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Diffstat (limited to 'src/PhysicsMath.h')
| -rw-r--r-- | src/PhysicsMath.h | 1190 |
1 files changed, 0 insertions, 1190 deletions
diff --git a/src/PhysicsMath.h b/src/PhysicsMath.h deleted file mode 100644 index c6c320c..0000000 --- a/src/PhysicsMath.h +++ /dev/null @@ -1,1190 +0,0 @@ -#ifndef _PHYSICSMATH_H_ - -#define _PHYSICSMATH_H_ - -#include <cmath> - -#include "Quaternions.h" - -//------------------------------------------------------------------------// - -// Misc. Constants - -//------------------------------------------------------------------------// - -const float pi = acosf(-1); - -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) sqrt(x*x + y*y + z*z); - -} - -inline void Vector::Normalize(void) - -{ - - float m = (float) 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 (abs(d) < 0.01f) - 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) 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 |