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#ifndef __VMATH_H__
#define __VMATH_H__
#define _USE_MATH_DEFINES 1 // Include constants defined in math.h
#include <math.h>
namespace vmath
{
template <typename T, const int w, const int h> class matNM;
template <typename T, const int len> class vecN;
template <typename T> class Tquaternion;
template <typename T>
inline T degrees(T angleInRadians)
{
return angleInRadians * static_cast<T>(180.0/M_PI);
}
template <typename T>
inline T radians(T angleInDegrees)
{
return angleInDegrees * static_cast<T>(M_PI/180.0);
}
template <typename T>
struct random
{
operator T ()
{
static unsigned int seed = 0x13371337;
unsigned int res;
unsigned int tmp;
seed *= 16807;
tmp = seed ^ (seed >> 4) ^ (seed << 15);
res = (tmp >> 9) | 0x3F800000;
return static_cast<T>(res);
}
};
template<>
struct random<float>
{
operator float()
{
static unsigned int seed = 0x13371337;
float res;
unsigned int tmp;
seed *= 16807;
tmp = seed ^ (seed >> 4) ^ (seed << 15);
*((unsigned int *) &res) = (tmp >> 9) | 0x3F800000;
return (res - 1.0f);
}
};
template<>
struct random<unsigned int>
{
operator unsigned int()
{
static unsigned int seed = 0x13371337;
unsigned int res;
unsigned int tmp;
seed *= 16807;
tmp = seed ^ (seed >> 4) ^ (seed << 15);
res = (tmp >> 9) | 0x3F800000;
return res;
}
};
template <typename T, const int len>
class vecN
{
public:
typedef class vecN<T,len> my_type;
typedef T element_type;
// Default constructor does nothing, just like built-in types
inline vecN()
{
// Uninitialized variable
}
// Copy constructor
inline vecN(const vecN& that)
{
assign(that);
}
// Construction from scalar
inline vecN(T s)
{
int n;
for (n = 0; n < len; n++)
{
data[n] = s;
}
}
// Assignment operator
inline vecN& operator=(const vecN& that)
{
assign(that);
return *this;
}
inline vecN& operator=(const T& that)
{
int n;
for (n = 0; n < len; n++)
data[n] = that;
return *this;
}
inline vecN operator+(const vecN& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] + that.data[n];
return result;
}
inline vecN& operator+=(const vecN& that)
{
return (*this = *this + that);
}
inline vecN operator-() const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = -data[n];
return result;
}
inline vecN operator-(const vecN& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] - that.data[n];
return result;
}
inline vecN& operator-=(const vecN& that)
{
return (*this = *this - that);
}
inline vecN operator*(const vecN& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] * that.data[n];
return result;
}
inline vecN& operator*=(const vecN& that)
{
return (*this = *this * that);
}
inline vecN operator*(const T& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] * that;
return result;
}
inline vecN& operator*=(const T& that)
{
assign(*this * that);
return *this;
}
inline vecN operator/(const vecN& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] / that.data[n];
return result;
}
