/*
  This is a simple modification of Tom Beddard's MandelbulbQuick.pbk.
  It is based on Knighty's ideas from the Kaleidoscopic IFS fractal:
  http://www.fractalforums.com/3d-fractal-generation/kaleidoscopic-%28escape-time-ifs%29/
  
  Mikael Hvidtfeldt Christensen (Syntopia), May 3rd 2010.
*/
 
/**
 * MandelbulbQuick.pbk
 * Last update: 14 December 2009
 *
 * Changelog:
 *		1.0		- Initial release
 *		1.0.1	- Fixed a missing asymmetry thanks to Chris King (http://www.dhushara.com)
 *				- Refinements in the colouring
 *      1.0.2   - Added radiolaria option for a funky hair-like effect
 * 				- Incorporated the scalar derivative method as described here:
 *			    - http://www.fractalforums.com/mandelbulb-implementation/realtime-renderingoptimisations/
 *		1.0.3	- Created a quick version of the script as using a boolean flag to determine
 *				  which distance estimation method created long compilation times.
 * 		1.0.4 	- Fixed issue with older graphic cards and the specular highlights
 *
 * 
 * Copyright (c) 2009 Tom Beddard
 * http://www.subblue.com
 *
 * For more Flash and PixelBender based generative graphics experiments see:
 * http://www.subblue.com/blog
 *
 * Licensed under the MIT License:
 * http://www.opensource.org/licenses/mit-license.php
 *
 *
 * Credits and references
 * ======================
 * For the story behind the 3D Mandelbrot see the following page:
 * http://www.skytopia.com/project/fractal/mandelbulb.html
 *
 * The original forum disussion with many implementation details can be found here:
 * http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/
 *
 * This implementation references the 4D Quaternion GPU Raytracer by Keenan Crane:
 * http://www.devmaster.net/forums/showthread.php?t=4448
 *
 * and the NVIDIA CUDA/OptiX implementation by cbuchner1:
 * http://forums.nvidia.com/index.php?showtopic=150985
 *
 */
 
#define PI 3.141592653
#define MIN_EPSILON 3e-7
 
<languageVersion : 1.0;>
 
kernel MandelbulbQuickDerivative
<	namespace : "com.subblue.filters";
	vendor : "Tom Beddard";
	version : 1;
	description : "Mandelbulb Fractal Ray Tracer - the quick version (Kaleidoscopic IFS Mod by Syntopia)";
>
 
 
{
	parameter int antialiasing
	<
		minValue:1;
		maxValue:3;
		defaultValue:1;
		description:"Super sampling quality. Number of samples squared per pixel.";
	>;
 
	parameter bool phong
	<
		defaultValue:true;
		description: "Enable phong shading.";
	>;
 
 
	parameter float shadows
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.0;
		description: "Enable ray traced shadows.";
	>;
 
	parameter float ambientOcclusion
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.8;
		description: "Enable fake ambient occlusion factor based on the orbit trap.";
	>;
 
	parameter float ambientOcclusionEmphasis
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.58;
		description: "Emphasise the structure edges based on the number of steps it takes to reach a point in the fractal.";
	>;
 
	parameter float bounding
	<
		minValue:1.0;
		maxValue:16.0;
		defaultValue:12.5;
		description: "Sets the bounding sphere radius to help accelerate the raytracing.";
	>;
 
	parameter float bailout
	<
		minValue:0.5;
		maxValue:12.0;
		defaultValue:4.0;
		description: "Sets the bailout value for the fractal calculation. Lower values give smoother less detailed results.";
	>;
 
	parameter float power
	<
		minValue:2.0;
		maxValue:32.0;
		defaultValue:8.0;
		description: "The power of the fractal.";
	>;
 
 
	parameter float3 cameraPosition
	<
		minValue:float3(-4, -4, -4);
		maxValue:float3(4, 4, 4);
		defaultValue:float3(0, -2.88, 0);
		description: "Camera position.";
	>;
 
