proposal-thesis-2011

I didnt include shattering

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.

On icosahedron and tetrahedron