lissajous.cpp

/******************************************************/
/*                                                    */
/* lissajous.cpp - Lissajous curves                   */
/*                                                    */
/******************************************************/
/* Copyright 2019 Pierre Abbat.
 * This file is part of PerfectTIN.
 *
 * PerfectTIN is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * PerfectTIN is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License and Lesser General Public License
 * for more details.
 *
 * You should have received a copy of the GNU General Public License
 * and Lesser General Public License along with PerfectTIN. If not, see
 * <http://www.gnu.org/licenses/>.
 */
#include <iostream>
#include <cmath>
#include "lissajous.h"
#include "relprime.h"
#define SPEED 5
using namespace std;

// num[i]/denom[i] is a rational approximation to quadirr[i].
int Lissajous::num[]=
{
  987,2131,1393,1519,1189,1801,1027,
  2111,135,379,1693,1249,357,365,
  1871,2069,659,1905,1171,1287,3431
};

int Lissajous::denom[]=
{
  1597,2911,3363,2705,3927,2789,1897,
  3009,701,1197,2193,3083,2549,1017,
  2351,2873,3037,3629,2759,1579,6043
};

Lissajous::Lissajous()
{
  width=610;
  height=377;
  xperiod=3194;
  yperiod=1974;
  xphase=yphase=0;
  step=5;
}

void Lissajous::test()
{
  int i;
  for (i=0;i<21;i++)
    cout<<i<<' '<<num[i]<<'/'<<denom[i]<<' '<<quadirr[i]<<' '<<(double)num[i]/denom[i]-quadirr[i]<<endl;
}

void Lissajous::resize(int w,int h)
{
  int i,newi,newxperiod,newyperiod;
  double ratio,r1r,bestr1r=INFINITY;
  if (w>0 && h>0)
  {
    if (w>h)
      ratio=(double)h/w;
    else
      ratio=(double)w/h;
    for (i=0;i<21;i++)
    {
      r1r=ratio/quadirr[i]+quadirr[i]/ratio;
      if (r1r<bestr1r)
      {
	bestr1r=r1r;
	newi=i;
      }
    }
    newxperiod=num[newi]*2;
    newyperiod=denom[newi]*2;
    if (w>h)
      swap(newxperiod,newyperiod);
    xphase=lrint(xphase*(double)newxperiod/xperiod);
    yphase=lrint(yphase*(double)newyperiod/yperiod);
    xperiod=newxperiod;
    yperiod=newyperiod;
    bestr1r=INFINITY;
    for (i=1;i<=3*SPEED*(double)(xperiod+yperiod)/(w+h);i+=2)
      if (gcd(i,xperiod)==1 && gcd(i,xperiod)==1)
      {
	r1r=i/(SPEED*(double)(xperiod+yperiod)/(w+h))+(SPEED*(double)(xperiod+yperiod)/(w+h))/i;
	if (r1r<bestr1r)
	{
	  bestr1r=r1r;
	  step=i;
	}
      }
    width=w;
    height=h;
    //cout<<w<<"×"<<h<<' '<<xperiod<<"×"<<yperiod<<" step "<<step<<endl;
  }
}

xy Lissajous::move()
{
  xphase=(xphase+step)%xperiod;
  yphase=(yphase+step)%yperiod;
  return xy((cos(2*M_PI*xphase/xperiod)+1)/2*width,(cos(2*M_PI*yphase/yperiod)+1)/2*height);
}