How do you represent a closed shape mathematically?

Question

I might like to explore scripting, and I'd like to understand mathematically how blender represents a closed shape. Is it a 3xN matrix, an Nx3 matrix? You can represent vertices as vectors, but how do you represent which ones are connected so as to form a closed surface? How do you tell a computer what "closed" means?

Answer 1 · 2025-07-17T05:55:46Z

Martin Bergwerf replied July 17, 2025 5:55am

It depends on what you mean by 'closed', but if you mean Manifold, than you can go through all the Edges and check if every Edge has exactly 2 neighbouring Faces.

1 love

Answer 2 · 2025-07-17T06:04:23Z

Martin Bergwerf replied July 17, 2025 6:04am

Or maybe you mean something this:

A Mesh is written as a 'list' of indexed Vertices and their Positions (mathematically not Vectors). Then a list of indexed Edges and which Vertices they connect and then a list of Faces and which Edges they are surrounded by.

1 love