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#include <iostream>
#include <sstream>
#include <utility>
#include <cmath>
#include <limits>
using namespace std::rel_ops;
template <class T>class C3_tpl {
public:
T x,y,z;
C3_tpl() {x=0;y=0;z=0;}
C3_tpl(T nx,T ny,T nz) {
x=nx;y=ny;z=nz;
}
C3_tpl(T nx,T ny) {
x=nx;y=ny;z=0;
}
C3_tpl(T n) {
x=n;y=n;z=n;
}
T dot(C3_tpl <T> p) { return x*p.x y*p.y z*p.z; }
T dot() { return x*x y*y z*z; }
double magnitude() { return sqrt(dot()); }
void normalize() {
double mag=magnitude();
x/=(T)mag;
y/=(T)mag;
z/=(T)mag;
}
void min() {
x=std::numeric_limits<T>::min();
y=std::numeric_limits<T>::min();
z=std::numeric_limits<T>::min();
}
void max() {
x=std::numeric_limits<T>::max();
y=std::numeric_limits<T>::max();
z=std::numeric_limits<T>::max();
}
T sum() { return fabs(x) fabs(y) fabs(z); }
bool isnull() {
if (z!=0) return false;
if (y!=0) return false;
if (x!=0) return false;
return true;
}
bool exceeds(T min,T max) {
if (x<min) return true;
if (x>max) return true;
if (y<min) return true;
if (y>max) return true;
if (z<min) return true;
if (z>max) return true;
return false;
}
C3_tpl <int> toint() {
C3_tpl <int> i;
i.x=static_cast<int>(x);
i.y=static_cast<int>(y);
i.z=static_cast<int>(z);
return i;
}
C3_tpl <float> tofloat() {
C3_tpl <float> i;
i.x=static_cast<float>(x);
i.y=static_cast<float>(y);
i.z=static_cast<float>(z);
return i;
}
C3_tpl <T> rotforward() {
C3_tpl <T> r;
static const float degtorad = M_PI/180;
r.x=cosf(y*degtorad);
r.y=sinf(x*degtorad);
r.z=sinf(y*degtorad);
return r;
}
float dist(C3_tpl <T>a) {
float c;
c=(a.x-x)*(a.x-x);
c =(a.y-y)*(a.y-y);
c =(a.z-z)*(a.z-z);
c=sqrtf(c);
return c;
}
bool too_far(C3_tpl <T>a,T max) {
T n;
n=a.x-x;
if (n>max) return true;
if (n<-max) return true;
n=a.y-y;
if (n>max) return true;
if (n<-max) return true;
n=a.z-z;
if (n>max) return true;
if (n<-max) return true;
return false;
}
bool dist_below(C3_tpl <T>a,T b) {
float c;
c=(a.x-x)*(a.x-x);
c =(a.y-y)*(a.y-y);
c =(a.z-z)*(a.z-z);
if (c<b) return true;
return false;
}
/////////
//Operators:
////////
friend bool operator<(const C3_tpl &a,const C3_tpl &b) {
unsigned int ia,ib;
ia=a.x a.y*100 a.z*10000;
ib=b.x b.y*100 b.z*10000;
if (ia<ib) return true;
return false;
}
friend bool operator==(const C3_tpl &a,const C3_tpl &b) {
if (a.x!=b.x) return false;
if (a.y!=b.y) return false;
if (a.z!=b.z) return false;
return true;
}
C3_tpl & operator =(const C3_tpl &a) {
x =a.x;
y =a.y;
z =a.z;
return (*this);
}
C3_tpl & operator =(const T &a) {
x =a;
y =a;
z =a;
return (*this);
}
C3_tpl operator (T b) {
C3_tpl <T> c;
c.x=x b;
c.y=y b;
c.z=z b;
return c;
}
C3_tpl operator (C3_tpl <T>a) {
C3_tpl <T> c;
c.x=a.x x;
c.y=a.y y;
c.z=a.z z;
return c;
}
C3_tpl & operator-=(const C3_tpl &a) {
x-=a.x;
y-=a.y;
z-=a.z;
return (*this);
}
C3_tpl & operator-=(const T &a) {
x-=a;
y-=a;
z-=a;
return (*this);
}
C3_tpl operator-(T b) {
C3_tpl <T> c;
c.x=x-b;
c.y=y-b;
c.z=z-b;
return c;
}
C3_tpl operator-(C3_tpl <T>a) {
C3_tpl <T> c;
c.x=x-a.x;
c.y=y-a.y;
c.z=z-a.z;
return c;
}
C3_tpl operator*(C3_tpl <T> b) {
C3_tpl <T> c;
c.x=x*b.x;
c.y=y*b.y;
c.z=z*b.z;
return c;
}
C3_tpl operator*(T b) {
C3_tpl <T> c;
c.x=x*b;
c.y=y*b;
c.z=z*b;
return c;
}
C3_tpl operator*=(T b) {
x*=b;
y*=b;
z*=b;
return (*this);
}
C3_tpl operator*=(C3_tpl <T> b) {
x*=b.x;
y*=b.y;
z*=b.z;
return (*this);
}
C3_tpl operator/=(C3_tpl <T> b) {
x/=b.x;
y/=b.y;
z/=b.z;
return (*this);
}
C3_tpl<T> operator/(T b) {
C3_tpl <T> c;
c.x=x/b;
c.y=y/b;
c.z=z/b;
return c;
}
C3_tpl<T> operator/(C3_tpl <T> b) {
C3_tpl <T> c;
c.x=x/b.x;
c.y=y/b.y;
c.z=z/b.z;
return c;
}
C3_tpl operator/=(T b) {
x/=b;
y/=b;
z/=b;
return (*this);
}
};
template <class T> std::ostream& operator<< (std::ostream& s, C3_tpl <T>& v) {
return s << v.x << " " << v.y << " " << v.z ;
}
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