/*****
* triple.h
* John Bowman
*
* Stores a three-dimensional point.
*
*****/

#ifndef TRIPLE_H
#define TRIPLE_H

#include <cassert>
#include <iostream>
#include <fstream>
#include <cmath>
#include <cstring>

#include "common.h"
#include "angle.h"
#include "pair.h"

#ifdef HAVE_LIBTIRPC
#include "xstream.h"
#endif

namespace camp {

typedef double Triple[3];

class triple;

bool isIdTransform3(const double* t);
void copyTransform3(double*& d, const double* s, GCPlacement placement=NoGC);
void multiplyTransform3(double*& t, const double* s, const double* r);

void boundstriples(double& x, double& y, double& z, double& X, double& Y,
                  double& Z, size_t n, const triple* v);

class triple : virtual public gc {
 double x;
 double y;
 double z;

public:
 triple() : x(0.0), y(0.0), z(0.0) {}
 triple(double x, double y=0.0, double z=0.0) : x(x), y(y), z(z) {}
 triple(const Triple& v) : x(v[0]), y(v[1]), z(v[2]) {}

 virtual ~triple() {}

 void set(double X, double Y=0.0, double Z=0.0) { x=X; y=Y; z=Z; }

 double getx() const { return x; }
 double gety() const { return y; }
 double getz() const { return z; }

 // transform by row-major matrix
 friend triple operator* (const double* t, const triple& v) {
   if(t == NULL)
     return v;

   double f=t[12]*v.x+t[13]*v.y+t[14]*v.z+t[15];
   if(f != 0.0) {
     f=1.0/f;

     return triple((t[0]*v.x+t[1]*v.y+t[2]*v.z+t[3])*f,
                   (t[4]*v.x+t[5]*v.y+t[6]*v.z+t[7])*f,
                   (t[8]*v.x+t[9]*v.y+t[10]*v.z+t[11])*f);
   }
   reportError("division by 0 in transform of a triple");
   return 0.0;
 }

 friend triple operator* (const triple& v, const double* t) {
   if(t == NULL)
     return v;

   double f=t[3]*v.x+t[7]*v.y+t[11]*v.z+t[15];
   if(f != 0.0) {
     f=1.0/f;
     return triple((v.x*t[0]+v.y*t[4]+v.z*t[8]+t[12])*f,
                   (v.x*t[1]+v.y*t[5]+v.z*t[9]+t[13])*f,
                   (v.x*t[2]+v.y*t[6]+v.z*t[10]+t[14])*f);
   }
   reportError("division by 0 in transform of a triple");
   return 0.0;
 }

 friend triple Transform3(const triple& v, const double* t) {
   return triple((t[0]*v.x+t[1]*v.y+t[2]*v.z),
                 (t[3]*v.x+t[4]*v.y+t[5]*v.z),
                 (t[6]*v.x+t[7]*v.y+t[8]*v.z));
 }

 friend triple Transform3(const double* t, const triple& v) {
   return triple(v.x*t[0]+v.y*t[3]+v.z*t[6],
                 v.x*t[1]+v.y*t[4]+v.z*t[7],
                 v.x*t[2]+v.y*t[5]+v.z*t[8]);
 }

 // return x and y components of v*t.
 friend pair Transform2T(const double* t, const triple& v)
 {
   double f=t[3]*v.x+t[7]*v.y+t[11]*v.z+t[15];
   f=1.0/f;
   return pair((t[0]*v.x+t[4]*v.y+t[8]*v.z+t[12])*f,
               (t[1]*v.x+t[5]*v.y+t[9]*v.z+t[13])*f);
 }

 friend void transformtriples(const double* t, size_t n, triple* d,
                              const triple* s)
 {
   if(n == 0 || d == NULL || s == NULL)
     return;

   for(size_t i=0; i < n; i++)
     d[i]=t*s[i];
 }

 friend void copytriples(size_t n, triple* d, const triple* s)
 {
   if(d == NULL || s == NULL)
     return;

   for(size_t i=0; i < n; i++) d[i]=s[i];
 }

 friend void boundstriples(triple& Min, triple& Max, size_t n, const triple* v)
 {
   if(n==0 || v==NULL)
     return;

   double x,y,z;
   double X,Y,Z;

