMP_EPSILON)
			return false;

		return true;
	}

	Basis diagonalize()
	{
		// I love copy paste

		if (!is_symmetric())
			return Basis();

		const int ite_max = 1024;

		real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];

		int ite = 0;
		Basis acc_rot;
		while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max ) {
			real_t el01_2 = elements[0][1] * elements[0][1];
			real_t el02_2 = elements[0][2] * elements[0][2];
			real_t el12_2 = elements[1][2] * elements[1][2];
			// Find the pivot element
			int i, j;
			if (el01_2 > el02_2) {
				if (el12_2 > el01_2) {
					i = 1;
					j = 2;
				} else {
					i = 0;
					j = 1;
				}
			} else {
				if (el12_2 > el02_2) {
					i = 1;
					j = 2;
				} else {
					i = 0;
					j = 2;
				}
			}

			// Compute the rotation angle
			real_t angle;
			if (::fabs(elements[j][j] - elements[i][i]) < CMP_EPSILON) {
				angle = Math_PI / 4;
			} else {
				angle = 0.5 * ::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
			}

			// Compute the rotation matrix
			Basis rot;
			rot.elements[i][i] = rot.elements[j][j] = ::cos(angle);
			rot.elements[i][j] = - (rot.elements[j][i] = ::sin(angle));

			// Update the off matrix norm
			off_matrix_norm_2 -= elements[i][j] * elements[i][j];

			// Apply the rotation
			*this = rot * *this * rot.transposed();
			acc_rot = rot * acc_rot;
		}

		return acc_rot;
	}

	operator Quat() const;


};

static const Basis _ortho_bases[24]={
	Basis(1, 0, 0, 0, 1, 0, 0, 0, 1),
	Basis(0, -1, 0, 1, 0, 0, 0, 0, 1),
	Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1),
	Basis(0, 1, 0, -1, 0, 0, 0, 0, 1),
	Basis(1, 0, 0, 0, 0, -1, 0, 1, 0),
	Basis(0, 0, 1, 1, 0, 0, 0, 1, 0),
	Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0),
	Basis(0, 0, -1, -1, 0, 0, 0, 1, 0),
	Basis(1, 0, 0, 0, -1, 0, 0, 0, -1),
	Basis(0, 1, 0, 1, 0, 0, 0, 0, -1),
	Basis(-1, 0, 0, 0, 1, 0, 0, 0, -1),
	Basis(0, -1, 0, -1, 0, 0, 0, 0, -1),
	Basis(1, 0, 0, 0, 0, 1, 0, -1, 0),
	Basis(0, 0, -1, 1, 0, 0, 0, -1, 0),
	Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0),
	Basis(0, 0, 1, -1, 0, 0, 0, -1, 0),
	Basis(0, 0, 1, 0, 1, 0, -1, 0, 0),
	Basis(0, -1, 0, 0, 0, 1, -1, 0, 0),
	Basis(0, 0, -1, 0, -1, 0, -1, 0, 0),
	Basis(0, 1, 0, 0, 0, -1, -1, 0, 0),
	Basis(0, 0, 1, 0, -1, 0, 1, 0, 0),
	Basis(0, 1, 0, 0, 0, 1, 1, 0, 0),
	Basis(0, 0, -1, 0, 1, 0, 1, 0, 0),
	Basis(0, -1, 0, 0, 0, -1, 1, 0, 0)
};


int Basis::get_orthogonal_index() const
{
	//could be sped up if i come up with a way
	Basis orth=*this;
	for(int i=0;i<3;i++) {
		for(int j=0;j<3;j++) {

			real_t v = orth[i][j];
			if (v>0.5)
				v=1.0;
			else if (v<-0.5)
				v=-1.0;
			else
				v=0;

			orth[i][j]=v;
		}
	}

	for(int i=0;i<24;i++) {

		if (_ortho_bases[i]==orth)
			return i;


	}

	return 0;
}


void Basis::set_orthogonal_index(int p_index){

	//there only exist 24 orthogonal bases in r3
	if (p_index >= 24) {
		__builtin_trap(); // kiiiiill me
		// I don't want to do shady stuff like that
		// @Todo WTF WTF
	}


	*this=_ortho_bases[p_index];

}



Basis::Basis(const Vector3& p_euler) {

	set_euler( p_euler );

}

}

#include "Quat.h"

namespace godot {

Basis::Basis(const Quat& p_quat) {

	real_t d = p_quat.length_squared();
	real_t s = 2.0 / d;
	real_t xs = p_quat.x * s,   ys = p_quat.y * s,   zs = p_quat.z * s;
	real_t wx = p_quat.w * xs,  wy = p_quat.w * ys,  wz = p_quat.w * zs;
	real_t xx = p_quat.x * xs,  xy = p_quat.x * ys,  xz = p_quat.x * zs;
	real_t yy = p_quat.y * ys,  yz = p_quat.y * zs,  zz = p_quat.z * zs;
	set(	1.0 - (yy + zz), xy - wz, xz + wy,
		xy + wz, 1.0 - (xx + zz), yz - wx,
		xz - wy, yz + wx, 1.0 - (xx + yy))	;

}

Basis::Basis(const Vector3& p_axis, real_t p_phi) {
	// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle

	Vector3 axis_sq(p_axis.x*p_axis.x,p_axis.y*p_axis.y,p_axis.z*p_axis.z);

	real_t cosine= ::cos(p_phi);
	real_t sine= ::sin(p_phi);

	elements[0][0] = axis_sq.x + cosine * ( 1.0 - axis_sq.x );
	elements[0][1] = p_axis.x * p_axis.y *  ( 1.0 - cosine ) - p_axis.z * sine;
	elements[0][2] = p_axis.z * p_axis.x * ( 1.0 - cosine ) + p_axis.y * sine;

	elements[1][0] = p_axis.x * p_axis.y * ( 1.0 - cosine ) + p_axis.z * sine;
	elements[1][1] = axis_sq.y + cosine  * ( 1.0 - axis_sq.y );
	elements[1][2] = p_axis.y * p_axis.z * ( 1.0 - cosine ) - p_axis.x * sine;

	elements[2][0] = p_axis.z * p_axis.x * ( 1.0 - cosine ) - p_axis.y * sine;
	elements[2][1] = p_axis.y * p_axis.z * ( 1.0 - cosine ) + p_axis.x * sine;
	elements[2][2] = axis_sq.z + cosine  * ( 1.0 - axis_sq.z );

}




}

#endif // BASIS_H