Understanding the Structure of 3D Shapes: PolyCubes and Curve-Skeletons

Abstract

Compact representations of three dimensional objects are very often usedin computer graphics to create effective ways to analyse, manipulate andtransmit 3D models. Their ability to abstract from the concrete shapes andexpose their structure is important in a number of applications, spanningfrom computer animation, to medicine, to physical simulations. This thesiswill investigate new methods for the generation of compact shape representations.In the first part, the problem of computing optimal PolyCube basecomplexes will be considered. PolyCubes are orthogonal polyhedra usedin computer graphics to map both surfaces and volumes. Their ability toresemble the original models and at the same time expose a very simple andregular structure is important in a number of applications, such as texturemapping, spline fitting and hex-meshing. The second part will focus onmedial descriptors. In particular, two new algorithms for the generationof curve-skeletons will be presented. These methods are completely basedon the visual appearance of the input, therefore they are independent fromthe type, number and quality of the primitives used to describe a shape,determining, thus, an advancement to the state of the art in the field.