1 files changed, 1432 insertions, 0 deletions
diff --git a/src/PhysicsMath.h b/src/PhysicsMath.h
new file mode 100644
index 0000000..c975941
--- /dev/null
+++ b/src/PhysicsMath.h
@@ -0,0 +1,1432 @@
+#ifndef _PHYSICSMATH_H_
+
+#define _PHYSICSMATH_H_
+
+
+
+#include <cmath>
+
+#include "Quaternions.h"
+
+
+
+//------------------------------------------------------------------------//
+
+// Misc. Constants
+
+//------------------------------------------------------------------------//
+
+
+
+float	const	pi	= 3.14159265f;
+
+float	const	g	= -32.174f;		// acceleration due to gravity, ft/s^2
+
+float	const	rho = 0.0023769f;	// desity of air at sea level, slugs/ft^3
+
+float	const	tol = 0.0000000001f;		// float type tolerance 
+
+
+
+
+
+//------------------------------------------------------------------------//
+
+// Misc. Functions
+
+//------------------------------------------------------------------------//
+
+inline	float	DegreesToRadians(float deg);
+
+inline	float	RadiansToDegrees(float rad);
+
+
+
+inline	float	DegreesToRadians(float deg)
+
+{
+
+	return deg * pi / 180.0f;
+
+}
+
+
+
+inline	float	RadiansToDegrees(float rad)
+
+{	
+
+	return rad * 180.0f / pi;
+
+}
+
+
+
+//------------------------------------------------------------------------//
+
+// Vector Class and vector functions
+
+//------------------------------------------------------------------------//
+
+class Vector {
+
+public:
+
+	float x;
+
+	float y;
+
+	float z;
+
+
+
+	Vector(void);
+
+	Vector(float xi, float yi, float zi);
+
+
+
+	float Magnitude(void);
+
+	void  Normalize(void);
+
+	void  Reverse(void);
+
+
+
+	Vector& operator+=(Vector u);	// vector addition
+
+	Vector& operator-=(Vector u);	// vector subtraction
+
+	Vector& operator*=(float s);	// scalar multiply
+
+	Vector& operator/=(float s);	// scalar divide
+
+
+
+	Vector operator-(void);
+
+
+
+};
+
+
+
+inline	Vector operator+(Vector u, Vector v);
+
+inline	Vector operator-(Vector u, Vector v);
+
+inline	Vector operator^(Vector u, Vector v);
+
+inline	float operator*(Vector u, Vector v);
+
+inline	Vector operator*(float s, Vector u);
+
+inline	Vector operator*(Vector u, float s);
+
+inline	Vector operator/(Vector u, float s);
+
+inline	float TripleScalarProduct(Vector u, Vector v, Vector w);
+
+
+
+inline Vector::Vector(void)
+
+{
+
+	x = 0;
+
+	y = 0;
+
+	z = 0;
+
+}
+
+
+
+inline Vector::Vector(float xi, float yi, float zi)
+
+{
+
+	x = xi;
+
+	y = yi;
+
+	z = zi;
+
+}
+
+
+