   X=x=v[0].getx();
   Y=y=v[0].gety();
   Z=z=v[0].getz();
   for(size_t i=1; i < n; ++i) {
     const double vx=v[i].getx();
     x=fmin(x,vx); X=fmax(X,vx);
     const double vy=v[i].gety();
     y=fmin(y,vy); Y=fmax(Y,vy);
     const double vz=v[i].getz();
     z=fmin(z,vz); Z=fmax(Z,vz);
   }

   Min.set(x,y,z);
   Max.set(X,Y,Z);
 }

 friend void ratiotriples(pair &b, double (*m)(double, double), bool &first,
                          size_t n, const triple* v)
 {
   if(n==0 || v==NULL)
     return;

   if(first) {
     first=false;
     const triple& v0=v[0];
     b=pair(v0.x/v0.z,v0.y/v0.z);
   }

   double x=b.getx();
   double y=b.gety();
   for(size_t i=0; i < n; ++i) {
     const triple& vi = v[i];
     x=m(x,vi.x/vi.z);
     y=m(y,vi.y/vi.z);
   }
   b=pair(x,y);
 }

 friend triple operator+ (const triple& z, const triple& w)
 {
   return triple(z.x + w.x, z.y + w.y, z.z + w.z);
 }

 friend triple operator- (const triple& z, const triple& w)
 {
   return triple(z.x - w.x, z.y - w.y, z.z - w.z);
 }

 friend triple operator- (const triple& z)
 {
   return triple(-z.x, -z.y, -z.z);
 }

 friend triple operator* (double s, const triple& z)
 {
   return triple(s*z.x, s*z.y, s*z.z);
 }

 friend triple operator* (const triple& z, double s)
 {
   return triple(z.x*s, z.y*s, z.z*s);
 }

 friend triple operator/ (const triple& z, double s)
 {
   if (s == 0.0)
     reportError("division by 0");
   s=1.0/s;
   return triple(z.x*s, z.y*s, z.z*s);
 }

 const triple& operator+= (const triple& w)
 {
   x += w.x;
   y += w.y;
   z += w.z;
   return *this;
 }

 const triple& operator-= (const triple& w)
 {
   x -= w.x;
   y -= w.y;
   z -= w.z;
   return *this;
 }

 friend bool operator== (const triple& z, const triple& w)
 {
   return z.x == w.x && z.y == w.y && z.z == w.z;
 }

 friend bool operator!= (const triple& z, const triple& w)
 {
   return z.x != w.x || z.y != w.y || z.z != w.z;
 }

 double abs2() const
 {
   return x*x+y*y+z*z;
 }

 friend double abs2(const triple &v)
 {
   return v.abs2();
 }

 double length() const /* r */
 {
   return sqrt(abs2());
 }

 friend double length(const triple& v)
 {
   return v.length();
 }

 double polar(bool warn=true) const /* theta */
 {
   double r=length();
   if(r == 0.0) {
     if(warn)
       reportError("taking polar angle of (0,0,0)");
     else
       return 0.0;
   }
   return acos(z/r);
 }

 double azimuth(bool warn=true) const /* phi */
 {
   return angle(x,y,warn);
 }

 friend triple unit(const triple& v)
 {
   double scale=v.length();
   if(scale == 0.0) return v;
   scale=1.0/scale;
   return triple(v.x*scale,v.y*scale,v.z*scale);
 }

 friend double dot(const triple& u, const triple& v)
 {
   return u.x*v.x+u.y*v.y+u.z*v.z;
 }

 friend triple cross(const triple& u, const triple& v)
 {
   return triple(u.y*v.z-u.z*v.y,
                 u.z*v.x-u.x*v.z,
                 u.x*v.y-u.y*v.x);
 }

