Abstract
The paper deals with the problem of remeshing and fairing of undersampled areas (called ”holes”) in triangular meshes. In this work, we are particularly interested in meshes constructed with geological data but the method can however be applied to any kind of data. With such input data, the point density is often drastically lesser in some regions than in others: this leads to what we call ”holes”. Once these holes identified, they are filled using a multistep approach. We iteratively: insert vertices in the hole in order to progressively converge towards the density of its neighbourhood, then deform this patch mesh (by minimizing a discrete thin-plate energy) in order to restore the local curvature and guarantee the smoothness of the hole boundary. The main goal of our method is to control both time and space complexity in order to handle huge models while producing quality meshes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brandel, S., Schneider, S., Guiard, N., Rainaud, J.F., Perrin, M.: Automatic building of structured geological models. Computing, Information Science and Engineering 5(2), 138–148 (2005)
Hjelle, O.: A triangulation template library (ttl): Generic design of triangulation software. Technical Report STF42 A00015, SINTEF (November 2000)
Hjelle, O.: Approximation of scattered data with multilevel b-splines. Technical Report STF42 A01011, SINTEF (November 2001)
Carr, J.C., Fright, W.R., Beatson, R.K.: Surface interpolation with radial basis functions for medical imaging. IEEE Transactions on Medical Imaging 16(1), 96–107 (1997)
Manuel, J.W., Oliveira, M.: Filling holes on locally smooth surfaces reconstructed from point clouds. Image and Vision Computing 25, 103–113 (2007)
Tekumalla, L.S., Cohen, E.: A hole-filling algorithm for triangular mesh. Uucs-04-019, University of Utah. (2004)
Davis, J., Marschner, S.R., Garr, M., Levoy, M.: Filling holes in complex surface using volumetric diffusion. In: Proceedings of the First international Symposium on 3D Data Processing, Visualization, Transmission, pp. 428–438 (2002)
Ju, T.: Robust repair of polygonal models. In: ACM SIGGRAPH, vol. 23(3) (2004)
Ju, T., Losasso, F., Schaffer, S., Warren, J.: Dual contouring of hermite data. ACM transactions on Graphics 21(3), 339–346 (2002)
Esteve, J., Brunet, P.A.V.: Approximation of variable density cloud of points by shrinking a discrete membrane. Computer Graphics Forum 24(4), 791–808 (2005)
Hornung, A.L.K.: Robust reconstruction of watertight 3d models from non-uniformly sampled clouds without normal information. In: Eurographics Symposium on Geometry Processing, pp. 41–50 (2006)
Liepa, P.: Filling holes in meshes. In: Eurographics Symposium on Geometry Processing, pp. 200–205 (2003)
Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.: Interactive multi-resolution modeling on arbitray meshes. In: Computer Graphics (SIGGRAPH 1998 Proceedings), pp. 105–114 (1998)
Pernot, J.P., Verron, P.: Filling holes in meshes using a mechanical model to simulate the curvature variation minimization. Computer and Graphics 30(6) (2006)
Schneider, R., Kobbelt, L.: Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design 18, 359–379 (2001)
Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Fibermesh: designing freeform surfaces with 3d curves. ACM Trans. Graph - Siggraph 26(3), 41 (2007)
Xu, G., Pan, Q.: Discrete surface modeling using partial differential equations. CAGD 23, 125–145 (2006)
Clarenz, U., Diewald, U., Dziuk, G., Rumpf, M., Rusu, R.: A finite element method for surface restoration with smooth boundary conditions. CAGD 21(5), 427–445 (2004)
Bobenko, A., Schröder, P.: Discrete willmore flow. In: Eurographics Symposium on Geometric Processing (2005)
Yoshizawa, S., Belyaev, A., Seidel, H.P.: Fast and robust detection of crest lines on meshes. Technical report, ACM Symposium on Solid and Physical Modeling (2005)
Pfeifle, R., Seidel, H.P.: Triangular b-splines for blending and filling of polygonal holes. In: Graphics Interface, pp. 186–193 (1996)
Frey, P.J., Borouchaki, H.: Surface mesh quality evaluation. International Journal for Numerical Methods in Engineering 45(45), 101–108 (1999)
Dyn, N., Hormann, K., Kim, S., Levin, D.: Optimizing 3d triangulations using discrete curvature analysis. In: Mathematical Methods for Curves and Surfaces, Oslo, pp. 135–146 (2000)
Greiner, G.: Variational design and fairing of spline surfaces. Computer Graphics Forum 13(3), 143–154 (1994)
Desbrun, M., Meyer, M., Schroder, P.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Computer Graphics Proceedings, Annual Conference Series, (August 1999), vol. 7, pp. 317–324 (1999)
Meyer, M., Desbrun, M., Schroder, P., Barr, H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Proceedings VisMath 2002, Berlin (2002)
Rienen, U.V.: Numerical methods in computational electrodynamics. linear systems in practical application. Lecture Notes in Computational Science and Engineering 12 (2001)
Desbrun, M., Mayer, M., Alliez, P.: Intrinsic parameterizations of surface meshes. In: Computer Graphics Forum (Proceedings of Eurographics 2002), vol. 21(3), pp. 209–218 (2002)
Aspert, N., Santa-Cruz, D., Ebrahimi, T.: Mesh: Measuring errors between surfaces using the hausdorff distance. In: Proceedings of the IEEE International Conference on Multimedia and Expo, vol. 1, pp. 705–708 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bac, A., Tran, NV., Daniel, M. (2008). A Multistep Approach to Restoration of Locally Undersampled Meshes. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-79246-8_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79245-1
Online ISBN: 978-3-540-79246-8
eBook Packages: Computer ScienceComputer Science (R0)