[WGL/P] Implemented correct ray rotation, following Riccardo Antonelli's formula

1 files changed, 20 insertions, 10 deletions

diff --git a/Year 2/Computer Graphics with WebGL/Project/shaders.js b/Year 2/Computer Graphics with WebGL/Project/shaders.js
index 152753a..3fe1e27 100644
--- a/Year 2/Computer Graphics with WebGL/Project/shaders.js
+++ b/Year 2/Computer Graphics with WebGL/Project/shaders.js
@@ -35,6 +35,8 @@
 var fShader = `

 	precision highp float;

 

+	#define MORE_MAGIC 0.01

+

 	uniform mat4 uProjectionMatrix;

 	uniform mat4 uViewMatrix;

 	uniform mat4 uModelMatrix;

@@ -74,21 +76,28 @@ var fShader = `
 

 	int rayMarchInBH(vec4 BH, inout vec3 ray, inout vec3 step) {

 		ray = spherePoint(ray, step, vec4(BH.xyz, BH.a * 3.0));

+

+		// h is used in the step changing calculation

+		float h = length(cross(ray, step));

+

 		for (int i = 0; i < 100; i++) {

-			float dist = linePointDistance(ray, step, BH.xyz);

+			float dist = distance(ray, BH.xyz);

+

 			if (dist <= BH.a) { // if inside event horizon

 				return 1;

 			}

-			if (dist > BH.a * 3.0) { // if outside ISCO

+			if (dist > BH.a * 3.0 + 1.0) { // if outside ISCO

 				return 2;

 			}

 

-			// Used the help of https://en.wikipedia.org/wiki/Gravitational_lens#Explanation_in_terms_of_spacetime_curvature

-			vec3 rayStep = ray + step;

-			float theta = 2.0 * BH.a / length(BH.xyz - ray);

-			float alpha = -theta - angleBetweenVectors(-step, BH.xyz - rayStep);

-			step += normalize(BH.xyz - rayStep) * abs(sin(theta) / sin(alpha) * length(step)) / 100.0;

-

+			// Gravity bends light (actually spacetime, which in turn changes it's path for outside observers).

+			// This is a more or less correct (as far as I can tell) implementation of Riccardo Antonelli's formula

+			// http://rantonels.github.io/starless/#MathJax-Element-29-Frame

+			// Though I found it difficult to understand, so I referred to some of the code from

+			// https://github.com/rantonels/starless/blob/7a0c3c4efdc0666f53dcfa48d310fb2164be2d1a/tracer.py

+			// and

+			// https://github.com/dbrant/BlackHoleRaytracer/blob/master/Equation/SchwarzschildBlackHoleEquation.cs

+			step += normalize(ray - BH.xyz) * -1.5 * (h*h) * MORE_MAGIC / (dist*dist*dist*dist*dist);

 			ray += step;

 		}

 		return 0; // orbits inside

@@ -119,11 +128,12 @@ var fShader = `
 			}

 		}

 

-		// if (bhStatus == 0) return vec4(1,0,0,1);

-		// if (bhStatus == 1) return vec4(0,1,0,1);

+		if (bhStatus == 0) return vec4(1,0,1,1);

+		if (bhStatus == 1) return vec4(0,1,0,1);

 		// if (bhStatus == 2) return vec4(1,1,0,1);

 		if (bhStatus < 2) {

 			return vec4(0,1,0,1);

+			// return vec4(1,0,0,1);

 		}

 

 		for (int i = 0; i < 5; i++) {