voxel analysis for implicit surfaces

This is my first test with implicit surfaces. I tried to voxelize a sort of rheotomic surface, defined by rules of iso-distance between nearest elements of two differtent groups (1 point+2 curves for first group and 2 points+1 curve for the second one).

In a first moment, I tested the brute-force samplyng method, in order to search for a way to sample points belonging to implicit surfaces. This expensive method consists of analyzing all possible solutions and the subsequent evaluation of results. In this case I needed to verify each point of my 3D grid and improving the resolution, i obtained  8^n points every n divisions of main domain.

A better solution consists in a progressive analysis: starting from a domain, and progressively dividing positive matched cubes (later I learned that this approach already exists with the name of Quadtree):

Sampling Scheme

Explanation of progressive sampling method.

Coding it with c# in grasshopper, I obtained a relatively complex point cloud:

Rheotomic surface_002

Point Cloud otup in grasshopper

This coarse approximation isn’t at the moment enough accurated for obtaining clean surfaces, however I tried to connect resulting point-cloud with MeshLab. After a quick editing in Blender, I rendered the output:

Rheotomic surface_001

Final Mesh

At the moment I’m working on the improvement of the quality of point-cloud and subsequent elegance of the resulting mesh.

2 commenti to “voxel analysis for implicit surfaces”

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