Understanding the Structure of 3D Shapes

Compact representations of three dimensional objects are very often used in computer graphics to create effective ways to analyse, manipulate and transmit 3D models. Their ability to abstract from the concrete shapes and expose their structure is important in a number of applications, spanning from computer animation, to medicine, to physical simulations. This thesis will investigate new methods for the generation of compact shape representations. In the first part, the problem of computing optimal PolyCube base complexes will be considered. PolyCubes are orthogonal polyhedra used in computer graphics to map both surfaces and volumes. Their ability to resemble the original models and at the same time expose a very simple and regular structure is important in a number of applications, such as texture mapping, spline fitting and hex-meshing. The second part will focus on medial descriptors. In particular, two new algorithms for the generation of curve-skeletons will be presented. These methods are completely based on the visual appearance of the input, therefore they are independent from the 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

Understanding the Structure of 3D Shapes

Compact representations of three dimensional objects are very often used in computer graphics to create effective ways to analyse, manipulate and transmit 3D models. Their ability to abstract from the concrete shapes and expose their structure is important in a number of applications, spanning from computer animation, to medicine, to physical simulations. This thesis will investigate new methods for the generation of compact shape representations. In the first part, the problem of computing optimal PolyCube base complexes will be considered. PolyCubes are orthogonal polyhedra used in computer graphics to map both surfaces and volumes. Their ability to resemble the original models and at the same time expose a very simple and regular structure is important in a number of applications, such as texture mapping, spline fitting and hex-meshing. The second part will focus on medial descriptors. In particular, two new algorithms for the generation of curve-skeletons will be presented. These methods are completely based on the visual appearance of the input, therefore they are independent from the 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

Rigid registration of different poses of animated shapes

Different poses of 3D models are very often given in different positions and orientations in space. Since most of the computer graphics algorithms do not satisfy geometric invariance, it is very important to bring shapes into a canonical coordinate frame before any processing. In this paper we consider the problem of finding the best alignment between two or more different poses of the same object represented by triangle meshes sharing the same connectivity. Firstly, we developed a method to select a region of interest (ROI) which has a perfect alignment over the two poses (up to a rigid movement). Secondary, we solved a simplified version of the Largest Common Point-set (LCP) problem with a-priori knowledge about point correspondence, in order to align the ROIs. We eventually align the poses performing least square rigid registration. Our method makes no assumption about the starting positions of the objects and can also be used with more than two poses at once. It is fast, non-iterative, easy to reproduce and brings the poses into the best alignment whatever the initial positions are