nuclear@0: #ifndef _N3DMATH_H_
nuclear@0: #define _N3DMATH_H_
nuclear@0: 
nuclear@0: //	- n3dmath.h - 
nuclear@0: //	Nuc3D 2 Header File
nuclear@0: //	written by: John Tsiombikas (10 Sep 2002)
nuclear@0: //	Last Modification: 14 April 2002
nuclear@0: //	---------------------------
nuclear@0: //	Mathematical stuff
nuclear@0: 
nuclear@0: #include <iostream>
nuclear@0: #include <cmath>
nuclear@0: 
nuclear@0: #ifdef NUC3D_VER_DIRECT3D
nuclear@0: #include "d3d8.h"	// Direct3D type definitions (D3DMATRIX)
nuclear@0: #endif	//NUC3D_VER_DIRECT3D
nuclear@0: 
nuclear@0: // forward declarations
nuclear@0: class Matrix4x4;
nuclear@0: class Matrix3x3;
nuclear@0: class Vector3;
nuclear@0: class Vector2;
nuclear@0: class Vector4;
nuclear@0: class Quaternion;
nuclear@0: 
nuclear@0: // mathematical constants
nuclear@0: const float Pi = 3.1415926535897932f;
nuclear@0: const float TwoPi = 6.2831853071795865f;// Pi * 2.0f;
nuclear@0: const float HalfPi = 1.5707963267948965f; //Pi * 0.5f;
nuclear@0: const float QuarterPi = 0.7853981633974483f; //Pi * 0.25f;
nuclear@0: const float ThreeQuartersPi = 2.3561944901923450f; //QuarterPi * 3.0f;
nuclear@0: 
nuclear@0: const float XSmallNumber = 1.e-8f;
nuclear@0: const float SmallNumber = 1.e-4f;
nuclear@0: 
nuclear@0: // basis vectors
nuclear@0: #define VECTOR3_I	(Vector3(1.0f, 0.0f, 0.0f))
nuclear@0: #define VECTOR3_J	(Vector3(0.0f, 1.0f, 0.0f))
nuclear@0: #define VECTOR3_K	(Vector3(0.0f, 0.0f, 1.0f))
nuclear@0: 
nuclear@0: #define VECTOR2_I	(Vector2(1.0f, 0.0f))
nuclear@0: #define VECTOR2_J	(Vector2(0.0f, 1.0f))
nuclear@0: 
nuclear@0: // angle conversion
nuclear@0: #define DEGTORAD(a)	(Pi * (a) / 180)
nuclear@0: #define RADTODEG(a) ((a) * 180 / Pi)
nuclear@0: 
nuclear@0: 
nuclear@0: 
nuclear@0: // ------------- Vector3 class -------------
nuclear@0: 
nuclear@0: #ifdef NUC3D_VER_DIRECT3D	// if we are using Direct3D version
nuclear@0: 
nuclear@0: class Vector3 : public D3DVECTOR {
nuclear@0: public:
nuclear@0: 
nuclear@0: #else	// not D3D
nuclear@0: 
nuclear@0: class Vector3 {
nuclear@0: public:
nuclear@0: 	float x, y, z;
nuclear@0: 
nuclear@0: #endif	//NUC3D_VER_DIRECT3D
nuclear@0: 
nuclear@0: 	Vector3();
nuclear@0: 	Vector3(float x, float y, float z);
nuclear@0: 
nuclear@0: 	inline float DotProduct(const Vector3 &vec) const;
nuclear@0: 	inline Vector3 CrossProduct(const Vector3 &vec) const;
nuclear@0: 
nuclear@0: 	inline Vector3 operator +(const Vector3 &vec) const;
nuclear@0: 	inline Vector3 operator -(const Vector3 &vec) const;
nuclear@0: 	inline Vector3 operator *(float scalar) const;
nuclear@0: 	inline Vector3 operator /(float scalar) const;
nuclear@0: 	inline void operator +=(const Vector3 &vec);
nuclear@0: 	inline void operator -=(const Vector3 &vec);
nuclear@0: 	inline void operator *=(float scalar);
nuclear@0: 	inline void operator /=(float scalar);
nuclear@0: 	inline Vector3 operator -() const;	// unary minus for inversion
nuclear@0: 
nuclear@0: 	inline bool operator >(const Vector3 &vec) const;
nuclear@0: 	inline bool operator <(const Vector3 &vec) const;
nuclear@0: 	inline bool operator >(float len) const;
nuclear@0: 	inline bool operator <(float len) const;
nuclear@0: 	inline bool operator ==(const Vector3 &vec) const;
