Master’s thesis

Subject is

Signed distance field representation of polygonal meshes

Problem is

Polygonal meshes are popular in computer graphics but they have major drawbacks. They cannot accurately represent smooth shapes, their validity can be broken with holes and self intersections. Moreover, it only defines the surface of an objects rather than the volume and is very clumsy at representing heterogeneous objects. Implicit surfaces, and more generally FReps can represent volumes and perform complex operations more easily, but they are less natural to work with and user-control is more complicated. Converting from one model to another is required. Generating a signed distance field  means generating a tri-variate function with distance properties to the surface. Usually, the sign would be negative inside the solid and positive outside. Although this problem has been partly solved, it is often a performance bottleneck, and problems may arise with open meshes, inverted normals and when trying to generate continuous values.

I will post the proposal later.

Update

halfedge structure can now read mixed meshes – so I can have arbitrary meshes with catmull clark

Creases

Creases implemented. For now all edges, because I dont have the editor to select the edges etc…

Loop subdivision

First, loop subdivision

On icosahedron and tetrahedron

Monkey head

The problem I met this time is, it is now difficult to render mixed meshes, one solution would be to store triangles and quads in separate arrays. Makes it a bit more complicated to go through face etc… For now I just remove the triangles, and orphan vertices are skipped.