	parameter float3 cameraPositionFine
	<
		minValue:float3(-0.1, -0.1, -0.1);
		maxValue:float3(0.1, 0.1, 0.1);
		defaultValue:float3(0, 0.0, 0.0);
		description: "Fine tune position.";
	>;
 
	parameter float3 cameraRotation
	<
		minValue:float3(-180, -180, -180);
		maxValue:float3(180, 180, 180);
		defaultValue:float3(-68.4, 7.2, -90);
		description: "Pointing angle in each axis of the camera.";
	>;
 
	parameter float cameraZoom
	<
		minValue:0.0;
		maxValue:10.0;
		defaultValue:0.0;
		description: "Zoom the camera view.";
	>;
 
	parameter float3 light
	<
		minValue:float3(-50, -50, -50);
		maxValue:float3(50, 50, 50);
		defaultValue:float3(38, -42, 38);
		description: "Position of point light.";
	>;
 
	parameter float3 colorBackground
	<
		minValue:float3(0, 0, 0);
		maxValue:float3(1, 1, 1);
		defaultValue:float3(0.0, 0.0, 0.0);
		description: "Background colour.";
        aeUIControl: "aeColor";
	>;
 
    parameter float colorBackgroundTransparency
	<
		minValue:float(0.0);
		maxValue:float(1.0);
		defaultValue:float(1.0);
		description: "Background transparency.";
	>;
 
	parameter float3 colorDiffuse
	<
		minValue:float3(0, 0, 0);
		maxValue:float3(1, 1, 1);
		defaultValue:float3(0.0, 0.85, 0.99);
		description: "Diffuse colour.";
        aeUIControl: "aeColor";
	>;
 
	parameter float3 colorAmbient
	<
		minValue:float3(0, 0, 0);
		maxValue:float3(1, 1, 1);
		defaultValue:float3(0.67, 0.85, 1.0);
		description: "Ambient light colour.";
        aeUIControl: "aeColor";
	>;
 
	parameter float colorAmbientIntensity
	<
		minValue:float(0);
		maxValue:float(1);
		defaultValue:float(0.4);
		description: "Ambient light intensity.";
	>;
 
	parameter float3 colorLight
	<
		minValue:float3(0, 0, 0);
		maxValue:float3(1, 1, 1);
		defaultValue:float3(0.48, 0.59, 0.66);
		description: "Light colour.";
        aeUIControl: "aeColor";
	>;
 
	parameter float colorSpread
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.2;
		description: "Vary the colour based on the normal direction.";
	>;
 
	parameter float rimLight
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.0;
		description: "Rim light factor.";
	>;
 
	parameter float specularity
	<
		minValue:0.0;
		maxValue:1.0;
		defaultValue:0.66;
		description: "Phone specularity";
	>;
 
	parameter float specularExponent
	<
		minValue:0.1;
		maxValue:50.0;
		defaultValue:15.0;
		description: "Phong shininess";
	>;
 
	parameter float3 rotation
	<
		minValue:float3(-180, -180, -180);
		maxValue:float3(180, 180, 180);
		defaultValue:float3(0, 36, 39.6);
		description: "Rotate the Mandelbulb in each axis.";
	>;
 
	parameter int maxIterations
	<
		minValue:1;
		maxValue:20;
		defaultValue:6;
		description: "More iterations reveal more detail in the fractal surface but takes longer to calculate.";
	>;
 
	parameter int stepLimit
	<
		minValue:10;
		maxValue:2000;
		defaultValue:310;
		description: "The maximum number of steps a ray should take.";
	>;
 
	parameter float epsilonScale
	<
		minValue:0.1;
		maxValue:1.0;
		defaultValue:1.0;
		description: "Scale the epsilon step distance. Smaller values are slower but will generate smoother results for thin areas.";
	>;
 
	parameter int2 size
	<
		minValue:int2(100, 100);
		maxValue:int2(2048, 2048);
		defaultValue:int2(640, 480);
		description: "The output size in pixels.";
	>;
 
	region generated()
	{
		return region(float4(0, 0, size.x, size.y));
	}
 
	dependent float bailout_sr, aspectRatio, sampleStep, sampleContribution, pixel_scale, eps_start;
	dependent float3 eye;
	dependent float3x3 viewRotation, objRotation;
	output pixel4 dst;
 