nuclear@0: 	inline bool operator ==(float len) const;
nuclear@0: 
nuclear@0: 	inline operator Vector2() const;
nuclear@0: 	inline operator Vector4() const;
nuclear@0: 
nuclear@0: 	inline float Length() const;
nuclear@0: 	inline float LengthSq() const;
nuclear@0: 	
nuclear@0: 	inline void Normalize();
nuclear@0: 	inline Vector3 Normalized() const;
nuclear@0: 
nuclear@0: 	inline Vector3 Reflection(const Vector3 &normal) const;
nuclear@0: 	Vector3 Refraction(const Vector3 &normal, float FromIOR, float ToIOR) const;
nuclear@0: 	
nuclear@0: 	void Transform(const Matrix4x4 &mat);	// transform a vector using a transformation matrix
nuclear@0: 	void Transform(const Quaternion &quat);	// transform by a quaternion
nuclear@0: 
nuclear@0: 	// Direct transformations on the vector
nuclear@0: 	void Translate(float x, float y, float z);
nuclear@0: 	void Rotate(float x, float y, float z);
nuclear@0: 	void Rotate(const Vector3 &axis, float angle);
nuclear@0: 	void Scale(float x, float y, float z);
nuclear@0: 
nuclear@0: 	float &operator [](int index);
nuclear@0: 
nuclear@0: 	friend std::ostream &operator <<(std::ostream &out, const Vector3 &vec);
nuclear@0: };
nuclear@0: 
nuclear@0: inline float DotProduct(const Vector3 &vec1, const Vector3 &vec2);
nuclear@0: inline Vector3 CrossProduct(const Vector3 &vec1, const Vector3 &vec2);
nuclear@0: 
nuclear@0: ////////////////////// 4-dimensional vectors ////////////////////////////
nuclear@0: class Vector4 {
nuclear@0: public:
nuclear@0: 	float x, y, z, w;
nuclear@0: 
nuclear@0: 	Vector4();
nuclear@0: 	Vector4(const Vector4 &vec);
nuclear@0: 	Vector4(const Vector3 &vec);	// create from a 3 dimensional vector setting w=1
nuclear@0: 	Vector4(float x, float y, float z, float w);
nuclear@0: 
nuclear@0: 	float DotProduct(const Vector4 &vec) const;
nuclear@0: 	Vector4 CrossProduct(const Vector4 &vec1, const Vector4 &vec2) const;
nuclear@0: 
nuclear@0: 	Vector4 operator +(const Vector4 &vec) const;
nuclear@0: 	Vector4 operator -(const Vector4 &vec) const;
nuclear@0: 	Vector4 operator *(float scalar) const;
nuclear@0: 	Vector4 operator /(float scalar) const;
nuclear@0: 	void operator +=(const Vector4 &vec);
nuclear@0: 	void operator -=(const Vector4 &vec);
nuclear@0: 	void operator *=(float scalar);
nuclear@0: 	void operator /=(float scalar);
nuclear@0: 	Vector4 operator -() const;	// unary minus for inversion
nuclear@0: 
nuclear@0: 	bool operator >(const Vector4 &vec) const;
nuclear@0: 	bool operator <(const Vector4 &vec) const;
nuclear@0: 	bool operator >(float len) const;
nuclear@0: 	bool operator <(float len) const;
nuclear@0: 	bool operator ==(const Vector4 &vec) const;
nuclear@0: 	bool operator ==(float len) const;
nuclear@0: 
nuclear@0: 	operator Vector3() const;
nuclear@0: 
nuclear@0: 	float Length() const;
nuclear@0: 	float LengthSq() const;
nuclear@0: 	
nuclear@0: 	void Normalize();
nuclear@0: 	Vector4 Normalized() const;
nuclear@0: 
nuclear@0: 	void Transform(const Matrix4x4 &mat);	// transform a vector using a transformation matrix
nuclear@0: 
nuclear@0: 	// Direct transformations on the vector
nuclear@0: 	void Translate(float x, float y, float z, float w);
nuclear@0: 	void Rotate(float x, float y, float z);
nuclear@0: 	void Rotate(const Vector3 &axis, float angle);
