/*
 * Equation for a Moebius strip
 */

#include <math.h>
#include <stdio.h>

#include "library.hh"
#include "moebius.hh"

Point MoebiusStrip::edgepoint(double t) {
  double theta= (t-0.5)*4.0*PI;
  double r= 1.0 - halfgap*(1.0 - sin(theta/2.0));
  return Point(r*sin(theta),
               -r*cos(theta),
               halfbreadth*cos(theta/2.0));
}

Point MoebiusStrip::middlepoint(double t, double u) {
  return edgepoint(t*0.5)*u + edgepoint((t+1)*0.5)*(1.0-u);
}

class Bezier {
  double e,f,g,h;
public:
  Bezier(double x0, double x1, double dx0, double dx1);
  double operator()(double t) { return h + t*(g + t*(f + t*e)); }
  void debug();
};

Bezier::Bezier(double x0, double x1, double dx0, double dx1) {
//  e= 2*x0 - 2*x1 + dx0 + dx1;
//  f= x1 - dx0 - x0 - e;
  h= x0;
  g= dx0;
  e= g + 2*h + dx1 - 2*x1;
  f= x1 - e - g - h;
}

void Bezier::debug() {
  fprintf(stderr,"bz e %7.4f f %7.4f g %7.4f h %7.4f\n",e,f,g,h);
}

// The first end is at [sin(theta/2),-cos(theta/2),0]
// The second end is at [-theta/pi,0,sin(theta)]
// The first end is oriented towards [0,cos(theta),sin(theta)]
// The second end is oriented towards [0,-1,0]

Point MoebiusEnfoldment::edgepoint(double t) {
  double theta= t*2.0*PI;
  return Point(sin(theta),cos(theta),0);
}

Point MoebiusEnfoldment::middlepoint(double t, double u) {
  if (t > bottomportion) {
    t -= bottomportion;
    t /= (1.0 - bottomportion);
    double sizehere= sqrt(1-t*t);
    return Point((u*2.0-1.0) * sizehere,
                 t,
                 sizehere * thickness * sin(u*2.0*PI));
  } else {
    t /= bottomportion;
    double theta= (.5-u)*2*PI;
    Bezier bx(sin(theta*.5), -theta/PI, 0, 0);
    double ypushiness= (1-cos(theta))*2.5+1;
//        double fudge= (PI*sin(theta*.5)*cos(theta*.5))*(.5-u)*(.5-u)*4;
    double fudge= (.5-u)*(.5-u)*4*cos(theta*.5);
    Bezier by(-cos(theta*.5), 0,
              cos(theta)*ypushiness + fudge*ypushiness,
              ypushiness);
//by.debug();
    Bezier bz(0, sin(theta), sin(theta), 0);
    return Point( bx(t), by(t), thickness * bz(t) );
  }
}