inline vecN& operator/=(const vecN& that)
{
assign(*this / that);
return *this;
}
inline vecN operator/(const T& that) const
{
my_type result;
int n;
for (n = 0; n < len; n++)
result.data[n] = data[n] / that;
return result;
}
inline vecN& operator/=(const T& that)
{
assign(*this / that);
return *this;
}
inline T& operator[](int n) { return data[n]; }
inline const T& operator[](int n) const { return data[n]; }
inline static int size(void) { return len; }
inline operator const T* () const { return &data[0]; }
static inline vecN random()
{
vecN result;
int i;
for (i = 0; i < len; i++)
{
result[i] = vmath::random<T>();
}
return result;
}
protected:
T data[len];
inline void assign(const vecN& that)
{
int n;
for (n = 0; n < len; n++)
data[n] = that.data[n];
}
};
template <typename T>
class Tvec2 : public vecN<T,2>
{
public:
typedef vecN<T,2> base;
// Uninitialized variable
inline Tvec2() {}
// Copy constructor
inline Tvec2(const base& v) : base(v) {}
// vec2(x, y);
inline Tvec2(T x, T y)
{
base::data[0] = x;
base::data[1] = y;
}
};
template <typename T>
class Tvec3 : public vecN<T,3>
{
public:
typedef vecN<T,3> base;
// Uninitialized variable
inline Tvec3() {}
// Copy constructor
inline Tvec3(const base& v) : base(v) {}
// vec3(x, y, z);
inline Tvec3(T x, T y, T z)
{
base::data[0] = x;
base::data[1] = y;
base::data[2] = z;
}
// vec3(v, z);
inline Tvec3(const Tvec2<T>& v, T z)
{
base::data[0] = v[0];
base::data[1] = v[1];
base::data[2] = z;
}
// vec3(x, v)
inline Tvec3(T x, const Tvec2<T>& v)
{
base::data[0] = x;
base::data[1] = v[0];
base::data[2] = v[1];
}
};
template <typename T>
class Tvec4 : public vecN<T,4>
{
public:
typedef vecN<T,4> base;
// Uninitialized variable
inline Tvec4() {}
// Copy constructor
inline Tvec4(const base& v) : base(v) {}
// vec4(x, y, z, w);
inline Tvec4(T x, T y, T z, T w)
{
base::data[0] = x;
base::data[1] = y;
base::data[2] = z;
base::data[3] = w;
}
// vec4(v, z, w);
inline Tvec4(const Tvec2<T>& v, T z, T w)
{
base::data[0] = v[0];
base::data[1] = v[1];
base::data[2] = z;
base::data[3] = w;
}
// vec4(x, v, w);
inline Tvec4(T x, const Tvec2<T>& v, T w)
{
base::data[0] = x;
base::data[1] = v[0];
base::data[2] = v[1];
base::data[3] = w;
}
// vec4(x, y, v);
inline Tvec4(T x, T y, const Tvec2<T>& v)
{
base::data[0] = x;
base::data[1] = y;
base::data[2] = v[0];
base::data[3] = v[1];
}
// vec4(v1, v2);
inline Tvec4(const Tvec2<T>& u, const Tvec2<T>& v)
{
base::data[0] = u[0];
base::data[1] = u[1];
base::data[2] = v[0];
base::data[3] = v[1];
}
// vec4(v, w);
inline Tvec4(const Tvec3<T>& v, T w)
{
base::data[0] = v[0];
base::data[1] = v[1];
base::data[2] = v[2];
base::data[3] = w;
}
// vec4(x, v);
inline Tvec4(T x, const Tvec3<T>& v)
{
base::data[0] = x;
base::data[1] = v[0];
base::data[2] = v[1];
base::data[3] = v[2];
}
};
// These types don't exist in GLSL and don't have full implementations
// (constructors and such). This is enough to get some template functions
// to compile correctly.