+inline	float Vector::Magnitude(void)
+
+{
+
+	return (float) fast_sqrt(x*x + y*y + z*z);
+
+}
+
+
+
+inline	void  Vector::Normalize(void)
+
+{
+
+	float m = (float) fast_sqrt(x*x + y*y + z*z);
+
+	if(m <= tol) m = 1;
+
+	x /= m;
+
+	y /= m;
+
+	z /= m;	
+
+
+
+	if (fabs(x) < tol) x = 0.0f;
+
+	if (fabs(y) < tol) y = 0.0f;
+
+	if (fabs(z) < tol) z = 0.0f;
+
+}
+
+
+
+inline	void  Vector::Reverse(void)
+
+{
+
+	x = -x;
+
+	y = -y;
+
+	z = -z;
+
+}
+
+
+
+inline Vector& Vector::operator+=(Vector u)
+
+{
+
+	x += u.x;
+
+	y += u.y;
+
+	z += u.z;
+
+	return *this;
+
+}
+
+
+
+inline	Vector& Vector::operator-=(Vector u)
+
+{
+
+	x -= u.x;
+
+	y -= u.y;
+
+	z -= u.z;
+
+	return *this;
+
+}
+
+
+
+inline	Vector& Vector::operator*=(float s)
+
+{
+
+	x *= s;
+
+	y *= s;
+
+	z *= s;
+
+	return *this;
+
+}
+
+
+
+inline	Vector& Vector::operator/=(float s)
+
+{
+
+	x /= s;
+
+	y /= s;
+
+	z /= s;
+
+	return *this;
+
+}
+
+
+
+inline	Vector Vector::operator-(void)
+
+{
+
+	return Vector(-x, -y, -z);
+
+}
+
+
+
+
+
+inline	Vector operator+(Vector u, Vector v)
+
+{
+
+	return Vector(u.x + v.x, u.y + v.y, u.z + v.z);
+
+}
+
+
+
+inline	Vector operator-(Vector u, Vector v)
+
+{
+
+	return Vector(u.x - v.x, u.y - v.y, u.z - v.z);
+
+}
+
+
+
+// Vector cross product (u cross v)
+
+inline	Vector operator^(Vector u, Vector v)
+
+{
+
+	return Vector(	u.y*v.z - u.z*v.y,
+
+					-u.x*v.z + u.z*v.x,
+
+					u.x*v.y - u.y*v.x );
+
+}
+
+
+
+// Vector dot product
+
+inline	float operator*(Vector u, Vector v)
+
+{
+
+	return (u.x*v.x + u.y*v.y + u.z*v.z);
+
+}
+
+
+
+inline	Vector operator*(float s, Vector u)
+
+{
+
+	return Vector(u.x*s, u.y*s, u.z*s);
+
+}
+
+
+
+inline	Vector operator*(Vector u, float s)
+
+{
+
+	return Vector(u.x*s, u.y*s, u.z*s);
+
+}
+
+
+
+inline	Vector operator/(Vector u, float s)
+
+{
+
+	return Vector(u.x/s, u.y/s, u.z/s);
+
+}
+
+
+
+// triple scalar product (u dot (v cross w))
+
+inline	float TripleScalarProduct(Vector u, Vector v, Vector w)
+
+{
+
+	return float(	(u.x * (v.y*w.z - v.z*w.y)) +
+
+					(u.y * (-v.x*w.z + v.z*w.x)) +
+
+					(u.z * (v.x*w.y - v.y*w.x)) );
+
+	//return u*(v^w);
+
+
+
+}
+
+
+
+
+
+
+
+//------------------------------------------------------------------------//
+
+// Matrix Class and matrix functions
+
+//------------------------------------------------------------------------//
+
+
+
+class Matrix3x3 {
+
+public:
+
+	// elements eij: i -> row, j -> column
+
+	float	e11, e12, e13, e21, e22, e23, e31, e32, e33;	
