EllipticAltFunc.java

/*
  JWildfire - an image and animation processor written in Java
  Copyright (C) 1995-2011 Andreas Maschke

  This 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 2.1 of the
  License, or (at your option) any later version.

  This software 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
  Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General Public License along with this software;
  if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
  02110-1301 USA, or see the FSF site: http://www.fsf.org.
*/
package org.jwildfire.create.tina.variation;

import static org.jwildfire.base.mathlib.MathLib.sqrt;
import static org.jwildfire.base.mathlib.MathLib.min;
import static org.jwildfire.base.mathlib.MathLib.max;
import static org.jwildfire.base.mathlib.MathLib.asin;

import org.jwildfire.create.tina.base.XForm;
import org.jwildfire.create.tina.base.XYZPoint;

public class EllipticAltFunc extends SimpleVariationFunc {
  private static final long serialVersionUID = 1L;

  private double sqrt1pm1(double x) {
    if (-0.0625 < x && x < 0.0625)
    {
      // [4,4] Pade approximant to degree 8 truncated Taylor series of sqrt(x+1)-1 about 0
      // computed with a Wolfram Alpha Open Code notebook
      // accurate to machine precision within this range?
      double num = 0;
      double den = 0;
      num += 1.0 / 32.0;
      den += 1.0 / 256.0;
      num *= x;
      den *= x;
      num += 5.0 / 16.0;
      den += 5.0 / 32.0;
      num *= x;
      den *= x;
      num += 3.0 / 4.0;
      den += 15.0 / 16.0;
      num *= x;
      den *= x;
      num += 1.0 / 2.0;
      den += 7.0 / 4.0;
      num *= x;
      den *= x;
      den += 1.0;
      return num / den;
    }
    return sqrt(1 + x) - 1;
  }

  @Override
  public void transform(FlameTransformationContext pContext, XForm pXForm, XYZPoint pAffineTP, XYZPoint pVarTP, double pAmount) {
      /* Alternate elliptic implementation by claude on discord fractal chat.
       * It has better precision when x is near ±1 and y is near 0.
       */
      double x2 = 2.0 * pAffineTP.x;
      double sq = pAffineTP.x * pAffineTP.x + pAffineTP.y * pAffineTP.y;
      double u = sq + x2;
      double v = sq - x2;
      double xmaxm1 = 0.5 * (sqrt1pm1(u) + sqrt1pm1(v));
      double a = pAffineTP.x / (1 + xmaxm1);
      double ssx = xmaxm1;
      double w = pAmount / 1.5707963267948966;
      if (ssx<0) ssx = 0; else ssx = sqrt(ssx);
      pVarTP.x = w * asin(max(-1, min(1, a))); //asin(clamp(a, -1, 1));
      if (pAffineTP.y > 0)
        pVarTP.y =  w * Math.log1p(xmaxm1 + ssx);
      else
        pVarTP.y = -w * Math.log1p(xmaxm1 + ssx);

    if (pContext.isPreserveZCoordinate()) pVarTP.z += pAmount * pAffineTP.z;
}

  @Override
  public String getName() {
    return "ellipticAlt";
  }

}