#ifndef VEC_H

#define VEC_H

#include <cassert>

#include <cmath>

#include <iostream>

#include "util.h"

// Defines a thin wrapper around fixed size C-style arrays, using template parameters,

// which is useful for dealing with vectors of different dimensions.

// For example, float[3] is equivalent to Vec<3,float>.

// Entries in the vector are accessed with the overloaded [] operator, so

// for example if x is a Vec<3,float>, then the middle entry is x[1].

// For convenience, there are a number of typedefs for abbreviation:

// Vec<3,float> -> Vec3f

// Vec<2,int> -> Vec2i

// and so on.

// Arithmetic operators are appropriately overloaded, and functions are defined

// for additional operations (such as dot-products, norms, cross-products, etc.)

template<unsigned int N, class T>

struct Vec

{

T v[N];

Vec<N,T>(void)

{}

explicit Vec<N,T>(T value_for_all)

{ for(unsigned int i=0; i<N; ++i) v[i]=value_for_all; }

template<class S>

explicit Vec<N,T>(const S *source)

{ for(unsigned int i=0; i<N; ++i) v[i]=(T)source[i]; }

template <class S>

explicit Vec<N,T>(const Vec<N,S>& source)

{ for(unsigned int i=0; i<N; ++i) v[i]=(T)source[i]; }

Vec<N,T>(T v0, T v1)

{

assert(N==2);

v[0]=v0; v[1]=v1;

}

Vec<N,T>(T v0, T v1, T v2)

{

assert(N==3);

v[0]=v0; v[1]=v1; v[2]=v2;

}

Vec<N,T>(T v0, T v1, T v2, T v3)

{

assert(N==4);

v[0]=v0; v[1]=v1; v[2]=v2; v[3]=v3;

}

Vec<N,T>(T v0, T v1, T v2, T v3, T v4)

{

assert(N==5);

v[0]=v0; v[1]=v1; v[2]=v2; v[3]=v3; v[4]=v4;

}

Vec<N,T>(T v0, T v1, T v2, T v3, T v4, T v5)

{

assert(N==6);

v[0]=v0; v[1]=v1; v[2]=v2; v[3]=v3; v[4]=v4; v[5]=v5;

}

T &operator[](int index)

{

assert(0<=index && (unsigned int)index<N);

return v[index];

}

const T &operator[](int index) const

{

assert(0<=index && (unsigned int)index<N);

return v[index];

}

bool nonzero(void) const

{

for(unsigned int i=0; i<N; ++i) if(v[i]) return true;

return false;

}

Vec<N,T> operator+=(const Vec<N,T> &w)

{

for(unsigned int i=0; i<N; ++i) v[i]+=w[i];

return *this;

}

Vec<N,T> operator+(const Vec<N,T> &w) const

{

Vec<N,T> sum(*this);

sum+=w;

return sum;

}

Vec<N,T> operator-=(const Vec<N,T> &w)

{

for(unsigned int i=0; i<N; ++i) v[i]-=w[i];

return *this;

}

Vec<N,T> operator-(void) const // unary minus

{

Vec<N,T> negative;

for(unsigned int i=0; i<N; ++i) negative.v[i]=-v[i];

return negative;

}

Vec<N,T> operator-(const Vec<N,T> &w) const // (binary) subtraction

{

Vec<N,T> diff(*this);

diff-=w;

return diff;

}

Vec<N,T> operator*=(T a)

{

for(unsigned int i=0; i<N; ++i) v[i]*=a;

return *this;

}

Vec<N,T> operator*(T a) const

{

Vec<N,T> w(*this);

w*=a;

return w;

}

Vec<N,T> operator*=(const Vec<N,T> &w)

{

for(unsigned int i=0; i<N; ++i) v[i]*=w.v[i];

return *this;

