Access the full text.
Sign up today, get DeepDyve free for 14 days.
P. Ghosh (1990)
A Solution of Polygon Containment, Spatial Planning, and Other Related Problems Using Minkowski OperationsComput. Vis. Graph. Image Process., 49
H Barki, F Denis, F Dupont (2010)
IEEE Int. Conf. on Shape Modeling
Uldarico Muico, J. Popović, Zoran Popovic (2011)
Composite control of physically simulated charactersACM Trans. Graph., 30
J. O'Rourke (1998)
Computational geometry in C (2nd ed.)
JM Lien (2008)
Proc. of Eigth Workshop on the Algorithmic Foundations of Robotics
S Pion, A Fabri (2006)
Proc. 2nd Library-Centric Software Design
Sylvain Pion, Andreas Fabri (2006)
A generic lazy evaluation scheme for exact geometric computationsSci. Comput. Program., 76
H. Barki, Florence Denis, F. Dupont (2011)
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedraACM Trans. Graph., 30
Y Kim, M Otaduy, M Lin, D Manocha (2003)
SCG ′03: Proc. of the Nineteenth Annual Symposium on Computational Geometry
F Chazal, A Lieutier, N Montana (2009)
SGP ′09: Proc. of the 2009 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Marc Alexa, Michael Kazhdan, F. Chazal, A. Lieutier, N. Montana
Eurographics Symposium on Geometry Processing 2009 Discrete Critical Values: a General Framework for Silhouettes Computation
M. Campen, L. Kobbelt (2010)
Polygonal Boundary Evaluation of Minkowski Sums and Swept VolumesComputer Graphics Forum, 29
J. O'Rourke (1998)
Computational Geometry in C: Arrangements
P. Ghosh (1993)
A unified computational framework for Minkowski operationsComput. Graph., 17
Anil Kaul, J. Rossignac (1991)
Solid-interpolating deformations: Construction and animation of PIPs
G Varadhan, D Manocha (2006)
Accurate Minkowski sum approximation of polyhedral modelsGraph. Models, 68
In-Kwon Lee, Myung-Soo Kim, G. Elber (1998)
Polynomial/Rational Approximation of Minkowski Sum Boundary CurvesGraph. Model. Image Process., 60
C. Barber, D. Dobkin, H. Huhdanpaa (1996)
The quickhull algorithm for convex hullsACM Trans. Math. Softw., 22
H. Barki, Florence Denis, F. Dupont (2009)
Contributing vertices-based Minkowski sum of a non-convex polyhedron without fold and a convex polyhedron2009 IEEE International Conference on Shape Modeling and Applications
R Evans, M O’connor, J Rossignac (1992)
Construction of Minkowski sums and derivatives morphological combinations of arbitrary polyhedra in CAD/CAM systems
A. Tuzikov, J. Roerdink, H. Heijmans (2000)
Similarity measures for convex polyhedra based on Minkowski additionPattern Recognit., 33
F. Preparata, M. Shamos (1985)
Computational Geometry
Tomas Lozano-Perez (1983)
Spatial Planning: A Configuration Space ApproachIEEE Transactions on Computers, C-32
J O’Rourke (1998)
Computational geometry in C
Jyh-Ming Lien (2008)
A Simple Method for Computing Minkowski Sum Boundary in 3D Using Collision Detection
H. Barki, Florence Denis, F. Dupont (2010)
A New Algorithm for the Computation of the Minkowski Difference of Convex Polyhedra2010 Shape Modeling International Conference
F Preparata, M Shamos (1985)
Computational geometry: an introduction
Peter Hachenberger (2007)
Exact Minkowksi Sums of Polyhedra and Exact and Efficient Decomposition of Polyhedra into Convex PiecesAlgorithmica, 55
Lutz Kettner (1999)
Using generic programming for designing a data structure for polyhedral surfacesComput. Geom., 13
H. Barki, Florence Denis, F. Dupont (2009)
Contributing vertices-based Minkowski sum computation of convex polyhedraComput. Aided Des., 41
Young Kim, M. Otaduy, M. Lin, Dinesh Manocha (2003)
Fast penetration depth estimation using rasterization hardware and hierarchical refinement
J. Serra (1983)
Image Analysis and Mathematical Morphology
Yi-King Choi, Xue-qing Li, Fengguang Rong, Wenping Wang, S. Cameron (2008)
Determining Directional Contact Range of Two Convex Polyhedra
Gokul Varadhan, Dinesh Manocha (2004)
Accurate Minkowski sum approximation of polyhedral models12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings.
Minkowski sum and difference, well known as dilation and erosion in image analysis, constitute the kernel of mathematical morphology. Extending the interesting results of the later theory from 2D images to 3D meshes is very promising. However, this requires the development of robust algorithms for the computation of Minkowski operations, which is far from being an easy task. The contributing vertices concept has been introduced for the computation of Minkowski sum of convex polyhedra, and later extended for the computation of non-convex/convex pairs of polyhedra. For Minkowski difference, the available literature is poor. In this work, we demonstrate the duality of the contributing vertices concept w.r.t. Minkowski operations, and propose an exact and efficient Contributing Vertices-based Minkowski Difference (CVMD) algorithm for polyhedra. Our algorithm operates on convex polyhedra and on pairs of convex/non-convex polyhedra without any modification. We also show its beneficial application where the second operand is represented in 3D by an implicit surface or a point cloud, among other possible representations. The conducted benchmarks show that CVMD largely outperforms an indirect Nef polyhedrabased approach we implemented in order to validate our results. All our implementations produce exact results and supplementary materials are provided [Figure not available: see fulltext.]
3D Research – Springer Journals
Published: Sep 26, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.