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UBC Theses and Dissertations

Robust sculpting using boundary represented solids Lee, Cedric C.


Boolean operations are often used in the computer modeling of 3-D mechanical parts and machineries and are known for their predictable behavior and ease of use. The use of Boolean operations in the interactive modeling of free-form models, however, has been rather limited. Some of the difficulties in realizing this include: selecting a model representation that may be displayed at interactive speed, applying Boolean operations robustly, and creating smooth surface transitions at the junctions between models. This thesis explores the use of the real number package of the Library of Efficient Datatypes and Algorithms (LEDA) for computing the Boolean combination of triangulated and boundary-represented solids robustly. This thesis also suggests a scheme for removing numerically unstable triangles which are detrimental to the validity of solids, and a surface blending scheme that simulates the smoothing of sharp surface junctions by modifying surface normals. Our scheme for computing Boolean operations is more robust than those used in two popular modeling applications but at the expense of longer computation time. Our scheme for removing numerically unstable triangles is effective in removing invalid surface triangulations while preserving the appearances of models and our simulated surface blending scheme is capable of smoothing non-trivial surface junctions at near-interactive rates. These features were implemented in a simple solid modeler and a set of models was created interactively using this system.

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