Computer graphics in IndiaA unified computational framework for Minkowski operations
References (26)
A mathematical model for shape description using Minkowski operators
A solution of polygon containment, spatial planning, and other related problems using Minkowski operations
An algebra of polygons through the notion of negative shapes
CVGIP: Image Understanding
(1991)- et al.
Solid-interpolating deformations: Construction and animation of PIPs
Comp. & Graph.
(1992) Finding the minimum distance between two convex polygons
- et al.
The brush-trajectory approach to figure specification: Some algebraic solutions
ACM Trans. Graph.
(1984) A Computational Theoretic Framework for Shape Representation and Analysis using Minkowski Addition and Decomposition Operators
Vision, geometry, and Minkowski operators
Contemp. Math.
(1991)- et al.
Morphological methods in image processing and signal processing
(1988) Convex Polytopes
(1967)
A kinetic framework for computational geometry
Computing convolutions by reciprocal search
Discrete Comp. Geom.
(1987)
Image analysis using mathematical morphology
IEEE Trans. PAMI
(1987)
Cited by (99)
Methodology for numerical evaluation of fracture resistance under pinch loading of spent nuclear fuel cladding containing reoriented hydrides
2024, Nuclear Engineering and TechnologyA unified algebraic framework for fast and precise planar swept volumes and Minkowski sums
2022, Computer Aided Geometric DesignClosed-form Minkowski sums of convex bodies with smooth positively curved boundaries
2022, CAD Computer Aided DesignCitation Excerpt :Although the focus of this article is convex bodies, it is still possible to extend the capability of our work to deal with non-convex bodies using convex decomposition methods. A unified framework based on slope diagram has been presented for both convex and non-convex bodies in both 2D and 3D spaces [21]. The idea is closely related to the Gauss map, which maps a surface point into its normal vector.
A new approach for grasp quality calculation using continuous boundary formulation of grasp wrench space
2022, Mechanism and Machine TheoryExact Minkowski sums of polygons with holes
2018, Computational Geometry: Theory and ApplicationsCitation Excerpt :They also tested different decomposition methods, but none of them handles polygons with holes. Ghosh [14] introduced slope diagrams—a data structure that was used later on by some of us to construct Minkowski sums of bounded convex polyhedra in 3D [15]. Hachenberger [8] constructed Minkowski sums of general polyhedra in 3D.
Continuous penetration depth computation for rigid models using dynamic Minkowski sums
2016, CAD Computer Aided Design
Copyright © 1993 Published by Elsevier Ltd.