}

Vec<N,T> operator*(const Vec<N,T> &w) const

{

Vec<N,T> componentwise_product;

for(unsigned int i=0; i<N; ++i) componentwise_product[i]=v[i]*w.v[i];

return componentwise_product;

}

Vec<N,T> operator/=(T a)

{

for(unsigned int i=0; i<N; ++i) v[i]/=a;

return *this;

}

Vec<N,T> operator/(T a) const

{

Vec<N,T> w(*this);

w/=a;

return w;

}

};

typedef Vec<2,double> Vec2d;

typedef Vec<2,float> Vec2f;

typedef Vec<2,int> Vec2i;

typedef Vec<2,unsigned int> Vec2ui;

typedef Vec<2,short> Vec2s;

typedef Vec<2,unsigned short> Vec2us;

typedef Vec<2,char> Vec2c;

typedef Vec<2,unsigned char> Vec2uc;

typedef Vec<3,double> Vec3d;

typedef Vec<3,float> Vec3f;

typedef Vec<3,int> Vec3i;

typedef Vec<3,unsigned int> Vec3ui;

typedef Vec<3,short> Vec3s;

typedef Vec<3,unsigned short> Vec3us;

typedef Vec<3,char> Vec3c;

typedef Vec<3,unsigned char> Vec3uc;

typedef Vec<4,double> Vec4d;

typedef Vec<4,float> Vec4f;

typedef Vec<4,int> Vec4i;

typedef Vec<4,unsigned int> Vec4ui;

typedef Vec<4,short> Vec4s;

typedef Vec<4,unsigned short> Vec4us;

typedef Vec<4,char> Vec4c;

typedef Vec<4,unsigned char> Vec4uc;

typedef Vec<6,double> Vec6d;

typedef Vec<6,float> Vec6f;

typedef Vec<6,unsigned int> Vec6ui;

typedef Vec<6,int> Vec6i;

typedef Vec<6,short> Vec6s;

typedef Vec<6,unsigned short> Vec6us;

typedef Vec<6,char> Vec6c;

typedef Vec<6,unsigned char> Vec6uc;

template<unsigned int N, class T>

T mag2(const Vec<N,T> &a)

{

T l=sqr(a.v[0]);

for(unsigned int i=1; i<N; ++i) l+=sqr(a.v[i]);

return l;

}

template<unsigned int N, class T>

T mag(const Vec<N,T> &a)

{ return sqrt(mag2(a)); }

template<unsigned int N, class T>

inline T dist2(const Vec<N,T> &a, const Vec<N,T> &b)

{

T d=sqr(a.v[0]-b.v[0]);

for(unsigned int i=1; i<N; ++i) d+=sqr(a.v[i]-b.v[i]);

return d;

}

template<unsigned int N, class T>

inline T dist(const Vec<N,T> &a, const Vec<N,T> &b)

{ return std::sqrt(dist2(a,b)); }

template<unsigned int N, class T>

inline void normalize(Vec<N,T> &a)

{ a/=mag(a); }

template<unsigned int N, class T>

inline Vec<N,T> normalized(const Vec<N,T> &a)

{ return a/mag(a); }

template<unsigned int N, class T>

inline T infnorm(const Vec<N,T> &a)

{

T d=std::fabs(a.v[0]);

for(unsigned int i=1; i<N; ++i) d=max(std::fabs(a.v[i]),d);

return d;

}

template<unsigned int N, class T>

void zero(Vec<N,T> &a)

{

for(unsigned int i=0; i<N; ++i)

a.v[i] = 0;

}

template<unsigned int N, class T>

std::ostream &operator<<(std::ostream &out, const Vec<N,T> &v)

{

out<<v.v[0];

for(unsigned int i=1; i<N; ++i)

out<<' '<<v.v[i];

return out;

}

template<unsigned int N, class T>

std::istream &operator>>(std::istream &in, Vec<N,T> &v)

{

in>>v.v[0];

for(unsigned int i=1; i<N; ++i)

in>>v.v[i];

return in;