 // Returns a unit triple in the direction (theta,phi), in radians.
 friend triple expi(double theta, double phi)
 {
   double sintheta=sin(theta);
   return triple(sintheta*cos(phi),sintheta*sin(phi),cos(theta));
 }

 friend istream& operator >> (istream& s, triple& z)
 {
   char c;
   s >> ws;
   bool paren=s.peek() == '('; // parenthesis are optional
   if(paren) s >> c;
   s >> z.x >> ws;
   if(s.peek() == ',') s >> c >> z.y >> ws;
   else {
     if(paren) s >> z.y >> ws;
     else z.y=0.0;
   }
   if(s.peek() == ',') s >> c >> z.z;
   else {
     if(paren) s >> z.z;
     else z.z=0.0;
   }
   if(paren) {
     s >> ws;
     if(s.peek() == ')') s >> c;
   }

   return s;
 }

 friend ostream& operator << (ostream& out, const triple& v)
 {
   out << "(" << v.x << "," << v.y << "," << v.z << ")";
   return out;
 }

 friend jsofstream& operator << (jsofstream& out, const triple& v)
 {
   out << "[" << v.x << "," << v.y << "," << v.z << "]";
   return out;
 }


#ifdef HAVE_LIBTIRPC
 friend xdr::oxstream& operator << (xdr::oxstream& out, triple const& v)
 {
   out << v.x << v.y << v.z;
   return out;
 }
#endif

};

triple expi(double theta, double phi);

// Return the component of vector v perpendicular to a unit vector u.
inline triple perp(triple v, triple u)
{
 return v-dot(v,u)*u;
}

double xratio(const triple& v);
double yratio(const triple& v);

inline void bounds(double& x, double &X, double v)
{
 if(v < x) x=v;
 else if(v > X) X=v;
}

inline void boundstriples(double& x, double& y, double& z,
                         double& X, double& Y, double& Z,
                         size_t n, const triple* v)
{
 X=x=v[0].getx();
 Y=y=v[0].gety();
 Z=z=v[0].getz();

 for(size_t i=1; i < n; ++i) {
   triple V=v[i];
   bounds(x,X,V.getx());
   bounds(y,Y,V.gety());
   bounds(z,Z,V.getz());
 }
}

extern const double third;

// return the maximum distance squared of points c0 and c1 from
// the respective internal control points of z0--z1.
inline double Straightness(const triple& z0, const triple& c0,
                          const triple& c1, const triple& z1)
{
 triple v=third*(z1-z0);
 return std::max(abs2(c0-v-z0),abs2(z1-v-c1));
}

// Return one ninth of the relative flatness squared of a--b and c--d.
inline double Flatness(const triple& a, const triple& b, const triple& c,
                      const triple& d)
{
 static double ninth=1.0/9.0;
 triple u=b-a;
 triple v=d-c;
 return ninth*std::max(abs2(cross(u,unit(v))),abs2(cross(v,unit(u))));
}

// Return one-half of the second derivative of the Bezier curve defined by
// a,b,c,d at t=0.
inline triple bezierPP(const triple& a, const triple& b, const triple& c) {
 return 3.0*(a+c)-6.0*b;
}

// Return one-sixth of the third derivative of the Bezier curve defined by
// a,b,c,d at t=0.
inline triple bezierPPP(const triple& a, const triple& b, const triple& c,
                       const triple& d) {
 return d-a+3.0*(b-c);
}

// Return four-thirds of the first derivative of the Bezier curve defined by
// a,b,c,d at t=1/2.
inline triple bezierPh(triple a, triple b, triple c, triple d)
{
 return c+d-a-b;
}

// Return two-thirds of the second derivative of the Bezier curve defined by
// a,b,c,d at t=1/2.
inline triple bezierPPh(triple a, triple b, triple c, triple d)
{
 return 3.0*a-5.0*b+c+d;
}

} //namespace camp

GC_DECLARE_PTRFREE(camp::triple);

#endif

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