Computer & Information Science |
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Curvatures estimation on triangular mesh |
DONG Chen-shi, WANG Guo-zhao |
Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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Abstract Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995) presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature, and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt’s method. Some comparison results are also shown in this paper.
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Received: 27 October 2004
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[1] |
Alrashdan, A., Motavali, S., Fallahi, B., 2000. Automatic segmentation of digitized data for reverse engineering applications. IIE Trans., 32:59-69.
|
|
|
[2] |
Chen, X., Schmitt, F., 1992. Intrinsic Surface Properties from Surface Triangulation. Proceedings of the European Conference on Computer Version, p.739-743.
|
|
|
[3] |
Chen, G., Wu, Y., 2004. Estimating normal vectors and curvatures by centroid weights. Computer Aided Geometric Design, 21:447-458.
|
|
|
[4] |
do Carmo, M.P., 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, NJ.
|
|
|
[5] |
Flynn, P.J., Jain, A.K., 1989. On Reliable Curvature Estimation. Proceeding of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, p.110-116.
|
|
|
[6] |
Gatzke, T., Grimm, C., 2003. Improved Curvature Estimation on Triangular Meshes. Eurographics Symposium on Geometry Processing, p.57-67.
|
|
|
[7] |
Goldfeather, J., Interrante, V., 2004. A novel cubic-order algorithm for approximating principal direction vectors. ACM Trans. on Graphics, 23(1):45-63.
|
|
|
[8] |
Karbacher, S., Häusler, G., 1998. A New Approach for Modeling and Smoothing of Scattered 3D Data. SPIE Proceedings for Three-Dimensional Image Capture and Application, 3313:168-177.
|
|
|
[9] |
Martin, R.,1998. Estimation of principal curvatures from range data. Int. J. of Shape Modeling, 3(4):99-109.
|
|
|
[10] |
Meek, D.S., Walton, D.J., 2000. On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Computer Aided Geometric Design, 17:521-543.
|
|
|
[11] |
Meyer, M., Desbrun, M., Schröder, P., Barr, A.H., 2003. Discrete Differential Geometry Operators for Triangulated 2-Manifolds. In: Hege, H.C., Polthier, K.(Eds), Visualization and Mathematics III. Springer Verlag, Heidelberg, Germany, p.35-57.
|
|
|
[12] |
Monga, O., Benayoun, S., Faugeras, O., 1992. From Partial Derivatives of 3D Density Images to Ridge Lines. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, p.354-359.
|
|
|
[13] |
Page, D.L., Sun, Y., Koschan, A.F., Paik, J., Abidi, M.A., 2002. Normal vector voting: crease detection and curvature estimation on large, noisy meshes. Graphical Models, 64:199-229.
|
|
|
[14] |
Petitjean, S., 2002. A survey of methods for recovering quadrics in triangular meshes. ACM Computing Surveys, 2(34):1-61.
|
|
|
[15] |
Sacchi, R., Poliakoff, J., Thomas, P., Häfele, K.H., 1999. Curvature Estimation for Segmentation of Triangulated Surfaces. Proc. of 2nd International Conference on 3D Imaging and Modeling. Ottawa, Canada, p.536-543.
|
|
|
[16] |
Sander, P.T., Zucker, S.W., 1990. Inferring surface trace and differential structure from 3D images. IEEE Trans. Pattern Anal. Mach. Intell., 12(9):833-854.
|
|
|
[17] |
Taubin, G., 1995. Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation. Proceedings of the Fifth International Conference on Computer Vision, p.902-907.
|
|
|
[18] |
Wollmann, C., 2000. Estimation of the principle curvatures of approximated surfaces. Computer Aided Geometric Design, 17:621-630.
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