+
+
+
+	Matrix3x3(void);
+
+	Matrix3x3(	float r1c1, float r1c2, float r1c3, 
+
+				float r2c1, float r2c2, float r2c3, 
+
+				float r3c1, float r3c2, float r3c3 );
+
+
+
+	float	det(void);
+
+	Matrix3x3	Transpose(void);
+
+	Matrix3x3	Inverse(void);
+
+
+
+	Matrix3x3& operator+=(Matrix3x3 m);
+
+	Matrix3x3& operator-=(Matrix3x3 m);
+
+	Matrix3x3& operator*=(float s);
+
+	Matrix3x3& operator/=(float s);
+
+};
+
+
+
+inline	Matrix3x3 operator+(Matrix3x3 m1, Matrix3x3 m2);
+
+inline	Matrix3x3 operator-(Matrix3x3 m1, Matrix3x3 m2);
+
+inline	Matrix3x3 operator/(Matrix3x3 m, float s);
+
+inline	Matrix3x3 operator*(Matrix3x3 m1, Matrix3x3 m2);
+
+inline	Matrix3x3 operator*(Matrix3x3 m, float s);
+
+inline	Matrix3x3 operator*(float s, Matrix3x3 m);
+
+inline	Vector operator*(Matrix3x3 m, Vector u);
+
+inline	Vector operator*(Vector u, Matrix3x3 m);
+
+
+
+
+
+
+
+
+
+
+
+inline	Matrix3x3::Matrix3x3(void)
+
+{
+
+	e11 = 0;
+
+	e12 = 0;
+
+	e13 = 0;
+
+	e21 = 0;
+
+	e22 = 0;
+
+	e23 = 0;
+
+	e31 = 0;
+
+	e32 = 0;
+
+	e33 = 0;
+
+}
+
+
+
+inline	Matrix3x3::Matrix3x3(	float r1c1, float r1c2, float r1c3, 
+
+								float r2c1, float r2c2, float r2c3, 
+
+								float r3c1, float r3c2, float r3c3 )
+
+{
+
+	e11 = r1c1;
+
+	e12 = r1c2;
+
+	e13 = r1c3;
+
+	e21 = r2c1;
+
+	e22 = r2c2;
+
+	e23 = r2c3;
+
+	e31 = r3c1;
+
+	e32 = r3c2;
+
+	e33 = r3c3;
+
+}
+
+
+
+inline	float	Matrix3x3::det(void)
+
+{
+
+	return	e11*e22*e33 - 
+
+			e11*e32*e23 + 
+
+			e21*e32*e13 - 
+
+			e21*e12*e33 + 
+
+			e31*e12*e23 - 
+
+			e31*e22*e13;	
+
+}
+
+
+
+inline	Matrix3x3	Matrix3x3::Transpose(void)
+
+{
+
+	return Matrix3x3(e11,e21,e31,e12,e22,e32,e13,e23,e33);
+
+}
+
+
+
+inline	Matrix3x3	Matrix3x3::Inverse(void)
+
+{
+
+	float	d = e11*e22*e33 - 
+
+				e11*e32*e23 + 
+
+				e21*e32*e13 - 
+
+				e21*e12*e33 + 
+
+				e31*e12*e23 - 
+
+				e31*e22*e13;
+
+
+
+	if (d == 0) d = 1;
+
+
+
+	return	Matrix3x3(	(e22*e33-e23*e32)/d,
+
+						-(e12*e33-e13*e32)/d,
+
+						(e12*e23-e13*e22)/d,
+
+						-(e21*e33-e23*e31)/d,
+
+						(e11*e33-e13*e31)/d,
+
+						-(e11*e23-e13*e21)/d,
+
+						(e21*e32-e22*e31)/d,
+
+						-(e11*e32-e12*e31)/d,
+
+						(e11*e22-e12*e21)/d );	
+
+}
+
+
+
+inline	Matrix3x3& Matrix3x3::operator+=(Matrix3x3 m)
+
+{
+
+	e11 += m.e11;
+
+	e12 += m.e12;
+
+	e13 += m.e13;
+
+	e21 += m.e21;
+
+	e22 += m.e22;
+
+	e23 += m.e23;
+
+	e31 += m.e31;
+
+	e32 += m.e32;
+
+	e33 += m.e33;
+
+	return *this;
+
+}
+
+
+