typedef vecN<float, 1> vec1;
typedef vecN<int, 1> ivec1;
typedef vecN<unsigned int, 1> uvec1;
typedef vecN<double, 1> dvec1;
typedef Tvec2<float> vec2;
typedef Tvec2<int> ivec2;
typedef Tvec2<unsigned int> uvec2;
typedef Tvec2<double> dvec2;
typedef Tvec3<float> vec3;
typedef Tvec3<int> ivec3;
typedef Tvec3<unsigned int> uvec3;
typedef Tvec3<double> dvec3;
typedef Tvec4<float> vec4;
typedef Tvec4<int> ivec4;
typedef Tvec4<unsigned int> uvec4;
typedef Tvec4<double> dvec4;
template <typename T, int n>
static inline const vecN<T,n> operator * (T x, const vecN<T,n>& v)
{
return v * x;
}
template <typename T>
static inline const Tvec2<T> operator / (T x, const Tvec2<T>& v)
{
return Tvec2<T>(x / v[0], x / v[1]);
}
template <typename T>
static inline const Tvec3<T> operator / (T x, const Tvec3<T>& v)
{
return Tvec3<T>(x / v[0], x / v[1], x / v[2]);
}
template <typename T>
static inline const Tvec4<T> operator / (T x, const Tvec4<T>& v)
{
return Tvec4<T>(x / v[0], x / v[1], x / v[2], x / v[3]);
}
template <typename T, int len>
static inline T dot(const vecN<T,len>& a, const vecN<T,len>& b)
{
int n;
T total = T(0);
for (n = 0; n < len; n++)
{
total += a[n] * b[n];
}
return total;
}
template <typename T>
static inline vecN<T,3> cross(const vecN<T,3>& a, const vecN<T,3>& b)
{
return Tvec3<T>(a[1] * b[2] - b[1] * a[2],
a[2] * b[0] - b[2] * a[0],
a[0] * b[1] - b[0] * a[1]);
}
template <typename T, int len>
static inline T length(const vecN<T,len>& v)
{
T result(0);
for (int i = 0; i < v.size(); ++i)
{
result += v[i] * v[i];
}
return (T)sqrt(result);
}
template <typename T, int len>
static inline vecN<T,len> normalize(const vecN<T,len>& v)
{
return v / length(v);
}
template <typename T, int len>
static inline T distance(const vecN<T,len>& a, const vecN<T,len>& b)
{
return length(b - a);
}
template <typename T, int len>
static inline T angle(const vecN<T,len>& a, const vecN<T,len>& b)
{
return arccos(dot(a, b));
}
template <typename T>
class Tquaternion
{
public:
inline Tquaternion()
{
}
inline Tquaternion(const Tquaternion& q)
: r(q.r),
v(q.v)
{
}
inline Tquaternion(T _r)
: r(_r),
v(T(0))
{
}
inline Tquaternion(T _r, const Tvec3<T>& _v)
: r(_r),
v(_v)
{
}
inline Tquaternion(const Tvec4<T>& _v)
: r(_v[0]),
v(_v[1], _v[2], _v[3])
{
}
inline Tquaternion(T _x, T _y, T _z, T _w)
: r(_x),
v(_y, _z, _w)
{
}
inline T& operator[](int n)
{
return a[n];
}
inline const T& operator[](int n) const
{
return a[n];
}
inline Tquaternion operator+(const Tquaternion& q) const
{
return quaternion(r + q.r, v + q.v);
}
inline Tquaternion& operator+=(const Tquaternion& q)
{
r += q.r;
v += q.v;
return *this;
}
inline Tquaternion operator-(const Tquaternion& q) const
{
return quaternion(r - q.r, v - q.v);
}
inline Tquaternion& operator-=(const Tquaternion& q)
{
r -= q.r;
v -= q.v;
return *this;
}
inline Tquaternion operator-() const
{
return Tquaternion(-r, -v);
}
inline Tquaternion operator*(const T s) const
{
return Tquaternion(a[0] * s, a[1] * s, a[2] * s, a[3] * s);
}
inline Tquaternion& operator*=(const T s)
{
r *= s;
v *= s;
return *this;
}
inline Tquaternion operator*(const Tquaternion& q) const
{
const T x1 = a[0];
const T y1 = a[1];
const T z1 = a[2];
const T w1 = a[3];
const T x2 = q.a[0];
const T y2 = q.a[1];
const T z2 = q.a[2];
const T w2 = q.a[3];
return Tquaternion(w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
w1 * y2 + y1 * w2 + z1 * x2 - x1 * z2,