nuclear@0: 	void Scale(float x, float y, float z, float w);
nuclear@0: 
nuclear@0: 	float &operator [](int index);
nuclear@0: 
nuclear@0: 	friend std::ostream &operator <<(std::ostream &out, const Vector3 &vec);
nuclear@0: };
nuclear@0: 
nuclear@0: float DotProduct(const Vector4 &vec1, const Vector4 &vec2);
nuclear@0: Vector4 CrossProduct(const Vector4 &vec1, const Vector4 &vec2, const Vector4 &vec3);
nuclear@0: 
nuclear@0: ///////////////////////////
nuclear@0: 
nuclear@0: class Vector2 {
nuclear@0: public:
nuclear@0: 	float x, y;
nuclear@0: 
nuclear@0: 	Vector2();
nuclear@0: 	Vector2(const Vector2 &vec);
nuclear@0: 	Vector2(float x, float y);
nuclear@0: 
nuclear@0: 	float DotProduct(const Vector2 &vec) const;
nuclear@0: 	//Vector2 CrossProduct(const Vector2 &vec) const;
nuclear@0: 
nuclear@0: 	Vector2 operator +(const Vector2 &vec) const;
nuclear@0: 	Vector2 operator -(const Vector2 &vec) const;
nuclear@0: 	Vector2 operator *(float scalar) const;
nuclear@0: 	Vector2 operator /(float scalar) const;
nuclear@0: 	void operator +=(const Vector2 &vec);
nuclear@0: 	void operator -=(const Vector2 &vec);
nuclear@0: 	void operator *=(float scalar);
nuclear@0: 	void operator /=(float scalar);
nuclear@0: 	Vector2 operator -() const;	// unary minus for inversion
nuclear@0: 
nuclear@0: 	bool operator >(const Vector2 &vec) const;
nuclear@0: 	bool operator <(const Vector2 &vec) const;
nuclear@0: 	bool operator >(float len) const;
nuclear@0: 	bool operator <(float len) const;
nuclear@0: 	bool operator ==(const Vector2 &vec) const;
nuclear@0: 	bool operator ==(float len) const;
nuclear@0: 
nuclear@0: 	operator Vector3() const;
nuclear@0: 	    
nuclear@0: 	float Length() const;
nuclear@0: 	float LengthSq() const;
nuclear@0: 	
nuclear@0: 	void Normalize();
nuclear@0: 	Vector2 Normalized() const;
nuclear@0: 
nuclear@0: 	Vector2 Reflection(const Vector2 &normal) const;
nuclear@0: 	Vector2 Refraction(const Vector2 &normal, float FromIOR, float ToIOR) const;
nuclear@0: 	
nuclear@0: 	void Transform(const Matrix3x3 &mat);	// transform a vector using a transformation matrix
nuclear@0: 
nuclear@0: 	// Direct transformations on the vector
nuclear@0: 	void Translate(float x, float y);
nuclear@0: 	void Rotate(float angle);
nuclear@0: 	void Scale(float x, float y);
nuclear@0: 
nuclear@0: 	float &operator [](int index);
nuclear@0: 
nuclear@0: 	friend std::ostream &operator <<(std::ostream &out, const Vector2 &vec);
nuclear@0: };
nuclear@0: 
nuclear@0: float DotProduct(const Vector3 &vec1, const Vector3 &vec2);
nuclear@0: 
nuclear@0: 
nuclear@0: struct Vector2i {
nuclear@0: 	int x, y;
nuclear@0: 
nuclear@0: 	Vector2i(int x=0, int y=0) {this->x = x; this->y = y;}
nuclear@0: };
nuclear@0: 
nuclear@0: 
nuclear@0: ////////////////// Quaternion ///////////////////////
nuclear@0: 
nuclear@0: class Quaternion {
nuclear@0: public:
nuclear@0: 	float s;
nuclear@0: 	Vector3 v;
nuclear@0: 
nuclear@0: 	Quaternion();
nuclear@0: 	Quaternion(float s, const Vector3 &v);
nuclear@0: 	Quaternion(float s, float x, float y, float z);	
nuclear@0: 
nuclear@0: 	Quaternion operator +(const Quaternion &quat) const;
nuclear@0: 	Quaternion operator -(const Quaternion &quat) const;
nuclear@0: 	Quaternion operator -() const;