+inline	Matrix3x3& Matrix3x3::operator-=(Matrix3x3 m)
+
+{
+
+	e11 -= m.e11;
+
+	e12 -= m.e12;
+
+	e13 -= m.e13;
+
+	e21 -= m.e21;
+
+	e22 -= m.e22;
+
+	e23 -= m.e23;
+
+	e31 -= m.e31;
+
+	e32 -= m.e32;
+
+	e33 -= m.e33;
+
+	return *this;
+
+}
+
+
+
+inline	Matrix3x3& Matrix3x3::operator*=(float s)
+
+{
+
+	e11 *= s;
+
+	e12 *= s;
+
+	e13 *= s;
+
+	e21 *= s;
+
+	e22 *= s;
+
+	e23 *= s;
+
+	e31 *= s;
+
+	e32 *= s;
+
+	e33 *= s;
+
+	return *this;
+
+}
+
+
+
+inline	Matrix3x3& Matrix3x3::operator/=(float s)
+
+{
+
+	e11 /= s;
+
+	e12 /= s;
+
+	e13 /= s;
+
+	e21 /= s;
+
+	e22 /= s;
+
+	e23 /= s;
+
+	e31 /= s;
+
+	e32 /= s;
+
+	e33 /= s;
+
+	return *this;
+
+}
+
+
+
+inline	Matrix3x3 operator+(Matrix3x3 m1, Matrix3x3 m2)
+
+{
+
+	return	Matrix3x3(	m1.e11+m2.e11,
+
+						m1.e12+m2.e12,
+
+						m1.e13+m2.e13,
+
+						m1.e21+m2.e21,
+
+						m1.e22+m2.e22,
+
+						m1.e23+m2.e23,
+
+						m1.e31+m2.e31,
+
+						m1.e32+m2.e32,
+
+						m1.e33+m2.e33);
+
+}
+
+
+
+inline	Matrix3x3 operator-(Matrix3x3 m1, Matrix3x3 m2)
+
+{
+
+	return	Matrix3x3(	m1.e11-m2.e11,
+
+						m1.e12-m2.e12,
+
+						m1.e13-m2.e13,
+
+						m1.e21-m2.e21,
+
+						m1.e22-m2.e22,
+
+						m1.e23-m2.e23,
+
+						m1.e31-m2.e31,
+
+						m1.e32-m2.e32,
+
+						m1.e33-m2.e33);
+
+}
+
+
+
+inline	Matrix3x3 operator/(Matrix3x3 m, float s)
+
+{	
+
+	return	Matrix3x3(	m.e11/s,
+
+						m.e12/s,
+
+						m.e13/s,
+
+						m.e21/s,
+
+						m.e22/s,
+
+						m.e23/s,
+
+						m.e31/s,
+
+						m.e32/s,
+
+						m.e33/s);
+
+}
+
+
+
+inline	Matrix3x3 operator*(Matrix3x3 m1, Matrix3x3 m2)
+
+{
+
+	return Matrix3x3(	m1.e11*m2.e11 + m1.e12*m2.e21 + m1.e13*m2.e31,
+
+						m1.e11*m2.e12 + m1.e12*m2.e22 + m1.e13*m2.e32,
+
+						m1.e11*m2.e13 + m1.e12*m2.e23 + m1.e13*m2.e33,
+
+						m1.e21*m2.e11 + m1.e22*m2.e21 + m1.e23*m2.e31,
+
+						m1.e21*m2.e12 + m1.e22*m2.e22 + m1.e23*m2.e32,
+
+						m1.e21*m2.e13 + m1.e22*m2.e23 + m1.e23*m2.e33,
+
+						m1.e31*m2.e11 + m1.e32*m2.e21 + m1.e33*m2.e31,
+
+						m1.e31*m2.e12 + m1.e32*m2.e22 + m1.e33*m2.e32,
+
+						m1.e31*m2.e13 + m1.e32*m2.e23 + m1.e33*m2.e33 );
+
+}
+
+
+
+inline	Matrix3x3 operator*(Matrix3x3 m, float s)
+
+{
+
+	return	Matrix3x3(	m.e11*s,
+
+						m.e12*s,
+
+						m.e13*s,
+
+						m.e21*s,
+
+						m.e22*s,
+
+						m.e23*s,
+
+						m.e31*s,
+
+						m.e32*s,
+
+						m.e33*s);
+
+}
+
+
+
+inline	Matrix3x3 operator*(float s, Matrix3x3 m)
+
+{
+
+	return	Matrix3x3(	m.e11*s,
+
+						m.e12*s,
+
+						m.e13*s,
+
+						m.e21*s,
+
