/* 
 * 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
 */
 
/* 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;
}
