Minkowski sum boundary surfaces of 3D-objects

Graphical Models

Volumn 69, Issue 3-4, 2007, Pages 180-190

  Peternell, Martin ^a   Steiner, Tibor ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Convolution surface; Envelope; Marching algorithm; Minkowski sum; Motion; Point set surface; Signed distance function; Translation

Indexed keywords

APPROXIMATION ALGORITHMS; COMPUTATIONAL METHODS; KINEMATICS; THREE DIMENSIONAL; TRANSLATION (LANGUAGES); VECTORS;

CONVOLUTION SURFACES; MARCHING ALGORITHM; MINKOWSKI SUM; POINT SET SURFACES; SIGNED DISTANCE FUNCTIONS;

OBJECT RECOGNITION;

ALGORITHM; KINEMATICS; SMOOTHING; THREE-DIMENSIONAL MODELING;

EID: 34548034676     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gmod.2007.01.001     Document Type: Article

References (18)

1. Bloomenthal J., and Shoemake K. Convolution Surfaces. Computer Graphics 25 4 (1991) 251-256
2. Farouki R.T. Minkowski combination of complex sets-Geometry, Algorithms and applications. In: Lyche T., Mazure M.-L., and Schumaker L.L. (Eds). Curve and Surface Design: Saint Malo 2002 (2003), Nashboro Press 123-146
3. Halperin D. Robust geometric computing in motion. The international Journal of Robotics Research 21 3 (2002) 219-232
4. Kaul A., and Farouki R.T. Computing Minkowski sums of planar curves. International Journal of Computational Geometry and Applications 5 (1995) 413-432
5. Kohler K., and Spreng M. Fast computation of the C-space of convex 2D algebraic objects. The International Journal of Robotics Research 14 6 (1995) 590-608
6. Lee I.-K., Kim M.-S., and Elber G. Polynomial/rational approximation of Minkowski sum boundary curves. Graphical Models 60 2 (1998) 136-165
7. I.K. Lee, M.-S. Kim, G. Elber, The Minkowski sum of 2D curved objects, in: Proceedings of Israel-Korea Bi-National Conference on New Themes in Computerized Geometrical Modeling, Tel-Aviv University, 1998, pp. 155-164.
8. Mühlthaler H., and Pottmann H. Computing the Minkowski sum of ruled surfaces. Graphical Models 65 (2003) 369-384
9. Oeltze S., and Preim B. Visualization of vasculature with convolution surfaces: method, validation and evaluation. IEEE Transactions on Medical Imaging 24 4 (2005) 540-548
10. O'Rourke J. Computational Geometry in C (1994), Cambridge University Press pp. 278-283
11. Peternell M., and Manhart F. The convolution of a paraboloid and a parametrized surface. Journal for Geometry and Graphics 7 (2003) 157-171
12. Peternell M., Pottmann H., Steiner T., and Zhao H. Swept volumes. Computer-Aided Design Application 2 (2005) 599-608
13. Pottmann H., Steiner T., Hofer M., Haider C., and Hanbury A. The isophotic metric and its application to feature sensitive morphology on surfaces. Computer Vision-ECCV 2004, Part IV. In: Pajdla T., and Matas J. (Eds). Lecture Notes in Computer Science vol. 3024 (2004), Springer 560-572
14. Sampoli M.L., Peternell M., and Jüttler B. The convolution of a paraboloid and a parametrized surface. Computer Aided Geometric Design 23 (2006) 179-192
15. J.-K. Seong, M.-S. Kim, K. Sugihara, The Minkowski sum of two simple surfaces generated by slope-monotone closed curves, in: Proceedings of Geometric Modeling and Processing 2002, Japan, 2002, pp. 33-42.
16. A. Sherstyuk, Convolution Surfaces in Computer Graphics. PhD thesis, Monash University, Australia, 1999.
17. Varadhan G., and Manocha D. Accurate minkowski sum approximation of polyhedral models. Pacific Conference on Computer Graphics and Applications (2004), IEEE Computer Society 392-401
18. Kim Y.J., Varadhan G., Lin M.C., and Manocha D. Fast swept volume approximation of complex polyhedral models. Computer Aided Design 36 (2004) 1013-1027