#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>
inline T radians(T angleInRadians)
{
return angleInRadians * static_cast<T>(180.0/M_PI);
}
template <const bool cond>
class ensure
{
public:
inline ensure() { switch (false) { case false: case cond: break; } }
};
template <typename T, const int len> class vecN;
template <typename T, const int len>
class vecN
{
public:
typedef class vecN<T,len> my_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 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);
}
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]; }
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];
}
};
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, 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);
}
// 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
{
ensure<w == h>();
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()
{
ensure<w == h>();
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;
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) ||
(n == f) ||
(n < 0.0) ||
(f < 0.0))
return result;
result[0][0] = (2.0f * n) / (right - left);
result[1][1] = (2.0f * n) / (top - bottom);
result[2][0] = (right + left) / (right - left);
result[2][1] = (top + bottom) / (top - bottom);
result[2][2] = -(f + n) / (f - n);
result[2][3]= -1.0f;
result[3][2] = -(2.0f * f * n) / (f - n);
result[3][3] = 0.0f;
return result;
}
static inline mat4 perspective(float fovy /* in degrees */, float aspect, float n, float f)
{
float top = n * tan(radians(0.5f*fovy)); // bottom = -top
float right = top * aspect; // left = -right
return frustum(-right, right, -top, top, n, f);
}
template <typename T>
static inline Tmat4<T> lookat(vecN<T,3> eye, vecN<T,3> center, vecN<T,3> up)
{
const Tvec3<T> f = normalize(center - eye);
const Tvec3<T> upN = normalize(up);
const Tvec3<T> s = cross(f, upN);
const Tvec3<T> u = cross(s, f);
const Tmat4<T> M = Tmat4<T>(Tvec4<T>(s[0], u[0], -f[0], T(0)),
Tvec4<T>(s[1], u[1], -f[1], T(0)),
Tvec4<T>(s[2], u[2], -f[2], T(0)),
Tvec4<T>(T(0), T(0), T(0), T(1)));
return M * translate(-eye);
}
template <typename T>
static inline Tmat4<T> translate(T x, T y, T z)
{
return Tmat4<T>(Tvec4<T>(1.0f, 0.0f, 0.0f, 0.0f),
Tvec4<T>(0.0f, 1.0f, 0.0f, 0.0f),
Tvec4<T>(0.0f, 0.0f, 1.0f, 0.0f),
Tvec4<T>(x, y, z, 1.0f));
}
template <typename T>
static inline Tmat4<T> translate(const vecN<T,3>& v)
{
return translate(v[0], v[1], v[2]);
}
template <typename T>
static inline Tmat4<T> scale(T x, T y, T z)
{
return Tmat4<T>(Tvec4<T>(x, 0.0f, 0.0f, 0.0f),
Tvec4<T>(0.0f, y, 0.0f, 0.0f),
Tvec4<T>(0.0f, 0.0f, z, 0.0f),
Tvec4<T>(0.0f, 0.0f, 0.0f, 1.0f));
}
template <typename T>
static inline Tmat4<T> scale(const Tvec4<T>& v)
{
return scale(v[0], v[1], v[2]);
}
template <typename T>
static inline Tmat4<T> scale(T x)
{
return Tmat4<T>(Tvec4<T>(x, 0.0f, 0.0f, 0.0f),
Tvec4<T>(0.0f, x, 0.0f, 0.0f),
Tvec4<T>(0.0f, 0.0f, x, 0.0f),
Tvec4<T>(0.0f, 0.0f, 0.0f, 1.0f));
}
template <typename T>
static inline Tmat4<T> rotate(T angle, T x, T y, T z)
{
Tmat4<T> result;
const T x2 = x * x;
const T y2 = y * y;
const T z2 = z * z;
float rads = float(angle) * 0.0174532925f;
const float c = cosf(rads);
const float s = sinf(rads);
const float omc = 1.0f - c;
result[0] = Tvec4<T>(T(x2 * omc + c), T(y * x * omc + z * s), T(x * z * omc - y * s), T(0));
result[1] = Tvec4<T>(T(x * y * omc - z * s), T(y2 * omc + c), T(y * z * omc + x * s), T(0));
result[2] = Tvec4<T>(T(x * z * omc + y * s), T(y * z * omc - x * s), T(z2 * omc + c), T(0));
result[3] = Tvec4<T>(T(0), T(0), T(0), T(1));
return result;
}
template <typename T>
static inline Tmat4<T> rotate(T angle, const vecN<T,3>& v)
{
return rotate<T>(angle, v[0], v[1], v[2]);
}
#ifdef min
#undef min
#endif
template <typename T>
static inline T min(T a, T b)
{
return a < b ? a : b;
}
#ifdef max
#undef max
#endif
template <typename T>
static inline T max(T a, T b)
{
return a >= b ? a : b;
}
template <typename T, const int N>
static inline vecN<T,N> min(const vecN<T,N>& x, const vecN<T,N>& y)
{
vecN<T,N> t;
int n;
for (n = 0; n < N; n++)
{
t[n] = min(x[n], y[n]);
}
return t;
}
template <typename T, const int N>
static inline vecN<T,N> max(const vecN<T,N>& x, const vecN<T,N>& y)
{
vecN<T,N> t;
int n;
for (n = 0; n < N; n++)
{
t[n] = max<T>(x[n], y[n]);
}
return t;
}
template <typename T, const int N>
static inline vecN<T,N> clamp(const vecN<T,N>& x, const vecN<T,N>& minVal, const vecN<T,N>& maxVal)
{
return min<T>(max<T>(x, minVal), maxVal);
}
template <typename T, const int N>
static inline vecN<T,N> smoothstep(const vecN<T,N>& edge0, const vecN<T,N>& edge1, const vecN<T,N>& x)
{
vecN<T,N> t;
t = clamp((x - edge0) / (edge1 - edge0), vecN<T,N>(T(0)), vecN<T,N>(T(1)));
return t * t * (vecN<T,N>(T(3)) - vecN<T,N>(T(2)) * t);
}
template <typename T, const int N, const int M>
static inline matNM<T,N,M> matrixCompMult(const matNM<T,N,M>& x, const matNM<T,N,M>& y)
{
matNM<T,N,M> result;
int i, j;
for (j = 0; j < M; ++j)
{
for (i = 0; i < N; ++i)
{
result[i][j] = x[i][j] * y[i][j];
}
}
return result;
}
template <typename T, const int N, const int M>
static inline vecN<T,N> operator*(const vecN<T,M>& vec, const matNM<T,N,M>& mat)
{
int n, m;
vecN<T,N> result(T(0));
for (m = 0; m < M; m++)
{
for (n = 0; n < N; n++)
{
result[n] += vec[m] * mat[n][m];
}
}
return result;
}
};
#endif /* __VMATH_H__ */