+						m.e22*s,
+
+						m.e23*s,
+
+						m.e31*s,
+
+						m.e32*s,
+
+						m.e33*s);
+
+}
+
+
+
+inline	Vector operator*(Matrix3x3 m, Vector u)
+
+{
+
+	return Vector(	m.e11*u.x + m.e12*u.y + m.e13*u.z,
+
+					m.e21*u.x + m.e22*u.y + m.e23*u.z,
+
+					m.e31*u.x + m.e32*u.y + m.e33*u.z);					
+
+}
+
+
+
+inline	Vector operator*(Vector u, Matrix3x3 m)
+
+{
+
+	return Vector(	u.x*m.e11 + u.y*m.e21 + u.z*m.e31,
+
+					u.x*m.e12 + u.y*m.e22 + u.z*m.e32,
+
+					u.x*m.e13 + u.y*m.e23 + u.z*m.e33);
+
+}
+
+
+
+//------------------------------------------------------------------------//
+
+// Quaternion Class and Quaternion functions
+
+//------------------------------------------------------------------------//
+
+
+
+class Quaternion {
+
+public:
+
+	float	n;	// number (scalar) part
+
+	Vector	v;	// vector part: v.x, v.y, v.z
+
+
+
+	Quaternion(void);
+
+	Quaternion(float e0, float e1, float e2, float e3);
+
+
+
+	float	Magnitude(void);
+
+	Vector	GetVector(void);
+
+	float	GetScalar(void);
+
+	Quaternion	operator+=(Quaternion q);
+
+	Quaternion	operator-=(Quaternion q);
+
+	Quaternion operator*=(float s);
+
+	Quaternion operator/=(float s);
+
+	Quaternion	operator~(void) const { return Quaternion(n, -v.x, -v.y, -v.z);}
+
+};
+
+
+
+inline	Quaternion operator+(Quaternion q1, Quaternion q2);
+
+inline	Quaternion operator-(Quaternion q1, Quaternion q2);
+
+inline	Quaternion operator*(Quaternion q1, Quaternion q2);
+
+inline	Quaternion operator*(Quaternion q, float s);
+
+inline	Quaternion operator*(float s, Quaternion q);
+
+inline	Quaternion operator*(Quaternion q, Vector v);
+
+inline	Quaternion operator*(Vector v, Quaternion q);
+
+inline	Quaternion operator/(Quaternion q, float s);
+
+inline	float QGetAngle(Quaternion q);
+
+inline	Vector QGetAxis(Quaternion q);
+
+inline	Quaternion QRotate(Quaternion q1, Quaternion q2);
+
+inline	Vector	QVRotate(Quaternion q, Vector v);
+
+inline	Quaternion	MakeQFromEulerAngles(float x, float y, float z);
+
+inline	Vector	MakeEulerAnglesFromQ(Quaternion q);
+
+
+
+
+
+inline	Quaternion::Quaternion(void)
+
+{
+
+	n = 0;
+
+	v.x = 0;
+
+	v.y =  0;
+
+	v.z = 0;
+
+}
+
+
+
+inline	Quaternion::Quaternion(float e0, float e1, float e2, float e3)
+
+{
+
+	n = e0;
+
+	v.x = e1;
+
+	v.y = e2;
+
+	v.z = e3;
+
+}
+
+
+
+inline	float	Quaternion::Magnitude(void)
+
+{
+
+	return (float) fast_sqrt(n*n + v.x*v.x + v.y*v.y + v.z*v.z);
+
+}
+
+
+
+inline	Vector	Quaternion::GetVector(void)
+
+{
+