 
	// The fractal calculation
	//
	// Calculate the closest distance to the fractal boundary and use this
	// distance as the size of the step to take in the ray marching.
	//
	float DE(float3 z0, inout float min_dist)
	{
    float r	 = length(z0);
	float scale = 3.1;
	float CX = 1.0;
    float CY = 1.0;
    float CZ = 1.0;
    float t = 0.0;
    int i = 0;
    for (i=0;i<maxIterations && r<60.0;i++){
 
     // Rotation around z-axis
       float angle = -0.1;
       float x2 = cos(angle)*z0.x + sin(angle)*z0.y;
       float y2 = -sin(angle)*z0.x + cos(angle)*z0.y;
       z0.x = x2; z0.y = y2;
 
 
      z0.x=abs( z0.x); z0.y=abs( z0.y); z0.z=abs( z0.z);
      if( z0.x- z0.y<0.0){t= z0.y; z0.y= z0.x; z0.x=t;}
      if( z0.x- z0.z<0.0){t= z0.z; z0.z= z0.x; z0.x=t;}
      if( z0.y- z0.z<0.0){t= z0.z; z0.z= z0.y; z0.y=t;}
 
        // Reverse rotation around z-axis
       angle = -angle;
       x2 = cos(angle)*z0.x + sin(angle)*z0.y;
       y2 = -sin(angle)*z0.x + cos(angle)*z0.y;
       z0.x = x2; z0.y = y2;
 
       z0.x=scale* z0.x-CX*(scale-1.0);
       z0.y=scale* z0.y-CY*(scale-1.0);
       z0.z=scale* z0.z;
      if( z0.z>0.5*CZ*(scale-1.0))  z0.z-=CZ*(scale-1.0);
 
 
      // Extra folding step
      if(z0.x+z0.y<1.0){t=-z0.y;z0.y=-z0.x;z0.x=t;}
      if(z0.x+z0.z<0.0){t=-z0.z;z0.z=-z0.x;z0.x=t;}
      if(z0.y+z0.z<0.0){t=-z0.z;z0.z=-z0.y;z0.y=t;}
 
 
      r=length(z0);
   }
   return (sqrt(r)-2.0)*pow(scale,float(-i));//the estimated distance
  }
 
 
	// Intersect bounding sphere
	//
	// If we intersect then set the tmin and tmax values to set the start and
	// end distances the ray should traverse.
	bool intersectBoundingSphere(float3 origin,
								 float3 direction,
								 out float tmin,
								 out float tmax)
	{
		bool hit = false;
 
		float b = dot(origin, direction);
		float c = dot(origin, origin) - bounding;
		float disc = b*b - c;			// discriminant
		tmin = tmax = 0.0;
 
		if (disc > 0.0) {
			// Real root of disc, so intersection
			float sdisc = sqrt(disc);
			float t0 = -b - sdisc;			// closest intersection distance
			float t1 = -b + sdisc;			// furthest intersection distance
 
			if (t0 >= 0.0) {
				// Ray intersects front of sphere
				float min_dist;
				float3 z = origin + t0 * direction;
				tmin = DE(z, min_dist);
				tmax = t0 + t1;
			} else if (t0 < 0.0) {
				// Ray starts inside sphere
				float min_dist;
				float3 z = origin;
				tmin = DE(z, min_dist);
				tmax = t1;
			}
			hit = true;
		}
 