}

template<unsigned int N, class T>

inline bool operator==(const Vec<N,T> &a, const Vec<N,T> &b)

{

bool t = (a.v[0] == b.v[0]);

unsigned int i=1;

while(i<N && t) {

t = t && (a.v[i]==b.v[i]);

++i;

}

return t;

}

template<unsigned int N, class T>

inline bool operator!=(const Vec<N,T> &a, const Vec<N,T> &b)

{

bool t = (a.v[0] != b.v[0]);

unsigned int i=1;

while(i<N && !t) {

t = t || (a.v[i]!=b.v[i]);

++i;

}

return t;

}

template<unsigned int N, class T>

inline Vec<N,T> operator*(T a, const Vec<N,T> &v)

{

Vec<N,T> w(v);

w*=a;

return w;

}

template<unsigned int N, class T>

inline T min(const Vec<N,T> &a)

{

T m=a.v[0];

for(unsigned int i=1; i<N; ++i) if(a.v[i]<m) m=a.v[i];

return m;

}

template<unsigned int N, class T>

inline Vec<N,T> min_union(const Vec<N,T> &a, const Vec<N,T> &b)

{

Vec<N,T> m;

for(unsigned int i=0; i<N; ++i) (a.v[i] < b.v[i]) ? m.v[i]=a.v[i] : m.v[i]=b.v[i];

return m;

}

template<unsigned int N, class T>

inline Vec<N,T> max_union(const Vec<N,T> &a, const Vec<N,T> &b)

{

Vec<N,T> m;

for(unsigned int i=0; i<N; ++i) (a.v[i] > b.v[i]) ? m.v[i]=a.v[i] : m.v[i]=b.v[i];

return m;

}

template<unsigned int N, class T>

inline T max(const Vec<N,T> &a)

{

T m=a.v[0];

for(unsigned int i=1; i<N; ++i) if(a.v[i]>m) m=a.v[i];

return m;

}

template<unsigned int N, class T>

inline T dot(const Vec<N,T> &a, const Vec<N,T> &b)

{

T d=a.v[0]*b.v[0];

for(unsigned int i=1; i<N; ++i) d+=a.v[i]*b.v[i];

return d;

}

template<class T>

inline Vec<2,T> rotate(const Vec<2,T>& a, float angle)

{

T c = cos(angle);

T s = sin(angle);

return Vec<2,T>(c*a[0] - s*a[1],s*a[0] + c*a[1]); // counter-clockwise rotation

}

template<class T>

inline Vec<2,T> perp(const Vec<2,T> &a)

{ return Vec<2,T>(-a.v[1], a.v[0]); } // counter-clockwise rotation by 90 degrees

template<class T>

inline T cross(const Vec<2,T> &a, const Vec<2,T> &b)

{ return a.v[0]*b.v[1]-a.v[1]*b.v[0]; }

template<class T>

inline Vec<3,T> cross(const Vec<3,T> &a, const Vec<3,T> &b)

{ return Vec<3,T>(a.v[1]*b.v[2]-a.v[2]*b.v[1], a.v[2]*b.v[0]-a.v[0]*b.v[2], a.v[0]*b.v[1]-a.v[1]*b.v[0]); }

template<class T>

inline T triple(const Vec<3,T> &a, const Vec<3,T> &b, const Vec<3,T> &c)

{ return a.v[0]*(b.v[1]*c.v[2]-b.v[2]*c.v[1])

+a.v[1]*(b.v[2]*c.v[0]-b.v[0]*c.v[2])

+a.v[2]*(b.v[0]*c.v[1]-b.v[1]*c.v[0]); }

template<unsigned int N, class T>

inline unsigned int hash(const Vec<N,T> &a)

{

unsigned int h=a.v[0];

for(unsigned int i=1; i<N; ++i)

h=hash(h ^ a.v[i]);

return h;

}

template<unsigned int N, class T>

inline void assign(const Vec<N,T> &a, T &a0, T &a1)

