A search algorithm for motion planning with six degrees of freedom
Artificial Intelligence
An algorithm to compute the Minkowski sum outer-face of two simple polygons
Proceedings of the twelfth annual symposium on Computational geometry
Polygon Placement Under Translation and Rotation
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
Polygon Decomposition for Efficient Construction of Minkowski Sums
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Minkowski sums of rotating convex polyhedra
Proceedings of the twenty-fourth annual symposium on Computational geometry
A kinetic framework for computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedra
ACM Transactions on Graphics (TOG)
SMI 2012: Full α-Decomposition of polygons
Computers and Graphics
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
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In many common real-world and virtual environments, there are a significant number of repeated objects, primarily varying in size. Similarly, in many complex machines, there are a significant number of parts which also vary in size rather than shape. This repetition saves in both design and production costs. Recent research in robotics has also shown that exploiting workspace repetition can significantly increase efficiency. In this paper, we address the need to support computation reuse in fundamental operations. To this end, we propose an algorithm to reuse the computation of the Minkowski sum when an object is transformed by uniform scaling. The Minkowski sum is a fundamental operation in many areas of robotics, such as motion planning, computer vision, and mathematical morphology, and has been studied extensively over the last four decades. We present two methods for dynamically updating Minkowski sums under scaling, the first of which updates the sum under uniform scaling of arbitrary polygons and polyhedra, and the second of which updates the sum under non-uniform scaling of convex polyhedra. Ours are the first methods that study the Minkowski sum under this type of transformation. Our results show speed gains between one and two orders of magnitude over recomputing the Minkowski sum from scratch for each repeated object, and we discuss applications for motion planning, CAD, rapid prototyping, and shape decomposition.