Fast Approximate Convex Decomposition

Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n_c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n_c + 1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods given in the Princeton Shape Benchmark

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