Geodesic Mesh Processing with Edge-Front based Data Structures
Hendrik Annuth, Christian-A. Bohn
2014
Abstract
In this paper a novel mesh processing data structure is presented which is efficient in runtime and has an exceptionally low memory consumption. The data structure is extremely versatile and allows investigating various mesh properties without requiring any pre-processing steps such as triangle subdivision or remeshing. The data structure uses an edge-front — a sealed path of mesh edges — whose expansion can by altered to account for individually problem cases. A basic implementation of this data structure — the Minimal Edge Front (MEF) — has already been successfully used to investigate and resolve inconsistently oriented surface regions in a surface reconstruction approach based on an iterative refinement strategy. The MEF is explained in detail and it is augmented to approximate geodesic distances. Due to the used working principal geodesic surface aspects can be analyzed independently of the mesh triangulation and the processing is limited to the investigated area. The edge-front allows to deal with open surfaces and to use points as well as lines as a starting point. The results of the process will be experimentally shown and discussed.
References
- Annuth, H. and Bohn, C.-A. (2010). Smart growing cells. In Proc. of the Int. Conf. on Neural Computation (ICNC2010), pages 227-237. Science and Technology Publications.
- Annuth, H. and Bohn, C.-A. (2012). Resolving Twisted Surfaces within an Iterative Refinement Surface Reconstruction Approach. In In Proc. of Vision, Modeling, and Visualization (VMV 2012), pages 175-182.
- Bommes, D. and Kobbelt, L. (2007). Accurate computation of geodesic distance fields for polygonal curves on triangle meshes. In Lensch, H. P. A., Rosenhahn, B., Seidel, H.-P., Slusallek, P., and Weickert, J., editors, VMV, pages 151-160. Aka GmbH.
- Bose, P., Maheshwari, A., Shu, C., and Wuhrer, S. (2011). A survey of geodesic paths on 3d surfaces. Comput. Geom. Theory Appl., 44(9):486-498.
- Chen, J. and Han, Y. (1990). Shortest paths on a polyhedron. In SCG 90: Proc. of the Sixth Annual Symposium on Computational geometry, pages 360-369. ACM Press.
- Crane, K., Weischedel, C., and Wardetzky, M. (2012). Geodesics in heat. CoRR, abs/1204.6216.
- Fritzke, B. (1993). Growing cell structures - a self-organizing network for unsupervised and supervised learning. Neural Networks, 7:1441-1460.
- Hilaga, M., Shinagawa, Y., Kohmura, T., and Kunii, T. L. (2001). Topology matching for fully automatic similarity estimation of 3d shapes. In Proc. of the 28th annual conference on Computer graphics and interactive techniques, SIGGRAPH 7801, pages 203-212, New York, NY, USA. ACM.
- Ivrissimtzis, I. P., Jeong, W.-K., and Seidel, H.-P. (2003). Using growing cell structures for surface reconstruction. In SMI 7803: Proc. of the Shape Modeling Int. 2003, page 78, Washington, DC, USA. IEEE Computer Soc.
- Kanai, T. and Suzuki, H. (2000). Approximate shortest path on polyhedral surface based on selective refinement of the discrete graph and its applications. In Proc. of the Geometric Modeling and Processing 2000, GMP 7800, pages 241-, Washington, DC, USA. IEEE Computer Soc.
- Kaneva, B. and O'Rourke, J. (2000). An implementation of chen & han's shortest paths algorithm. In CCCG.
- Katz, S. and Tal, A. (2003). Hierarchical mesh decomposition using fuzzy clustering and cuts. In ACM SIGGRAPH 2003 Papers, SIGGRAPH 7803, pages 954-961, New York, NY, USA. ACM.
- Kimmel, R. and Sethian, J. A. (1998). Computing geodesic paths on manifolds. In Proc. Natl. Acad. Sci. USA, pages 8431-8435.
- Krishnamurthy, V. and Levoy, M. (1996). Fitting smooth surfaces to dense polygon meshes. In SIGGRAPH, pages 313-324.
- Lanthier, M., Maheshwari, A., and Sack, J.-R. (1997). Approximating weighted shortest paths on polyhedral surfaces. In Proc. of the thirteenth annual symposium on Computational geometry, SCG 7897, pages 485-486, New York, NY, USA. ACM.
- Mitchell, J. S. B., Mount, D. M., and Papadimitriou, C. H. (1987). The discrete geodesic problem. SIAM J. Comput., 16(4):647-668.
- Oliveira, G. N., Torchelsen, R. P., Comba, J. L. D., Walter, M., and Bastos, R. (2010). Geotextures: A multisource geodesic distance field approach for procedural texturing of complex meshes. In Proc. of the 2010 23rd SIBGRAPI Conf. on Graphics, Patterns and Images, SIBGRAPI 7810, pages 126-133, Washington, DC, USA. IEEE Computer Soc.
- Sethian, J. A. (1995). A fast marching level set method for monotonically advancing fronts. In Proc. Nat. Acad. Sci, pages 1591-1595.
- Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S. J., and Hoppe, H. (2005). Fast exact and approximate geodesics on meshes. In ACM SIGGRAPH 2005 Papers, SIGGRAPH 7805, pages 553-560, New York, NY, USA. ACM.
- Zigelman, G., Kimmel, R., and Kiryati, N. (2002). Texture mapping using surface flattening via multidimensional scaling. IEEE Trans. on Visualization and Computer Graphics, 8(2):198-207.
Paper Citation
in Harvard Style
Annuth H. and Bohn C. (2014). Geodesic Mesh Processing with Edge-Front based Data Structures . In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014) ISBN 978-989-758-002-4, pages 64-75. DOI: 10.5220/0004718900640075
in Bibtex Style
@conference{grapp14,
author={Hendrik Annuth and Christian-A. Bohn},
title={Geodesic Mesh Processing with Edge-Front based Data Structures},
booktitle={Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014)},
year={2014},
pages={64-75},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004718900640075},
isbn={978-989-758-002-4},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014)
TI - Geodesic Mesh Processing with Edge-Front based Data Structures
SN - 978-989-758-002-4
AU - Annuth H.
AU - Bohn C.
PY - 2014
SP - 64
EP - 75
DO - 10.5220/0004718900640075