Umbilics and lines of curvature for shape interrogation

Computer Aided Geometric Design

Volumn 13, Issue 2, 1996, Pages 133-161

  Maekawa, T ^a   Wolter, F E ^b   Patrikalakis, N M ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

CAD; CAGD; Lines of curvature; Monge form; Perturbation; Shape recognition; Umbilics; Vision

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER AIDED DESIGN; COMPUTER VISION; FUNCTIONS; MATHEMATICAL TRANSFORMATIONS; PATTERN RECOGNITION; PERTURBATION TECHNIQUES;

LINES OF CURVATURE; MONGE FORM; PRINCIPAL CURVATURE FUNCTIONS; SHAPE INTERROGATION; SURFACE RECOGNITION; TAYLOR EXPANSION; UMBILICAL POINTS;

COMPUTATIONAL GEOMETRY;

EID: 0030104854     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-8396(95)00018-6     Document Type: Article

References (28)

1. Alourdas, P.G., Hottel, G.R. and Tuohy, S.T. (1990), A design and interrogation system for modeling with rational splines, in: S.K. Chakrabarti et al., eds., Proc. Ninth International Symposium on OMAE, Volume I, Part B, Houston, TX, February 1990, ASME, New York, 555-565.
2. Banchoff, T., Gaffney, T. and McCrory, C. (1992), Cusps of Gauss Mappings, Pittman, Boston, MA.
3. Beck, J.M., Farouki, R.T. and Hinds, J.K. (1986), Surface analysis methods. IEEE Comput. Graph. Appl. 6(12), 18-36.
4. Berry, M.V. and Hannay, J.H. (1977), Umbilic points on Gaussian random surfaces, J. Phys. A 10(11), 1809-1821.
5. Brady, M., Ponce, J., Yuille, A. and Asada, H. (1985), Describing surfaces, Comput. Vision Graph. Image Process. 32(1), 1-28.
6. Darboux, G. (1896), Leçons Sur la Théorie Générale des Surfaces, Vol. 4. Gauthier-Villars, Paris.
7. do Carmo., P.M. (1976), Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ.
8. Dutta, D., Martin, R.R. and Pratt, M.J. (1993), Cyclides in surface and solid modeling, IEEE Comput. Graph. Appl. 13(1), 53-59.
9. Farouki, R.T. (1987), Graphical methods for surface differential geometry, in R.R. Martin, ed., The Mathematics of Surfaces II, Clarendon Press, Oxford, 363-385.
10. Hilbert, D. and Cohn-Vossen, S. (1952), Geometry and the Imagination, Chelsea, New York.
11. Jessop, H.T. and Harris, F.C. (1950), Photoelasticity, Principles and Methods, Dover, New York.
12. Koenderink, J.J. (1990), Solid Shape, MIT Press, Cambridge, MA.
13. Maekawa, T. (1993), Robust computational methods for shape interrogation, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
14. Maekawa, T. and Patrikalakis, N.M. (1993), Computation of singularities and intersections of offsets of planar curves, Computer Aided Geometric Design 10(5), 407-429.
15. Maekawa, T. and Patrikalakis, N.M. (1994), Interrogation of differential geometry properties for design and manufacture, Visual Comput. 10(4), 216-237.
16. Martin, R.R. (1983), Principal patches-a new class of surface patch based on differential geometry, in: P.J.W. Ten Hagen, ed., Eurographics '83, Proc. 4th Ann. European Association for Computer Graphics Conference and Exhibition, Zagreb, Yugoslavia, North-Holland, Amsterdam, 47-55.
17. Munchmeyer, F.C. (1987), On surface imperfections, in: R. Martin, ed., Mathematics of Surfaces II, Oxford University Press, Oxford, 459-474.
18. Patrikalakis, N.M., Maekawa, T., Sherbrooke, E.C. and Zhou, J. (1992), Computation of singularities for engineering design, in: T.L. Kunii and Y. Shinagawa, eds., Modern Geometric Computing for Visualization, Springer, Tokyo, 167-191.
19. Pegna, J. and Wolter, F.E. (1992), Geometrical criteria to guarantee curvature continuity of blend surfaces, J. Mech. Design, ASME Trans. 114(1), 201-210.
20. Porteous, I.R. (1987), Ridges and umbilics of surfaces, in: R. Martin, ed., The Mathematics of Surfaces II, Oxford University Press, Oxford, 447-458.
21. Porteous, I.R. (1988), The circles of a surface, in: R. Martin, ed., The Mathematics of Surfaces III, Oxford University Press, Oxford, 135-143.
22. Pratt, M.J. (1990), Cyclides in computer aided geometric design, Computer Aided Geometric Design 7(1-4), 221-242.
23. Sander, P.T. and Zucker, S.W. (1988), Singularities of principal direction fields from 3-D images, in: IEEE Second Internat. Conf. on Computer Vision, Tampa, FL, 666-670.
24. Sherbrooke, E.C. and Patrikalakis, N.M. (1993), Computation of the solutions of nonlinear polynomial systems, Computer Aided Geometric Design 10(5), 379-405.
25. Sinha, S.S. and Besl, P.J. (1990), Principal patches a viewpoint-invariant surface description, in: IEEE Internat. Robotics and Automation, Cincinnati, OH, 226-231.
26. Spivak, M. (1967), Calculus, W.A. Benjamin, New York.
27. Struik, D.J. (1950), Lectures on Classical Differential Geometry, Addison-Wesley, Cambridge, MA.
28. Zhou, J., Sherbrooke, E.C. and Patrikalakis, N.M. (1993), Computation of stationary points of distance functions, Eng. Comput. 9(4), 231-246.