		return hit;
	}
 
 
	// Calculate the gradient in each dimension from the intersection point
	float3 estimate_normal(float3 z, float e)
	{
		float min_dst;	// Not actually used in this particular case
		float3 z1 = z + float3(e, 0, 0);
		float3 z2 = z - float3(e, 0, 0);
		float3 z3 = z + float3(0, e, 0);
		float3 z4 = z - float3(0, e, 0);
		float3 z5 = z + float3(0, 0, e);
		float3 z6 = z - float3(0, 0, e);
 
		float dx = DE(z1, min_dst) - DE(z2, min_dst);
		float dy = DE(z3, min_dst) - DE(z4, min_dst);
		float dz = DE(z5, min_dst) - DE(z6, min_dst);
 
		return normalize(float3(dx, dy, dz) / (2.0*e));
	}
 
 
	// Computes the direct illumination for point pt with normal N due to
	// a point light at light and a viewer at eye.
	float3 Phong(float3 pt, float3 N, out float specular)
	{
		float3 diffuse	= float3(0, 0, 0);			// Diffuse contribution
		float3 color	= float3(0, 0, 0);
        specular = 0.0;
 
		float3 L = normalize(light * objRotation - pt); // find the vector to the light
		float  NdotL = dot(N, L);			// find the cosine of the angle between light and normal
 
		if (NdotL > 0.0) {
			// Diffuse shading
			diffuse = colorDiffuse + abs(N) * colorSpread;
			diffuse *= colorLight * NdotL;
 
			// Phong highlight
			float3 E = normalize(eye - pt);		// find the vector to the eye
			float3 R = L - 2.0 * NdotL * N;		// find the reflected vector
			float  RdE = dot(R,E);
 
			if (RdE <= 0.0) {
				specular = specularity * pow(abs(RdE), specularExponent);
            }
		} else {
			diffuse = colorDiffuse * abs(NdotL) * rimLight;
		}
 
		return (colorAmbient * colorAmbientIntensity) + diffuse;
	}
 
 
	// Define the ray direction from the pixel coordinates
	float3 rayDirection(float2 p)
	{
		float3 direction = float3( 2.0 * aspectRatio * p.x / float(size.x) - aspectRatio,
								  -2.0 * p.y / float(size.y) + 1.0,
								  -2.0 * exp(cameraZoom));
		return normalize(direction * viewRotation * objRotation);
	}
 
 
	// Calculate the output colour for each input pixel
	float4 renderPixel(float2 pixel)
	{
		float tmin, tmax;
		float3 ray_direction = rayDirection(pixel);
		float4 color;
        color.rgb = colorBackground.rgb;
        color.a = colorBackgroundTransparency;
 
		if (intersectBoundingSphere(eye, ray_direction, tmin, tmax)) {
			float3 ray = eye + tmin * ray_direction;
 
			float dist, ao;
			float min_dist = 4.0;
			float ray_length = tmin;
			float eps = MIN_EPSILON;
 
			// number of raymarching steps scales inversely with factor
			int max_steps = int(float(stepLimit) / epsilonScale);
			int i;
			float f;
 
			for (i = 0; i < max_steps; ++i) {
				dist = DE(ray, min_dist);
 
				// March ray forward
				f = epsilonScale * dist;
				ray += f * ray_direction;
				ray_length += f * dist;
 
				// Are we within the intersection threshold or completely missed the fractal
				if (dist < eps || ray_length > tmax) break;
 
				// Set the intersection threshold as a function of the ray length from the camera
				eps = max(MIN_EPSILON, pixel_scale * ray_length);
			}
 
 
			// Found intersection?
			if (dist < eps) {
				ao	= 1.0 - clamp(1.0 - min_dist * min_dist, 0.0, 1.0) * ambientOcclusion;
 
				if (phong) {
					float3 normal = estimate_normal(ray, eps/2.0);
					float specular = 0.0;
					color.rgb = Phong(ray, normal, specular);
 
					if (shadows > 0.0) {
						// The shadow ray will start at the intersection point and go
						// towards the point light. We initially move the ray origin
						// a little bit along this direction so that we don't mistakenly
						// find an intersection with the same point again.
						float3 light_direction = normalize((light - ray) * objRotation);
						ray += normal * eps * 2.0;
 
						float min_dist2;
						dist = 4.0;
 
						for (int j = 0; j < max_steps; ++j) {
							dist = DE(ray, min_dist2);
 
