Michael Hansmeyer
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Platonic Solids - Technical Background

The processes at the core of this project are the Catmull-Clark and Doo-Sabin algorithms. They were both conceived of in the late 1970's with the aim of generating smooth surfaces from coarses polygonal meshes.

The processes can be understood by considering their two parts: topological rules and weighting rules. The topological rules specify how to obtain the combinatorics of the refined mesh from the combinatorics of the input mesh by generating new vertices, edges and faces. The weighting rules specify how to calculate the positions of these new vertices based on interpolation between vertices of the input mesh.

By introducing parameters to allow for variations in these weighting rules, non-rounded forms with highly diverse attributes can be produced. Whereas the traditional weighting rules specify the positions of new vertices strictly as interpolations of previous-generation vertices, these rules are amended to allow for extrusion along face, edge and vertex normals. It is primarily through these two changes to the established schemes the complex geometries in this project become possible.

View the forms in 3D as anaglyphs (requires red-cyan glasses):
Platonic Solids Anaglyphs (Flash, 3Mb)

Form affected by increasing subdivision iterations