+++ /dev/null
-/*
-Copyright (C) 2003, 2010 - Wolfire Games
-Copyright (C) 2010-2016 - Lugaru contributors (see AUTHORS file)
-
-This file is part of Lugaru.
-
-Lugaru is free software; you can redistribute it and/or modify
-it under the terms of the GNU General Public License as published by
-the Free Software Foundation; either version 2 of the License, or
-(at your option) any later version.
-
-Lugaru is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License
-along with Lugaru. If not, see <http://www.gnu.org/licenses/>.
-*/
-
-#ifndef _PHYSICSMATH_H_
-#define _PHYSICSMATH_H_
-
-//#include <Carbon.h>
-
-#include "MacCompatibility.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);
-/*
-float fast_sqrt2 (register float arg);
-float fast_sqrt2 (register float arg)
-{
-// Can replace with slower return std::sqrt(arg);
-register float result;
-
-if (arg == 0.0) return 0.0;
-
-asm {
-frsqrte result,arg // Calculate Square root
-}
-
-// Newton Rhapson iterations.
-result = result + 0.5 * result * (1.0 - arg * result * result);
-result = result + 0.5 * result * (1.0 - arg * result * result);
-
-return result * arg;
-}
-*/
-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 (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) 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 * acosf(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;
- 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) {
- double r12 = 2 * (q.v.x * q.v.y - q.n * q.v.z);
- double 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) asinf(-r31)); // pitch
- u.z = RadiansToDegrees((float) atan2(r21, r11)); // yaw
- return u;
-
-
-}
-
-
-
-
-
-#endif
projects / lugaru.git / blobdiff