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sccao

Whilst clunky, it seems like most major 3d modelers use primarily polygons, and I've also heard that quads are the way to go. I feel like intuitively, implicit definitions have its good points as well; however, I don't think many modelling software uses them as its forte. Why is that? Is it because GPUs are specialized towards triangles? I thought they were also good at math?

Max

MeshEdit should help illuminate these tradeoffs - polygons are generally nicer to model with, and with some restrictions, support operations like subdivision & extrusion. Quads are particularly good for that. Some modeling programs support binary operations on shapes as well as signed distance fields, but it can be difficult and fragile to create complex/realistic objects with them. (But definitely not impossible! Check this and out and this for more.)

As for GPUs, they really only render triangles by default - everything else either has to be converted or use a more specialized rendering path like per-pixel ray marching/sphere tracing (for signed distance functions).

ryanmelon

This data structure is similar to how .obj files storing the data of a model. All the normal, texture coordinates information are also connected to vertexes with id.