{

assert(N==2);

a0=a.v[0]; a1=a.v[1];

}

template<unsigned int N, class T>

inline void assign(const Vec<N,T> &a, T &a0, T &a1, T &a2)

{

assert(N==3);

a0=a.v[0]; a1=a.v[1]; a2=a.v[2];

}

template<unsigned int N, class T>

inline void assign(const Vec<N,T> &a, T &a0, T &a1, T &a2, T &a3)

{

assert(N==4);

a0=a.v[0]; a1=a.v[1]; a2=a.v[2]; a3=a.v[3];

}

template<unsigned int N, class T>

inline void assign(const Vec<N,T> &a, T &a0, T &a1, T &a2, T &a3, T &a4, T &a5)

{

assert(N==6);

a0=a.v[0]; a1=a.v[1]; a2=a.v[2]; a3=a.v[3]; a4=a.v[4]; a5=a.v[5];

}

template<unsigned int N, class T>

inline Vec<N,int> round(const Vec<N,T> &a)

{

Vec<N,int> rounded;

for(unsigned int i=0; i<N; ++i)

rounded.v[i]=lround(a.v[i]);

return rounded;

}

template<unsigned int N, class T>

inline Vec<N,int> floor(const Vec<N,T> &a)

{

Vec<N,int> rounded;

for(unsigned int i=0; i<N; ++i)

rounded.v[i]=(int)floor(a.v[i]);

return rounded;

}

template<unsigned int N, class T>

inline Vec<N,int> ceil(const Vec<N,T> &a)

{

Vec<N,int> rounded;

for(unsigned int i=0; i<N; ++i)

rounded.v[i]=(int)ceil(a.v[i]);

return rounded;

}

template<unsigned int N, class T>

inline Vec<N,T> fabs(const Vec<N,T> &a)

{

Vec<N,T> result;

for(unsigned int i=0; i<N; ++i)

result.v[i]=fabs(a.v[i]);

return result;

}

template<unsigned int N, class T>

inline void minmax(const Vec<N,T> &x0, const Vec<N,T> &x1, Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i)

minmax(x0.v[i], x1.v[i], xmin.v[i], xmax.v[i]);

}

template<unsigned int N, class T>

inline void minmax(const Vec<N,T> &x0, const Vec<N,T> &x1, const Vec<N,T> &x2, Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i)

minmax(x0.v[i], x1.v[i], x2.v[i], xmin.v[i], xmax.v[i]);

}

template<unsigned int N, class T>

inline void minmax(const Vec<N,T> &x0, const Vec<N,T> &x1, const Vec<N,T> &x2, const Vec<N,T> &x3,

Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i)

minmax(x0.v[i], x1.v[i], x2.v[i], x3.v[i], xmin.v[i], xmax.v[i]);

}

template<unsigned int N, class T>

inline void minmax(const Vec<N,T> &x0, const Vec<N,T> &x1, const Vec<N,T> &x2, const Vec<N,T> &x3, const Vec<N,T> &x4,

Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i)

minmax(x0.v[i], x1.v[i], x2.v[i], x3.v[i], x4.v[i], xmin.v[i], xmax.v[i]);

}

template<unsigned int N, class T>

inline void minmax(const Vec<N,T> &x0, const Vec<N,T> &x1, const Vec<N,T> &x2, const Vec<N,T> &x3, const Vec<N,T> &x4,

const Vec<N,T> &x5, Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i)

minmax(x0.v[i], x1.v[i], x2.v[i], x3.v[i], x4.v[i], x5.v[i], xmin.v[i], xmax.v[i]);

}

template<unsigned int N, class T>

inline void update_minmax(const Vec<N,T> &x, Vec<N,T> &xmin, Vec<N,T> &xmax)

{

for(unsigned int i=0; i<N; ++i) update_minmax(x[i], xmin[i], xmax[i]);

}

#endif