nuclear@0: 	Quaternion operator *(const Quaternion &quat) const;
nuclear@0: 	
nuclear@0: 	void operator +=(const Quaternion &quat);
nuclear@0: 	void operator -=(const Quaternion &quat);
nuclear@0: 	void operator *=(const Quaternion &quat);
nuclear@0: 
nuclear@0: 	void ResetIdentity();
nuclear@0: 
nuclear@0: 	Quaternion Conjugate() const;
nuclear@0: 
nuclear@0: 	float Length() const;
nuclear@0: 	float LengthSq() const;
nuclear@0: 	
nuclear@0: 	void Normalize();
nuclear@0: 	Quaternion Normalized() const;
nuclear@0: 
nuclear@0: 	Quaternion Inverse() const;
nuclear@0: 
nuclear@0: 	void SetRotation(const Vector3 &axis, float angle);
nuclear@0: 	void Rotate(const Vector3 &axis, float angle);
nuclear@0: 
nuclear@0: 	Matrix3x3 GetRotationMatrix() const;
nuclear@0: };
nuclear@0: 
nuclear@0: 	
nuclear@0: 
nuclear@0: ////////////////////////// Matrices //////////////////////////////
nuclear@0: 
nuclear@0: #ifdef NUC3D_VER_DIRECT3D	// if we are using Direct3D version
nuclear@0: 
nuclear@0: class Matrix4x4 : public D3DMATRIX {
nuclear@0: public:
nuclear@0: 
nuclear@0: #else	// Software or OpenGL version
nuclear@0: 
nuclear@0: class Matrix4x4 {
nuclear@0: public:
nuclear@0: 	float m[4][4];
nuclear@0: 
nuclear@0: #endif	//NUC3D_VER_DIRECT3D
nuclear@0: 
nuclear@0: 	Matrix4x4();
nuclear@0: 	Matrix4x4(const Matrix4x4 &mat);
nuclear@0: 	Matrix4x4(const Matrix3x3 &mat);
nuclear@0: 	Matrix4x4(	float m00, float m01, float m02, float m03,
nuclear@0: 				float m10, float m11, float m12, float m13,
nuclear@0: 				float m20, float m21, float m22, float m23,
nuclear@0: 				float m30, float m31, float m32, float m33 );
nuclear@0: 
nuclear@0: 	// basic operations on matrices
nuclear@0: 	Matrix4x4 operator +(const Matrix4x4 &mat) const;
nuclear@0: 	Matrix4x4 operator -(const Matrix4x4 &mat) const;
nuclear@0: 	Matrix4x4 operator *(const Matrix4x4 &mat) const;
nuclear@0: 	Matrix4x4 operator *(float scalar) const;
nuclear@0: 	void operator +=(const Matrix4x4 &mat);
nuclear@0: 	void operator -=(const Matrix4x4 &mat);
nuclear@0: 	void operator *=(const Matrix4x4 &mat);
nuclear@0: 	void operator *=(float scalar);
nuclear@0: 
nuclear@0: 	void ResetIdentity();
nuclear@0: 
nuclear@0: 	// concatenate various transformation matrices with our current matrix
nuclear@0: 	void Translate(float x, float y, float z);
nuclear@0: 	void Rotate(float x, float y, float z);
nuclear@0: 	void Rotate(const Vector3 &axis, float rads);
nuclear@0: 	void Scale(float x, float y, float z);
nuclear@0: 
nuclear@0: 	// set the matrix to a specific transformation matrix
nuclear@0: 	void SetTranslation(float x, float y, float z);
nuclear@0: 	void SetRotation(float x, float y, float z);
nuclear@0: 	void SetRotation(const Vector3 &axis, float angle);
nuclear@0: 	void SetScaling(float x, float y, float z);
nuclear@0: 
nuclear@0: 	// row and column accessors
nuclear@0: 	void SetColumnVector(const Vector4 &vec, int columnindex);
nuclear@0: 	void SetRowVector(const Vector4 &vec, int rowindex);
nuclear@0: 	Vector4 GetColumnVector(int columnindex) const;
nuclear@0: 	Vector4 GetRowVector(int rowindex) const;
nuclear@0: 
nuclear@0: 	// other operations on matrices
nuclear@0: 	void Transpose();
nuclear@0: 	Matrix4x4 Transposed() const;
nuclear@0: 
nuclear@0: 	float Determinant() const;
