Category Archives: Mathematics

What is a solid?

In this post, I am going to go into a bit of a mathematical digression about the fundamentals of solid modeling.  In a nutshell, solid modeling is the study of digital representations of physical shapes.  This was a hot topic … Continue reading

Posted in Mathematics, Shape Modeling | Tagged , | 1 Comment

Simplifying Isosurfaces (Part 2)

To briefly recap, our goal is to render large volumetric environments.  For the sake of both efficiency and image quality, we want to introduce some form of level of detail simplification for distant geometry.  Last time, we discussed two general … Continue reading

Posted in Mathematics, Programming, Voxels | 13 Comments

Simplifying Isosurfaces (Part 1)

I just got back to the US after spending 3 months in Berlin, and I’ve now got plenty of ideas kicking around that I need to get on to paper.   Recall that lately I’ve been blogging about solid modeling and … Continue reading

Posted in Mathematics, Programming, Voxels | 3 Comments

Smooth Voxel Terrain (Part 2)

Last time we formulated the problem of isosurface extraction and discussed some general approaches at a high level.  Today, we’re going to get very specific and look at meshing in particular. For the sake of concreteness, let us suppose that … Continue reading

Posted in Mathematics, Programming, Voxels | 27 Comments

Smooth Voxel Terrain (Part 1)

My god…  I’ve now written three blog posts about Minecraft.  If you are at all like me, you may be getting just a bit tired of all those cubes.  To avoid fatigue, I think now is a good time to change … Continue reading

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Meshing in a Minecraft Game (Part 2)

Last time, I wrote about how to generate meshes in a Minecraft-style voxel engine.  I got a lot of interesting feedback, and so today I’m going to do a follow up highlighting some of the points that came up in the … Continue reading

Posted in Mathematics, Programming, Voxels | 30 Comments

Meshing in a Minecraft Game

The last post I wrote on Minecraft-like engines got a lot of attention, and so I figured it might be interesting to write a follow up.  This time I’ll try to tackle a different problem: Meshing One of the main … Continue reading

Posted in Mathematics, Programming, Voxels | 44 Comments