Saturday, October 25, 2008

GI - Photon Mapping - Post 5

Basic Features
Here is a list of renders representing the still very basic state of the ray tracer.
you can see here flat planes, spheres, quadrics and triangles, points lights, flat shading, lambertian diffuse, blinn-phong specular, hard shadows, reflections, refractions, exposure, super sampling and wavefront .obj loading (using the code by 'Micah Taylor' a.k.a kixornet found here), and finally multi core rendering in 2 flavors (Task Thread Scheduler, OpenMP).

2 renders show artifacts (also known as surface acne).

Self Shadowing Artifacts
The 1st artifacts were caused by 'self shadowing', numerical imprecision causes the calculated intersection point to lie inside the surface it intersects, shooting a new ray to determine light visibility from the intersection point cause an intersection again with the surface itself, a common problem... There is more than 1 solution to the problem but I chose to avoid 'epsilons' whenever possible.
I solved this without epsilons in a way that works for primitives that do not self shadow, which is for the now the case of all the supported primitives:

when a ray-primitive intersect function is called on primitive (A), a flag is passed to indicate if the ray's origin was also obtained by intersection with (A), for flat surfaces like planes and triangles I directly conclude that there is no new intersection possible.

For Spheres and general quadrics I also use the flag, if the flag is false (intersection coming from another primitive) I switch to the normal intersection test (finding the smallest non negative root). However if the flag is true, I use a 'smarter' and a tiny bit more expensive algorithm, based on our knowledge that the ray's origin is on the surface, we have 3 cases based on the 2 possible roots (tMin and tMax)

1. we obtain 2 positive roots: this can only mean the imprecision pushed the intersection point into the primitive with the ray's direction pointing out of the primitive (most probably a refraction ray), therefore we return tMax.

2. we obtain 2 negative roots: this can only mean the imprecision pushed the intersection out of the primitive with the ray's direction pointing into the primitive (most probably a light or reflection), therefore there is no intersection.

3. we obtain roots with opposite signs: the point was pushed inside the primitive, in this case we signal an intersection only if the positive root is larger than the absolute value of the negative root.

This solves the problem for general quadrics (including spheres) without using epsilon or some iterative technique, of course this might not be feasible for other types of surfaces, if I add such surfaces later I will add other techniques and the technique will be chosen based on the primitive, or at least ... that's the current plan...

Big Float / Small Float Loss of precision Artifacts
The second kind of artifact is seen in the Test Cornell Box Render (Test because it uses one point light). The point lights are currently represented by spheres, this scene is 540 units in heigh, the light sphere is created with a radius of 0.1 units. The problem was occuring because, when trying to shoot a ray from a surface point toward the light, the sphere was missed at times, this was due to the fact that normalizing the distance (point to light) vector was causing enough loss or precision for the intersection tests with the sphere to report no intersection! My first idea was not to normalize the direction vector, this eliminated the artifact, but produced others, now, there were intersections being detected between the ray and close by triangles, there were only very few of the artifacts, but still, they were there, So I went back to normalizing the direction vector, and simply increased the radius of the light sphere. This is probably not the best solution, I will look into this some more ...

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