Li

/*
    Li Apophysis Plugin
    Copyright 2011 Branden Brown, a.k.a. zephyrtronium

    This plugin is free software; you can redistribute it and/or modify
    them under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.

    This plugin is distributed in the hope that they 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 for more details.

    You should have received a copy of the GNU General Public License
    along with this plugin; if not, see <http://www.gnu.org/licenses/>.

*/

typedef struct
{
} Variables;

#include "apoplugin.h"

APO_PLUGIN("Li");

APO_VARIABLES(
);

int PluginVarPrepare(Variation* vp)
{
    return TRUE;
}

static const double c[64] =
{
0.5, 0.3333333333333333, 0.25, 0.2, 0.16666666666666666, 0.14285714285714285,
0.125, 0.1111111111111111, 0.1, 0.09090909090909091, 0.08333333333333333,
0.07692307692307693, 0.07142857142857142, 0.06666666666666667, 0.0625,
0.058823529411764705, 0.05555555555555555, 0.05263157894736842, 0.05,
0.047619047619047616, 0.045454545454545456, 0.043478260869565216,
0.041666666666666664, 0.04, 0.038461538461538464, 0.037037037037037035,
0.03571428571428571, 0.034482758620689655, 0.03333333333333333,
0.03225806451612903, 0.03125, 0.030303030303030304, 0.029411764705882353,
0.02857142857142857, 0.027777777777777776, 0.02702702702702703,
0.02631578947368421, 0.02564102564102564, 0.025, 0.024390243902439025,
0.023809523809523808, 0.023255813953488372, 0.022727272727272728,
0.022222222222222223, 0.021739130434782608, 0.02127659574468085,
0.020833333333333332, 0.02040816326530612, 0.02, 0.0196078431372549,
0.019230769230769232, 0.018867924528301886, 0.018518518518518517,
0.01818181818181818, 0.017857142857142856, 0.017543859649122806,
0.017241379310344827, 0.01694915254237288, 0.016666666666666666,
0.01639344262295082, 0.016129032258064516, 0.015873015873015872, 0.015625
};


int PluginVarCalc(Variation* vp)
{
    double x, y, sx, sy, tx, ty;
    x = 0.5 * log(sqr(FTy) + sqr(FTx)));
    y = atan2(FTy, FTx);
    sx = tx = x;
    sy = ty = y;
    int k;

    for(k = 0; k < 64; k++)
    {
        double ik = c[k];
        double a = (tx * x - ty * y) * ik, b = (tx * y + ty * x) * ik;
        double rx = a * ik, ry = b * ik;
        if (sqr(rx) + sqr(ry) < EPS)
            break;
        tx = a;
        ty = b;
        sx += rx;
        sy += ry;
    }
    FPx += VVAR * (sx + 0.57721566490153286061 + 0.5 * log(sqr(y) + sqr(x)));
    FPy += VVAR * (sy + atan2(y, x));

    return TRUE;
}