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Abstract The Doubly Connected Edge List (DCEL) is an edge-list structure widely used in spatial applications, primarily for planar topological and geometric computations. However, it is also applicable to various types of data, including 3D models and geographic data. An essential operation is theoverlay operation, which combines the DCELs of two input polygon layers and can easily support spatial queries on polygons like the intersection, union, and difference between these layers. However, existing techniques for spatial overlay operations suffer from two main limitations. First, they fail to handle many large datasets practically used in real applications. Second, they cannot handle arbitrary spatial lines that practically form polygons, e.g., city blocks, but they are given as a set of scattered lines. This work proposes a distributed and scalable way to compute the overlay operation and its related supported queries. Our operations also support arbitrary spatial lines through a scalable polygonization process. We address the issues of efficiently distributing the lines and overlay operators and offer various optimizations that improve performance. Our experiments demonstrate that the proposed scalable solution can efficiently compute the overlay of large real datasets.
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Integer coordinates for intrinsic geometry processing
This paper describes a numerically robust data structure for encoding intrinsic triangulations of polyhedral surfaces. Many applications demand a correspondence between the intrinsic triangulation and the input surface, but existing data structures either rely on floating point values to encode correspondence, or do not support remeshing operations beyond basic edge flips. We instead provide an integer-based data structure that guarantees valid correspondence, even for meshes with near-degenerate elements. Our starting point is the framework ofnormal coordinatesfrom geometric topology, which we extend to the broader set of operations needed for mesh processing (vertex insertion, edge splits,etc.). The resulting data structure can be used as a drop-in replacement for earlier schemes, automatically improving reliability across a wide variety of applications. As a stress test, we successfully compute an intrinsic Delaunay refinement and associated subdivision for all manifold meshes in the Thingi10k dataset. In turn, we can compute reliable and highly accurate solutions to partial differential equations even on extremely low-quality meshes.
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- Award ID(s):
- 1943123
- PAR ID:
- 10602930
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- ACM Transactions on Graphics
- Volume:
- 40
- Issue:
- 6
- ISSN:
- 0730-0301
- Format(s):
- Medium: X Size: p. 1-13
- Size(s):
- p. 1-13
- Sponsoring Org:
- National Science Foundation
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