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/*
* Copyright 2013, Blender Foundation.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program 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 for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*
* Lyapunov Shader - in memory of great mathematician Aleksandr Mikhailovich Lyapunov
* Original code: Sylvio Sell - maitag.de - Rostock Germany 2013
* OSL port by Thomas Dinges
* More information: https://developer.blender.org/T32305
*/
/* Fac_Type
* 0, SPREAD, Spread indices for fac output
* 1, ABS, Absolute values from indices
* 2, COLOR, Get fac output from used colors
* 3, REAL, Real indices
*/
/* Render_Type
* 0, NEG, Negative Lyapunov indices only
* 1, POS, Positive Lyapunov indices only
* 2, ALL, Positive and negative indices
*/
float lyapunov(point p, float iteration_pre, float iteration_main, float p1, float p2)
{
/* Coordinates */
float a = p[0];
float b = p[1];
float c = p[2];
int iter_pre = (int)floor(iteration_pre);
int iter_main = (int)floor(iteration_main);
float nabla_pre = iteration_pre - (float)iter_pre;
float nabla_main = iteration_main - (float)iter_main;
float x = 0.0;
float index = 0.0;
float derivation = 0.0;
int iter = 0;
/* Pre-iteration */
for(int i = 0; i < iter_pre; i++) {
x = p1*sin(x+a) * sin(x+a)+p2;
x = p1*sin(x+b) * sin(x+b)+p2;
x = p1*sin(x+c) * sin(x+c)+p2;
}
if (nabla_pre != 0.0) {
float x_pre = x;
x = p1*sin(x+a)*sin(x+a)+p2;
x = p1*sin(x+b)*sin(x+b)+p2;
x = p1*sin(x+c)*sin(x+c)+p2;
x = x*nabla_pre + x_pre*(1.0-nabla_pre);
}
/* Main-iteration */
for(int i = 0; i < iter_main; i++) {
x = p1*sin(x+a)*sin(x+a)+p2;
derivation = 2.0*p1*sin(x+a)*cos(x+a);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
x = p1*sin(x+b)*sin(x+b)+p2;
derivation = 2.0*p1*sin(x+b)*cos(x+b);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
x = p1*sin(x+c)*sin(x+c)+p2;
derivation = 2.0*p1*sin(x+c)*cos(x+c);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
}
if (nabla_main == 0.0) {
index = (iter != 0) ? index/(float)(iter) : 0.0;
}
else {
float index_pre = (iter != 0) ? index/(float)(iter) : 0.0;
x = p1*sin(x+a)*sin(x+a)+p2;
derivation = 2.0*p1*sin(x+a)*cos(x+a);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
x = p1*sin(x+b)*sin(x+b)+p2;
derivation = 2.0*p1*sin(x+b)*cos(x+b);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
x = p1*sin(x+c)*sin(x+c)+p2;
derivation = 2.0*p1*sin(x+c)*cos(x+c);
if (derivation != 0.0) { index += log(fabs(derivation)); iter++; }
index = (iter != 0) ? index/(float)(iter) : 0.0;
index = index*nabla_main + index_pre*(1.0-nabla_main);
}
return index;
}
shader node_lyapunov(
color Pos_Color = color(1.0, 0.0, 0.0),
color Mid_Color = color(0.0, 0.0, 0.0),
color Neg_Color = color(0.0, 0.0, 1.0),
float Pre_Iteration = 0.0,
float Main_Iteration = 1.0,
float Pos_Scale = 0.5,
float Neg_Scale = 0.5,
float Param1 = 2.0,
float Param2 = 2.0,
int Fac_Type = 0,
int Render_Type = 2,
float Scale = 0.25,
point Pos = P,
output float Fac = 0.0,
output color Color = 0.0)
{
/* Calculate Texture */
float index = lyapunov(Pos*Scale, Pre_Iteration, Main_Iteration, Param1, Param2);
/* Calculate Color */
if(index > 0.0 && (Render_Type != 0)) {
index *= Pos_Scale;
if(index > 1.0) { index = 1.0; }
Color = (Pos_Color - Mid_Color) * index + Mid_Color;
}
else if (index < 0.0 && (Render_Type != 1)) {
index *= Neg_Scale;
if (index < -1.0) { index = -1.0; }
Color = (Mid_Color - Neg_Color) * index + Mid_Color;
}
else {
Color = Mid_Color;
}
/* Adjust Index */
if (Fac_Type == 0) {
index = 0.5 + index * 0.5;
}
else if (Fac_Type == 1) {
index = fabs(index);
}
else if (Fac_Type == 2) {
index = (Color[0]+Color[1]+Color[2]) * (1.0/3.0);
}
Fac = index;
}
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