## Algoritmo de Point3D.

Cualquier duda no dudes en contactar.

``````/**
* Author: Ulf Lundstrom with inspiration from tinyKACTL
* Date: 2009-04-14
* Source:
* Description: Class to handle points in 3D space.
* 	T can be e.g. double or long long.
* Usage:
* Status: tested, except for phi and theta
*/
#pragma once

template <class T> struct Point3D {
typedef Point3D P;
typedef const P& R;
T x, y, z;
explicit Point3D(T x=0, T y=0, T z=0) : x(x), y(y), z(z) {}
bool operator<(R p) const {
return tie(x, y, z) < tie(p.x, p.y, p.z); }
bool operator==(R p) const {
return tie(x, y, z) == tie(p.x, p.y, p.z); }
P operator+(R p) const { return P(x+p.x, y+p.y, z+p.z); }
P operator-(R p) const { return P(x-p.x, y-p.y, z-p.z); }
P operator*(T d) const { return P(x*d, y*d, z*d); }
P operator/(T d) const { return P(x/d, y/d, z/d); }
T dot(R p) const { return x*p.x + y*p.y + z*p.z; }
P cross(R p) const {
return P(y*p.z - z*p.y, z*p.x - x*p.z, x*p.y - y*p.x);
}
T dist2() const { return x*x + y*y + z*z; }
double dist() const { return sqrt((double)dist2()); }
//Azimuthal angle (longitude) to x-axis in interval [-pi, pi]
double phi() const { return atan2(y, x); }
//Zenith angle (latitude) to the z-axis in interval [0, pi]
double theta() const { return atan2(sqrt(x*x+y*y),z); }
P unit() const { return *this/(T)dist(); } //makes dist()=1
//returns unit vector normal to *this and p
P normal(P p) const { return cross(p).unit(); }
//returns point rotated 'angle' radians ccw around axis
P rotate(double angle, P axis) const {
double s = sin(angle), c = cos(angle); P u = axis.unit();
return u*dot(u)*(1-c) + (*this)*c - cross(u)*s;
}
};
``````