w1 * z2 + z1 * w2 + x1 * y2 - y1 * x2,
w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2);
}
inline Tquaternion operator/(const T s) const
{
return Tquaternion(a[0] / s, a[1] / s, a[2] / s, a[3] / s);
}
inline Tquaternion& operator/=(const T s)
{
r /= s;
v /= s;
return *this;
}
inline operator Tvec4<T>&()
{
return *(Tvec4<T>*)&a[0];
}
inline operator const Tvec4<T>&() const
{
return *(const Tvec4<T>*)&a[0];
}
inline bool operator==(const Tquaternion& q) const
{
return (r == q.r) && (v == q.v);
}
inline bool operator!=(const Tquaternion& q) const
{
return (r != q.r) || (v != q.v);
}
inline matNM<T,4,4> asMatrix() const
{
matNM<T,4,4> m;
const T xx = x * x;
const T yy = y * y;
const T zz = z * z;
const T ww = w * w;
const T xy = x * y;
const T xz = x * z;
const T xw = x * w;
const T yz = y * z;
const T yw = y * w;
const T zw = z * w;
m[0][0] = T(1) - T(2) * (yy + zz);
m[0][1] = T(2) * (xy - zw);
m[0][2] = T(2) * (xz + yw);
m[0][3] = T(0);
m[1][0] = T(2) * (xy + zw);
m[1][1] = T(1) - T(2) * (xx + zz);
m[1][2] = T(2) * (yz - xw);
m[1][3] = T(0);
m[2][0] = T(2) * (xz - yw);
m[2][1] = T(2) * (yz + xw);
m[2][2] = T(1) - T(2) * (xx + yy);
m[2][3] = T(0);
m[3][0] = T(0);
m[3][1] = T(0);
m[3][2] = T(0);
m[3][3] = T(1);
return m;
}
/*
inline T length() const
{
return vmath::length( Tvec4<T>(r, v) );
}
*/
private:
union
{
struct
{
T r;
Tvec3<T> v;
};
struct
{
T x;
T y;
T z;
T w;
};
T a[4];
};
};
typedef Tquaternion<float> quaternion;
typedef Tquaternion<int> iquaternion;
typedef Tquaternion<unsigned int> uquaternion;
typedef Tquaternion<double> dquaternion;
template <typename T>
static inline Tquaternion<T> operator*(T a, const Tquaternion<T>& b)
{
return b * a;
}
template <typename T>
static inline Tquaternion<T> operator/(T a, const Tquaternion<T>& b)
{
return Tquaternion<T>(a / b[0], a / b[1], a / b[2], a / b[3]);
}
template <typename T>
static inline Tquaternion<T> normalize(const Tquaternion<T>& q)
{
return q / length(vecN<T,4>(q));
}
template <typename T, const int w, const int h>
class matNM
{
public:
typedef class matNM<T,w,h> my_type;
typedef class vecN<T,h> vector_type;
// Default constructor does nothing, just like built-in types
inline matNM()
{
// Uninitialized variable
}
// Copy constructor
inline matNM(const matNM& that)
{
assign(that);
}
// Construction from element type
// explicit to prevent assignment from T
explicit inline matNM(T f)
{
for (int n = 0; n < w; n++)
{
data[n] = f;
}
}
// Construction from vector
inline matNM(const vector_type& v)
{
for (int n = 0; n < w; n++)
{
data[n] = v;
}
}
// Assignment operator
inline matNM& operator=(const my_type& that)
{
assign(that);
return *this;
}
inline matNM operator+(const my_type& that) const
{
my_type result;
int n;
for (n = 0; n < w; n++)
result.data[n] = data[n] + that.data[n];
return result;
}
inline my_type& operator+=(const my_type& that)
{
return (*this = *this + that);
}
inline my_type operator-(const my_type& that) const
{
my_type result;
int n;
for (n = 0; n < w; n++)
result.data[n] = data[n] - that.data[n];
return result;
}
inline my_type& operator-=(const my_type& that)
{
return (*this = *this - that);
}
inline my_type operator*(const T& that) const
{
my_type result;
int n;
for (n = 0; n < w; n++)
result.data[n] = data[n] * that;
return result;
}
inline my_type& operator*=(const T& that)
{
int n;
for (n = 0; n < w; n++)
data[n] = data[n] * that;
return *this;
}
// Matrix multiply.
