magicavoxel

Ellipsoid SDF Primitive

Added 2023-07-08 17:20:41 +0000 UTC

My recent focus is exploring some advanced Signed Distance Field (SDF) editing features which have better quality but may be expensive to compute.

Take ellipsoid as an example. It's the fundamental primitive for modeling curved surfaces (such as heads and muscles). However, though the surface of ellipsoid is very simple to be defined in Cartesian coordinates or Spherical coordinate system, the L2-norm SDF of ellipsoid has no analytic solution.

Therefore, several approximation methods are implemented in MagicaCSG. Here we discuss the pros and cons of each method. All of these methods have the correct representation for the surface of ellipsoid but are different in the blending regions /interior shell shapes and performance.

1. Exact L2-Norm

This new method of mine computes the exact L2 distance in brute force. It has equal-distance rounded blending region and interior shell (Half X/Y/Z + Shell) which is ideal for modeling smooth surfaces.

But it's over 2x slower than the other methods, so make sure you don't use too many ellipsoids with large blending factors at high resolution.

2. L∞-Norm (or max-norm)

This method is used in Dreams on PS4. It's very fast and stable. But the blended region and interior shell is squared and edged. It may be good for stylistic modeling or something like rocks or meteorite.

3. Scaled L2-Norm

This is the default method used in previous versions. It is fast and has rounded blended regions, but when the ellipsoid is flat, the blended region is scaled and stretched which is inconvenient in some cases. Besides that, it has an extra "Power" parameter to make the shape less "spherical".

Summary

You may choose the method that best fits your purpose or your machine specification.

I'm also thinking about having different quality controls for Live Editing and Final Fused Model.