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-rw-r--r--Source/PhysicsMath.h1431
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diff --git a/Source/PhysicsMath.h b/Source/PhysicsMath.h
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+++ b/Source/PhysicsMath.h
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+#ifndef _PHYSICSMATH_H_
+
+#define _PHYSICSMATH_H_
+
+
+
+#include <math.h>
+
+#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 \ No newline at end of file
generated by cgit v1.2.3 (git 2.25.1) at 2026-01-20 22:14:18 +0000