							// March ray forward
							f = epsilonScale * dist;
							ray += f * light_direction;
 
							// Are we within the intersection threshold or completely missed the fractal
							if (dist < eps || dot(ray, ray) > bounding * bounding) break;
						}
 
						// Again, if our estimate of the distance to the set is small, we say
						// that there was a hit and so the source point must be in shadow.
						if (dist < eps) {
							color.rgb *= 1.0 - shadows;
						} else {
							// Only add specular component when there is no shadow
							color.rgb += specular;
						}
					} else {
						color.rgb += specular;
					}
				} else {
					// Just use the base colour
					color.rgb = colorDiffuse;
				}
 
				ao *= 1.0 - (float(i) / float(max_steps)) * ambientOcclusionEmphasis * 2.0;
				color.rgb *= ao;
                color.a = 1.0;
			}
		}
 
		return clamp(color, 0.0, 1.0);
	}
 
 
	// Common values used by all pixels
	void evaluateDependents()
	{
		aspectRatio = float(size.x) / float(size.y);
 
		// Camera orientation
		float c1 = cos(radians(-cameraRotation.x));
		float s1 = sin(radians(-cameraRotation.x));
		float3x3 viewRotationY = float3x3( c1, 0, s1,
											0, 1, 0,
										  -s1, 0, c1);
 
		float c2 = cos(radians(-cameraRotation.y));
		float s2 = sin(radians(-cameraRotation.y));
		float3x3 viewRotationZ = float3x3( c2, -s2, 0,
										   s2, c2, 0,
											0, 0, 1);
 
		float c3 = cos(radians(-cameraRotation.z));
		float s3 = sin(radians(-cameraRotation.z));
		float3x3 viewRotationX = float3x3( 1, 0, 0,
										   0, c3, -s3,
										   0, s3, c3);
 
		viewRotation = viewRotationX * viewRotationY * viewRotationZ;
 
		// Object rotation
		c1 = cos(radians(-rotation.x));
		s1 = sin(radians(-rotation.x));
		float3x3 objRotationY = float3x3( c1, 0, s1,
											0, 1, 0,
										  -s1, 0, c1);
 
		c2 = cos(radians(-rotation.y));
		s2 = sin(radians(-rotation.y));
		float3x3 objRotationZ = float3x3( c2, -s2, 0,
										   s2, c2, 0,
											0, 0, 1);
 
		c3 = cos(radians(-rotation.z));
		s3 = sin(radians(-rotation.z));
		float3x3 objRotationX = float3x3( 1, 0, 0,
										   0, c3, -s3,
										   0, s3, c3);
 
		objRotation = objRotationX * objRotationY * objRotationZ;
 
		eye = (cameraPosition + cameraPositionFine);
		if (eye == float3(0, 0, 0)) eye = float3(0, 0.0001, 0);
 
		eye *= objRotation;
 
		// Super sampling
		sampleStep = 1.0 / float(antialiasing);
		sampleContribution = 1.0 / pow(float(antialiasing), 2.0);
		pixel_scale = 1.0 / max(float(size.x), float(size.y));
	}
 
 
	// The main loop
	void evaluatePixel()
	{
		float4 color = float4(0, 0, 0, 0);
 
		if (antialiasing > 1) {
			// Average antialiasing^2 points per pixel
			for (float i = 0.0; i < 1.0; i += sampleStep)
				for (float j = 0.0; j < 1.0; j += sampleStep)
					color += sampleContribution * renderPixel(float2(outCoord().x + i, outCoord().y + j));
		} else {
			color = renderPixel(outCoord());
		}
 
		// Return the final color which is still the background color if we didn't hit anything.
		dst = color;
	}
}