Added Basis.h and stub Quat.h

include/godot/core/Basis.h

@@ -0,0 +1,644 @@
+#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
+
+
+	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);
+	}
+
+	Vector3 get_rotation() const; // need?!
+
+	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 isequal_approx(const Basis& a, const Basis& b) const; // need?
+
+	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
+
+	bool is_orthogonal() const; // need?
+	bool is_rotation() const; // need?
+
+	operator String() const;
+
+	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

include/godot/core/Quat.h

@@ -0,0 +1,171 @@
+#ifndef QUAT_H
+#define QUAT_H
+
+#include <cmath>
+
+#include "Vector3.h"
+
+namespace godot {
+
+#define CMP_EPSILON 0.00001
+
+typedef float real_t;
+
+class Quat{
+public:
+
+	real_t x,y,z,w;
+
+	real_t length_squared() const;
+	real_t length() const;
+	void normalize();
+	Quat normalized() const;
+	Quat inverse() const;
+	real_t dot(const Quat& q) const;
+	void set_euler(const Vector3& p_euler);
+	Vector3 get_euler() const;
+	Quat slerp(const Quat& q, const real_t& t) const;
+	Quat slerpni(const Quat& q, const real_t& t) const;
+	Quat cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const;
+
+	void 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);
+	}
+
+	void operator*=(const Quat& q);
+	Quat operator*(const Quat& q) const;
+
+
+
+	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 xform(const Vector3& v) const {
+
+		Quat q = *this * v;
+		q *= this->inverse();
+		return Vector3(q.x,q.y,q.z);
+	}
+
+	void operator+=(const Quat& q);
+	void operator-=(const Quat& q);
+	void operator*=(const real_t& s);
+	void operator/=(const real_t& s);
+	Quat operator+(const Quat& q2) const;
+	Quat operator-(const Quat& q2) const;
+	Quat operator-() const;
+	Quat operator*(const real_t& s) const;
+	Quat operator/(const real_t& s) const;
+
+
+	bool operator==(const Quat& p_quat) const;
+	bool operator!=(const Quat& p_quat) const;
+
+	operator String() const;
+
+	inline void set( real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
+		x=p_x; y=p_y; z=p_z; w=p_w;
+	}
+	inline Quat(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
+		x=p_x; y=p_y; z=p_z; w=p_w;
+	}
+	Quat(const Vector3& axis, const real_t& angle);
+
+	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;
+		}
+	}
+
+	inline Quat() {x=y=z=0; w=1; }
+
+
+};
+
+
+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 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 {
+	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;
+}
+
+
+}
+
+#endif // QUAT_H