+	return Vector(v.x, v.y, v.z);
+
+}
+
+
+
+inline	float	Quaternion::GetScalar(void)
+
+{
+
+	return n;
+
+}
+
+
+
+inline	Quaternion	Quaternion::operator+=(Quaternion q)
+
+{
+
+	n += q.n;
+
+	v.x += q.v.x;
+
+	v.y += q.v.y;
+
+	v.z += q.v.z;
+
+	return *this;
+
+}
+
+
+
+inline	Quaternion	Quaternion::operator-=(Quaternion q)
+
+{
+
+	n -= q.n;
+
+	v.x -= q.v.x;
+
+	v.y -= q.v.y;
+
+	v.z -= q.v.z;
+
+	return *this;
+
+}
+
+
+
+inline	Quaternion Quaternion::operator*=(float s)
+
+{
+
+	n *= s;
+
+	v.x *= s;
+
+	v.y *= s;
+
+	v.z *= s;
+
+	return *this;
+
+}
+
+
+
+inline	Quaternion Quaternion::operator/=(float s)
+
+{
+
+	n /= s;
+
+	v.x /= s;
+
+	v.y /= s;
+
+	v.z /= s;
+
+	return *this;
+
+}
+
+
+
+/*inline	Quaternion	Quaternion::operator~()
+
+{
+
+	return Quaternion(n, -v.x, -v.y, -v.z);
+
+}*/
+
+
+
+inline	Quaternion operator+(Quaternion q1, Quaternion q2)
+
+{
+
+	return	Quaternion(	q1.n + q2.n,
+
+							q1.v.x + q2.v.x,
+
+							q1.v.y + q2.v.y,
+
+							q1.v.z + q2.v.z);
+
+}
+
+
+
+inline	Quaternion operator-(Quaternion q1, Quaternion q2)
+
+{
+
+	return	Quaternion(	q1.n - q2.n,
+
+							q1.v.x - q2.v.x,
+
+							q1.v.y - q2.v.y,
+
+							q1.v.z - q2.v.z);
+
+}
+
+
+
+inline	Quaternion operator*(Quaternion q1, Quaternion q2)
+
+{
+
+	return	Quaternion(	q1.n*q2.n - q1.v.x*q2.v.x - q1.v.y*q2.v.y - q1.v.z*q2.v.z,
+
+							q1.n*q2.v.x + q1.v.x*q2.n + q1.v.y*q2.v.z - q1.v.z*q2.v.y,
+
+							q1.n*q2.v.y + q1.v.y*q2.n + q1.v.z*q2.v.x - q1.v.x*q2.v.z,
+
+							q1.n*q2.v.z + q1.v.z*q2.n + q1.v.x*q2.v.y - q1.v.y*q2.v.x);							
+
+}
+
+
+
+inline	Quaternion operator*(Quaternion q, float s)
+
+{
+
+	return	Quaternion(q.n*s, q.v.x*s, q.v.y*s, q.v.z*s);
+
+}
+
+
+
+inline	Quaternion operator*(float s, Quaternion q)
+
+{
+
+	return	Quaternion(q.n*s, q.v.x*s, q.v.y*s, q.v.z*s);
+
+}
+
+
+
+inline	Quaternion operator*(Quaternion q, Vector v)
+
+{
+
+	return	Quaternion(	-(q.v.x*v.x + q.v.y*v.y + q.v.z*v.z),
+
+							q.n*v.x + q.v.y*v.z - q.v.z*v.y,
+
+							q.n*v.y + q.v.z*v.x - q.v.x*v.z,
+
+							q.n*v.z + q.v.x*v.y - q.v.y*v.x);
+
+}
+
+
+
+inline	Quaternion operator*(Vector v, Quaternion q)
+
+{
+
+	return	Quaternion(	-(q.v.x*v.x + q.v.y*v.y + q.v.z*v.z),
+
+							q.n*v.x + q.v.z*v.y - q.v.y*v.z,
+
+							q.n*v.y + q.v.x*v.z - q.v.z*v.x,
+
+							q.n*v.z + q.v.y*v.x - q.v.x*v.y);
+
+}
+
+
+
+inline	Quaternion operator/(Quaternion q, float s)
+
+{
+
+	return	Quaternion(q.n/s, q.v.x/s, q.v.y/s, q.v.z/s);
+
+}
+
+
+