// TODO: This only works for square matrices. Need more template skill to make a non-square version.
inline my_type operator*(const my_type& that) const
{
my_type result(0);
for (int j = 0; j < w; j++)
{
for (int i = 0; i < h; i++)
{
T sum(0);
for (int n = 0; n < w; n++)
{
sum += data[n][i] * that[j][n];
}
result[j][i] = sum;
}
}
return result;
}
inline my_type& operator*=(const my_type& that)
{
return (*this = *this * that);
}
inline vector_type& operator[](int n) { return data[n]; }
inline const vector_type& operator[](int n) const { return data[n]; }
inline operator T*() { return &data[0][0]; }
inline operator const T*() const { return &data[0][0]; }
inline matNM<T,h,w> transpose(void) const
{
matNM<T,h,w> result;
int x, y;
for (y = 0; y < w; y++)
{
for (x = 0; x < h; x++)
{
result[x][y] = data[y][x];
}
}
return result;
}
static inline my_type identity()
{
my_type result(0);
for (int i = 0; i < w; i++)
{
result[i][i] = 1;
}
return result;
}
static inline int width(void) { return w; }
static inline int height(void) { return h; }
protected:
// Column primary data (essentially, array of vectors)
vecN<T,h> data[w];
// Assignment function - called from assignment operator and copy constructor.
inline void assign(const matNM& that)
{
int n;
for (n = 0; n < w; n++)
data[n] = that.data[n];
}
};
/*
template <typename T, const int N>
class TmatN : public matNM<T,N,N>
{
public:
typedef matNM<T,N,N> base;
typedef TmatN<T,N> my_type;
inline TmatN() {}
inline TmatN(const my_type& that) : base(that) {}
inline TmatN(float f) : base(f) {}
inline TmatN(const vecN<T,4>& v) : base(v) {}
inline my_type transpose(void)
{
my_type result;
int x, y;
for (y = 0; y < h; y++)
{
for (x = 0; x < h; x++)
{
result[x][y] = data[y][x];
}
}
return result;
}
};
*/
template <typename T>
class Tmat4 : public matNM<T,4,4>
{
public:
typedef matNM<T,4,4> base;
typedef Tmat4<T> my_type;
inline Tmat4() {}
inline Tmat4(const my_type& that) : base(that) {}
inline Tmat4(const base& that) : base(that) {}
inline Tmat4(const vecN<T,4>& v) : base(v) {}
inline Tmat4(const vecN<T,4>& v0,
const vecN<T,4>& v1,
const vecN<T,4>& v2,
const vecN<T,4>& v3)
{
base::data[0] = v0;
base::data[1] = v1;
base::data[2] = v2;
base::data[3] = v3;
}
};
typedef Tmat4<float> mat4;
typedef Tmat4<int> imat4;
typedef Tmat4<unsigned int> umat4;
typedef Tmat4<double> dmat4;
template <typename T>
class Tmat3 : public matNM<T,3,3>
{
public:
typedef matNM<T,3,3> base;
typedef Tmat3<T> my_type;
inline Tmat3() {}
inline Tmat3(const my_type& that) : base(that) {}
inline Tmat3(const base& that) : base(that) {}
inline Tmat3(const vecN<T,3>& v) : base(v) {}
inline Tmat3(const vecN<T,3>& v0,
const vecN<T,3>& v1,
const vecN<T,3>& v2)
{
base::data[0] = v0;
base::data[1] = v1;
base::data[2] = v2;
}
};
typedef Tmat3<float> mat3;
typedef Tmat3<int> imat3;
typedef Tmat3<unsigned int>umat3;
typedef Tmat3<double> dmat3;
template <typename T>
class Tmat2 : public matNM<T,2,2>
{
public:
typedef matNM<T,2,2> base;
typedef Tmat2<T> my_type;
inline Tmat2() {}
inline Tmat2(const my_type& that) : base(that) {}
inline Tmat2(const base& that) : base(that) {}
inline Tmat2(const vecN<T,2>& v) : base(v) {}
inline Tmat2(const vecN<T,2>& v0,
const vecN<T,2>& v1)
{
base::data[0] = v0;
base::data[1] = v1;
}
};
typedef Tmat2<float> mat2;
static inline mat4 frustum(float left, float right, float bottom, float top, float n, float f)
{
mat4 result(mat4::identity());
if ((right == left) ||
(top == bottom) ||
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