Uniform offsetting of polygonal model based on Layered Depth-Normal Images |
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Authors: | Yong Chen Charlie CL Wang |
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Affiliation: | aEpstein Department of Industrial and Systems Engineering, University of Southern California, 90089 Los Angeles, CA, United States;bDepartment of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong |
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Abstract: | Uniform offsetting is an important geometric operation for computer-aided design and manufacturing (CAD/CAM) applications such as rapid prototyping, NC machining, coordinate measuring machines, robot collision avoidance, and Hausdorff error calculation. We present a novel method for offsetting (grown and shrunk) a solid model by an arbitrary distance r. First, offset polygons are directly computed for each face, edge, and vertex of an input solid model. The computed polygonal meshes form a continuous boundary; however, such a boundary is invalid since there exist meshes that are closer to the original model than the given distance r as well as self-intersections. Based on the problematic polygonal meshes, we construct a well-structured point-based model, Layered Depth-Normal Image (LDNI), in three orthogonal directions. The accuracy of the generated point-based model can be controlled by setting the tessellation and sampling rates during the construction process. We then process all the sampling points in the model by using a set of point filters to delete all the invalid points. Based on the remaining points, we construct a two-manifold polygonal contour as the resulting offset boundary. Our method is general, simple and efficient. We report experimental results on a variety of CAD models and discuss various applications of the developed uniform offsetting method. |
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Keywords: | Offset surfaces Geometric modeling Trimming self-intersections Layered Depth-Normal Images Point-sampled geometry |
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