+inline	float QGetAngle(Quaternion q)
+
+{
+
+	return	(float) (2*acos(q.n));
+
+}
+
+
+
+inline	Vector QGetAxis(Quaternion q)
+
+{
+
+	Vector v;
+
+	float m;
+
+
+
+	v = q.GetVector();
+
+	m = v.Magnitude();
+
+	
+
+	if (m <= tol)
+
+		return Vector();
+
+	else
+
+		return v/m;	
+
+}
+
+
+
+inline	Quaternion QRotate(Quaternion q1, Quaternion q2)
+
+{
+
+	return	q1*q2*(~q1);
+
+}
+
+
+
+inline	Vector	QVRotate(Quaternion q, Vector v)
+
+{
+
+	Quaternion t;
+
+
+
+
+
+	t = q*v*(~q);
+
+
+
+	return	t.GetVector();
+
+}
+
+
+
+inline	Quaternion	MakeQFromEulerAngles(float x, float y, float z)
+
+{
+
+	Quaternion	q;
+
+	double	roll = DegreesToRadians(x);
+
+	double	pitch = DegreesToRadians(y);
+
+	double	yaw = DegreesToRadians(z);
+
+	
+
+	double	cyaw, cpitch, croll, syaw, spitch, sroll;
+
+	double	cyawcpitch, syawspitch, cyawspitch, syawcpitch;
+
+
+
+	cyaw = cos(0.5f * yaw);
+
+	cpitch = cos(0.5f * pitch);
+
+	croll = cos(0.5f * roll);
+
+	syaw = sin(0.5f * yaw);
+
+	spitch = sin(0.5f * pitch);
+
+	sroll = sin(0.5f * roll);
+
+
+
+	cyawcpitch = cyaw*cpitch;
+
+	syawspitch = syaw*spitch;
+
+	cyawspitch = cyaw*spitch;
+
+	syawcpitch = syaw*cpitch;
+
+
+
+	q.n = (float) (cyawcpitch * croll + syawspitch * sroll);
+
+	q.v.x = (float) (cyawcpitch * sroll - syawspitch * croll); 
+
+	q.v.y = (float) (cyawspitch * croll + syawcpitch * sroll);
+
+	q.v.z = (float) (syawcpitch * croll - cyawspitch * sroll);
+
+
+
+	return q;
+
+}
+
+
+
+inline	Vector	MakeEulerAnglesFromQ(Quaternion q)
+
+{
+
+	double	r11, r21, r31, r32, r33, r12, r13;
+
+	double	q00, q11, q22, q33;
+
+	double	tmp;
+
+	Vector	u;
+
+
+
+	q00 = q.n * q.n;
+
+	q11 = q.v.x * q.v.x;
+
+	q22 = q.v.y * q.v.y;
+
+	q33 = q.v.z * q.v.z;
+
+
+
+	r11 = q00 + q11 - q22 - q33;
+
+	r21 = 2 * (q.v.x*q.v.y + q.n*q.v.z);
+
+	r31 = 2 * (q.v.x*q.v.z - q.n*q.v.y);
+
+	r32 = 2 * (q.v.y*q.v.z + q.n*q.v.x);
+
+	r33 = q00 - q11 - q22 + q33;
+
+
+
+	tmp = fabs(r31);
+
+	if(tmp > 0.999999)
+
+	{
+
+		r12 = 2 * (q.v.x*q.v.y - q.n*q.v.z);
+
+		r13 = 2 * (q.v.x*q.v.z + q.n*q.v.y);
+
+
+
+		u.x = RadiansToDegrees(0.0f); //roll
+
+		u.y = RadiansToDegrees((float) (-(pi/2) * r31/tmp)); // pitch
+
+		u.z = RadiansToDegrees((float) atan2(-r12, -r31*r13)); // yaw
+
+		return u;
+
+	}
+
+
+
+	u.x = RadiansToDegrees((float) atan2(r32, r33)); // roll
+
+	u.y = RadiansToDegrees((float) asin(-r31));		 // pitch
+
+	u.z = RadiansToDegrees((float) atan2(r21, r11)); // yaw
+
+	return u;
+
+	
+
+
+
+}
+
+
+
+
+
+
+
+
+
+
+
+#endif
+