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I optimized the raytracing of gaussian metaballs. Here we have a negative ball followed by a positive ball (they are segments since I show them in a single dimension). The pink graphic shows the pseudo-distance field, function of the point in space (the space is the Real line here), blue is y=0, red is y=1, green is y=-1.

The first graph shows how the sphere tracing (represented by dark green circless) evolved before when I only normalized the field with the lipschitzian constant. There are a lot of steps until we reach the intersection with y=0 (the boundary with the object), so the algorithm was slow.

The second graph shows the same thing, but this time I conditioned the field to make it closer to a true distance field. There are far less steps so it’s faster. However, this conditioning only works on a group of positive balls. You can see the field is not continuous because we only work with positive balls first. When we reach a certain threshold, we fall back on the old method which account for all the balls, but is efficient enough to be used when we’re close to the object.

This is a new set where I experiment metaballs based on Perlin noise, and more based on electrical fields. You can find out more about it on the internet.

Usually, implementations of this family of objects use the marching cubes algorithm. This is indeed quite efficient when using a rasterizer, which is the rendering model used by your graphic card and DirectX/OpenGL. It’s still possible to use it in raytracing, but it’s an approximation, and you end up with a polygon mesh or a voxel buffer. I don’t like them, so I’m left with two solutions. Either I run a volumetric raytracing with a fixed step (this is raymarching, still an approximation), or I keep using the distance field raytracing I was already using so much before (this is sphere tracing). The only problem is, these things are NOT distance fields. The electrical field is a bunch of 3D gaussian “curves” mashed together, and the object is defined when its value goes above a certain threshold. Fundamentally the same for the 3D Perlin noise.

Last part of the set.

Second part of the set. More volumetric rendering. I also introduce the Schlick material as a citizen of the uncountable amount of Physically Based Rendering methods, replacing the less realistic Phong material (I still keep it in a corner though).

Here is the first part of the second set (why is there a limit of 10 pictures ? ;_; ), showing some progress while I was piling up features and trying to figure out how to fix and tweak them. The time range for the entire set spans from March 22 to April 9. Lighting and aspect ratio had been fixed beforehand.

I was wondering where to put my raytracing gallery, and then I remembered I had a tumblr account. Brilliant. These two are actually stereoscopic images (crossed vision). The first one uses harmonic metaballs (February 25), the second one uses CSG (March 8 -- the lighting and aspect ratio are wrong, but don’t mind).

Every rendered image posted here is entirely generated with my own software unless stated otherwise. I usually program with C++, and I’m fond of Common Lisp too. I’ve also a bit less substantial experience with Java, javascript, and much less experience (or rather, I haven’t used them for a while) with SPARC and x86 ASM, TI-Basic.