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  • /* 
     * 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://projects.blender.org/blender/blender/issues/32305
    
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    /* 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 */
    
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    	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;
    
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    		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);
    
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    	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++; }
    
    
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    		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++; }
    
    
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    		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) {
    
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    		index = (iter != 0) ? index / (float)(iter) : 0.0;
    
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    		float index_pre = (iter != 0) ? index / (float)(iter) : 0.0;
    
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    		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++; }
    
    
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    		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++; }
    
    
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    		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++; }
    
    
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    		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 */
    
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    	float index = lyapunov(Pos * Scale, Pre_Iteration, Main_Iteration, Param1, Param2);
    
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    	if (index > 0.0 && (Render_Type != 0)) {
    
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    		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) {
    
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    		index = (Color[0] + Color[1] + Color[2]) * (1.0 / 3.0);