Lightweight preprocessing and fast query of geodesic distance via proximity graph
Computing geodesic distance on a mesh surface efficiently and accurately is a central task in numerous computer graphics applications. In order to deal with high-resolution mesh surfaces, a lightweight preprocessing is a proper choice to make a balance between query accuracy and speed. In the prepr...
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| Main Authors: | , , , , , , |
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| 其他作者: | |
| 格式: | Article |
| 語言: | English |
| 出版: |
2019
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| 主題: | |
| 在線閱讀: | https://hdl.handle.net/10356/85378 http://hdl.handle.net/10220/49218 |
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| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | Computing geodesic distance on a mesh surface efficiently and accurately is a central task in numerous computer graphics applications. In order to deal with high-resolution mesh surfaces, a lightweight preprocessing is a proper choice to make a balance between query accuracy and speed. In the preprocessing stage, we build a proximity graph with regard to a set of sample points and keep the exact geodesic distance between any pair of nearby sample points. In the query stage, given two query points and , we augment the proximity graph by adding and on-the-fly, and then use the shortest path between and on the augmented proximity graph to approximate the exact geodesic path between and . We establish an empirical relationship between the number of samples and expected accuracy (measured in relative error), which facilitates fast and accurate query of geodesic distance with a lightweight processing cost. We exhibit the uses of the new approach in two applications—real-time computation of discrete exponential map for texture mapping and interactive design of spline curves on surfaces. |
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