The goal of this thesis is to introduce new methods to create intricate perforated shapes in a computing environment. Modeling shapes with a large number of holes and handles, while requiring minimal human interaction, is an unsolved research problem in computer graphics. In this thesis, we have developed two methods for interactively modeling such shapes. Both methods developed create perforated shapes by building a framework of tube like elements, such that each edge of a given mesh is replaced by a pipe. The first method called Wire modeling replaces each edge with a pipe that has a square cross-section. The result looks like a shape that is created by a framework of matchsticks. The second method, called Column modeling allows more rounded cross-sections for the pipes. The cross-sections can be any uniform polygon, and the users are able to control the number of the segments in the cross-section. These methods are implemented as an extension to an existing modeling system guaranteeing that the pipes are connected and the resulting shape can be physically constructed. Our methods require an initial input mesh that can either be imported from a commercially available software package, or created directly in this modeling system. The system also allows the users to export the models in obj file format, so that the models can be animated and rendered in other software packages.

The goal of this thesis is to introduce new methods to create intricate perforated shapes in a computing environment. Modeling shapes with a large number of holes and handles, while requiring minimal human interaction, is an unsolved research problem in computer graphics. In this thesis, we have developed two methods for interactively modeling such shapes. Both methods developed create perforated shapes by building a framework of tube like elements, such that each edge of a given mesh is replaced by a pipe. The first method called Wire modeling replaces each edge with a pipe that has a square cross-section. The result looks like a shape that is created by a framework of matchsticks. The second method, called Column modeling allows more rounded cross-sections for the pipes. The cross-sections can be any uniform polygon, and the users are able to control the number of the segments in the cross-section. These methods are implemented as an extension to an existing modeling system guaranteeing that the pipes are connected and the resulting shape can be physically constructed. Our methods require an initial input mesh that can either be imported from a commercially available software package, or created directly in this modeling system. The system also allows the users to export the models in obj file format, so that the models can be animated and rendered in other software packages.

The goal of this research is to develop new, interactive methods for creating very high genus 2-manifold meshes. The various approaches investigated in this research can be categorized into two groups -- interactive methods, where the user primarily controls the creation of the high-genus mesh, and automatic methods, where there is minimal user interaction and the program automatically creates the high-genus mesh. In the interactive category, two different methods have been developed. The first allows the creation of multi-segment, curved handles between two different faces, which can belong to the same mesh or to geometrically distinct meshes. The second method, which is referred to as ``rind modeling'', provides for easy creation of surfaces resembling peeled and punctured rinds. The automatic category also includes two different methods. The first one automates the process of creating generalized Sierpinski polyhedra, while the second one allows the creation of Menger sponge-type meshes. Efficient and robust algorithms for these approaches and user-friendly tools for these algorithms have been developed and implemented.