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/*****
* pair.h
* Andy Hammerlindl 2002/05/16
*
* Stores a two-dimensional point similar to the pair type in MetaPost.
* In some cases, pairs behave as complex numbers.
*
* A pair is a guide as a pair alone can be used to describe a path.
* The solve and subsolve methods are fairly straight forward as solve
* returns a path with just the pair and subsolve just adds the pair to
* the structure.
*****/
#ifndef PAIR_H
#define PAIR_H
#include <cassert>
#include <cmath>
#include "common.h"
#include "angle.h"
namespace camp {
class pair : public gc {
double x;
double y;
public:
pair() : x(0.0), y(0.0) {}
pair(double x, double y=0.0) : x(x), y(y) {}
double getx() const { return x; }
double gety() const { return y; }
bool isreal() {return y == 0;}
friend pair operator+ (const pair& z, const pair& w)
{
return pair(z.x+w.x,z.y+w.y);
}
friend pair operator- (const pair& z, const pair& w)
{
return pair(z.x-w.x,z.y-w.y);
}
friend pair operator- (const pair& z)
{
return pair(-z.x,-z.y);
}
// Complex multiplication
friend pair operator* (const pair& z, const pair& w)
{
return pair(z.x*w.x-z.y*w.y,z.x*w.y+w.x*z.y);
}
const pair& operator+= (const pair& w)
{
x += w.x;
y += w.y;
return *this;
}
const pair& operator-= (const pair& w)
{
x -= w.x;
y -= w.y;
return *this;
}
const pair& operator*= (const pair& w)
{
(*this) = (*this) * w;
return (*this);
}
const pair& operator/= (const pair& w)
{
(*this) = (*this) / w;
return (*this);
}
const pair& scale (double xscale, double yscale)
{
x *= xscale;
y *= yscale;
return *this;
}
friend pair operator/ (const pair &z, double t)
{
if (t == 0.0)
reportError("division by 0");
t=1.0/t;
return pair(z.x*t, z.y*t);
}
friend pair operator/ (const pair& z, const pair& w)
{
if (!w.nonZero())
reportError("division by pair (0,0)");
double t = 1.0 / (w.x*w.x + w.y*w.y);
return pair(t*(z.x*w.x + z.y*w.y),
t*(-z.x*w.y + w.x*z.y));
}
friend bool operator== (const pair& z, const pair& w)
{
return z.x == w.x && z.y == w.y;
}
friend bool operator!= (const pair& z, const pair& w)
{
return z.x != w.x || z.y != w.y;
}
double abs2() const
{
return x*x + y*y;
}
double length() const
{
return sqrt(abs2());
}
friend double length(const pair& z)
{
return z.length();
}
double angle() const
{
return camp::angle(x,y);
}
friend double angle(const pair& z)
{
return z.angle();
}
friend pair unit(const pair& z)
{
double scale=z.length();
if(scale != 0.0) scale=1.0/scale;
return pair(z.x*scale,z.y*scale);
}
friend pair conj(const pair& z)
{
return pair(z.x,-z.y);
}
friend double dot(const pair& z, const pair& w)
{
return z.x*w.x+z.y*w.y;
}
friend double cross(const pair& z, const pair& w)
{
return z.x*w.y-z.y*w.x;
}
// Return the principal branch of the square root (non-negative real part).
friend pair Sqrt(const pair& z) {
double mag=z.length();
if(mag == 0.0) return pair(0.0,0.0);
else if(z.x > 0) {
double re=sqrt(0.5*(mag+z.x));
return pair(re,0.5*z.y/re);
} else {
double im=sqrt(0.5*(mag-z.x));
if(z.y < 0) im=-im;
return pair(0.5*z.y/im,im);
}
}
bool nonZero() const
{
return x != 0.0 || y != 0.0;
}
friend istream& operator >> (istream& s, pair& z)
{
char c;
s >> std::ws;
bool paren=s.peek() == '('; // parenthesis are optional
if(paren) s >> c;
s >> z.x >> std::ws;
if(!s.eof() && s.peek() == ',') s >> c >> z.y;
else z.y=0.0;
if(paren) {
s >> std::ws;
if(s.peek() == ')') s >> c;
}
return s;
}
friend ostream& operator << (ostream& out, const pair& z)
{
out << "(" << z.x << "," << z.y << ")";
return out;
}
friend class box;
};
// Calculates exp(i * theta), useful for unit vectors.
inline pair expi(double theta)
{
if(theta == 0.0) return pair(1.0,0.0); // Frequently occurring case
return pair(cos(theta),sin(theta));
}
// Complex exponentiation
inline pair pow(const pair& z, const pair& w)
{
double u=w.getx();
double v=w.gety();
if(z == 0.0) return w == 0.0 ? 1.0 : 0.0;
double logr=0.5*log(z.abs2());
double th=z.angle();
return exp(logr*u-th*v)*expi(logr*v+th*u);
}
} //namespace camp
GC_DECLARE_PTRFREE(camp::pair);
#endif
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