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Minkowski sum is a fundamental operation in many geometric applications, including
robotics, penetration depth estimation, solid modeling, and virtual
prototyping. In this work, we propose
to represent the boundary of the Minkowski sum approximately using only points.
Our results show that this point-based representation can be generated efficiently.
An important feature of our method is its
straightforward implementation and parallelization.
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Benefits of point-based Minkowski sum
- efficiency,
- robustness (can even work for non-manifold models with open surfaces),
- easy implementation (i.e., no convex decomposition and no need to perform union),
- easy parallelization,
- multiresolution representations, and
- similar functionality as mesh-based representations
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Publications
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Jyh-Ming Lien. "Point-Based Minkowski Sum Boundary",
Proceedings of the Pacific Conference on Computer Graphics and Applications (Pacific Graphics), Maui, Hawaii,
Nov. 2007, page 261--270.
[pdf]
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Software
| pm+3d version 0.5 (Oct 2007) |
| download binary: win 32 |
linux | mac |
| Note:
- You may need to have glut library if you want to visualize the results. You can get glut
from freeglut for linux and from
this page for win32.
- Source code (in C++) is available on request
- Report bugs to jmlien@cs.gmu.edu
| | ReadMe file contains the command line options and the gui control keys of the program
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Examples
| Input models: dancing children+unit cube |
Minkowski sum |
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| Input models: pig+path |
Minkowski sum |
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| Input models: baby+torus |
Minkowski sum |
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| Input models: hooks |
Minkowski sum |
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| Input models: octpus+(-dragon) |
Minkowski sum |
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Related Links
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