nuclear@0: 	Matrix4x4 Adjoint() const;
nuclear@0: 	Matrix4x4 Inverse() const;
nuclear@0: };
nuclear@0: 
nuclear@0: 
nuclear@0: ////////////////// Matrix3x3 //////////////////
nuclear@0: class Matrix3x3 {
nuclear@0: public:
nuclear@0: 	float m[3][3];
nuclear@0: 
nuclear@0: 	Matrix3x3();
nuclear@0: 	Matrix3x3(const Matrix3x3 &mat);
nuclear@0: 	Matrix3x3(	float m00, float m01, float m02,
nuclear@0: 				float m10, float m11, float m12,
nuclear@0: 				float m20, float m21, float m22 );
nuclear@0: 
nuclear@0: 	// basic operations on matrices
nuclear@0: 	Matrix3x3 operator +(const Matrix3x3 &mat) const;
nuclear@0: 	Matrix3x3 operator -(const Matrix3x3 &mat) const;
nuclear@0: 	Matrix3x3 operator *(const Matrix3x3 &mat) const;
nuclear@0: 	Matrix3x3 operator *(float scalar) const;
nuclear@0: 	void operator +=(const Matrix3x3 &mat);
nuclear@0: 	void operator -=(const Matrix3x3 &mat);
nuclear@0: 	void operator *=(const Matrix3x3 &mat);
nuclear@0: 	void operator *=(float scalar);
nuclear@0: 
nuclear@0: 	void ResetIdentity();
nuclear@0: 
nuclear@0: 	// concatenate various transformation matrices with our current matrix
nuclear@0: 	void Translate(float x, float y);
nuclear@0: 	void Rotate(float angle);
nuclear@0: 	void Scale(float x, float y);
nuclear@0: 	
nuclear@0: 	// set the matrix to a specific transformation matrix
nuclear@0: 	void SetTranslation(float x, float y);
nuclear@0: 	void SetRotation(float angle);
nuclear@0: 	void SetScaling(float x, float y);
nuclear@0: 
nuclear@0: 	// row and column accessors
nuclear@0: 	void SetColumnVector(const Vector3 &vec, int columnindex);
nuclear@0: 	void SetRowVector(const Vector3 &vec, int rowindex);
nuclear@0: 	Vector3 GetColumnVector(int columnindex) const;
nuclear@0: 	Vector3 GetRowVector(int rowindex) const;
nuclear@0: 
nuclear@0: 	// other operations on matrices
nuclear@0: 	void Transpose();
nuclear@0: 	Matrix3x3 Transposed() const;
nuclear@0: 
nuclear@0: 	void OrthoNormalize();
nuclear@0: 	Matrix3x3 OrthoNormalized();
nuclear@0: 
nuclear@0: 	//float Determinant() const; // NYI
nuclear@0: 	//Matrix3x3 Adjoint() const;
nuclear@0: 	//Matrix3x3 Inverse() const;
nuclear@0: };
nuclear@0: 
nuclear@0: ///////////////// ray /////////////////
nuclear@0: 
nuclear@0: class Ray {
nuclear@0: public:
nuclear@0: 	Vector3 Origin;
nuclear@0: 	Vector3 Direction;
nuclear@0: 	float Energy;
nuclear@0: 	float CurrentIOR;
nuclear@0: 
nuclear@0: 	Ray();
nuclear@0: 	Ray(const Vector3 &origin, const Vector3 &direction);
nuclear@0: };
nuclear@0: 
nuclear@0: // a coordinate system basis
nuclear@0: class Base {
nuclear@0: public:
nuclear@0: 	Vector3 i, j, k;
nuclear@0: 
nuclear@0: 	Base();
nuclear@0: 	Base(const Vector3 &i, const Vector3 &j, const Vector3 &k);
nuclear@0: 	Base(const Vector3 &dir, bool LeftHanded=true);
nuclear@0: 
nuclear@0: 	void Rotate(float x, float y, float z);
nuclear@0: 	void Rotate(const Vector3 &axis, float angle);
nuclear@0: 	void Rotate(const Matrix4x4 &mat);
nuclear@0: 	void Rotate(const Quaternion &quat);
nuclear@0: 
nuclear@0: 	Matrix3x3 CreateRotationMatrix() const;
nuclear@0: };
nuclear@0: 
nuclear@0: 
nuclear@0: 
nuclear@0: float frand(float range);
nuclear@0: 
nuclear@0: 
nuclear@0: #include "n3dmath.inl"
nuclear@0: 
nuclear@0: #endif	// _N3DMATH_H_