Abstract
Along with the rapid growth of industrial X-ray CT scanning systems, it is now possible to non-destructively acquire the entire meshes of assemblies consisting of a set of parts. For the advanced inspections of the assemblies, such as estimation of their assembling errors or examinations of their behaviors in the motions, based on their CT scanned meshes, it is necessary to accurately decompose the mesh and to extract a set of partial meshes each of which correspond to a part. Moreover it is required to create models which can be used for the real-product based simulations. In this paper, we focus on CT scanned meshes of gear assemblies as examples and propose beneficial methods for establishing such advance inspections of the assemblies. We first propose a method that accurately decomposes the mesh into partial meshes each of which corresponds to a gear based on periodicity recognitions. The key idea is first to accurately recognize the periodicity of each gear and then to extract the partial meshes as sets of topologically connected mesh elements where periodicities are valid. Our method can robustly and accurately recognize periodicities from noisy scanned meshes. In contrast to previous methods, our method can deal with single-material CT scanned meshes and can estimate the correct boundaries of neighboring parts with no previous knowledge. Moreover it can efficiently extract the partial meshes from large scanned meshes containing about one million triangles in a few minutes. We also propose a method for creating simulation models which can be used for a gear teeth contact evaluation using extracted partial meshes and their periodicities. Such an evaluation of teeth contacts is one of the most important functions in kinematic simulations of gear assemblies for predicting the power transmission efficiency, noise and vibration. We demonstrate the effectiveness of our method on a variety of artificial and CT scanned meshes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Suzuki, H.: Convergence engineering based on X-ray CT scanning technologies. In: Proc. JSME Digital Engineering Workshop, pp. 74–77 (2005)
Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Transactions on Graphics 22(3), 954–961 (2003)
Katz, S., Leifman, G., Tal, A.: Mesh Segmentation using Feature Point and Core Extraction. The Visual Computer 21(8-10), 649–658 (2005)
Shammaa, H.M., Suzuki, H., Michikawa, T.: Registration of CAD mesh models with CT volumetric model of assembly of machine parts. The Visual Computer 23(12), 965–974 (2007)
Shammaa, H.M., Suzuki, H., Ohtake, Y.: Extraction of isosurfaces from multi-material CT volumetric data of mechanical parts. In: Proc. ACM symposium on Solid and Physical Modeling, pp. 213–220 (2008)
Lin, H.C., Wang, L.L., Yang, S.N.: Extracting periodicity of a regular texture based on autocorrelation functions. Pattern Recognition Letters 18, 433–443 (1997)
Liu, Y., Collins, T.T., Tsin, Y.: A computational model for pattern perception based on frieze and wallpaper groups. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(3), 354–371 (2006)
Müller, P., Zeng, G., Wonka, P., Gool, L.V.: Image-based procedural modeling of facades. ACM Transactions on Graphics 26(3), 85 (2007)
Mitra, N.J., Guibas, L.J., Pauly, M.: Partial and approximate symmetry detection for 3D geometry. ACM Transactions on Graphics 25(3), 560–568 (2006)
Podolak, J., Shilane, P., Golovinskiy, A., Rusinkiewicz, S., Funkhouser, T.: A planar-reflective symmetry transform for 3D shapes. ACM Transactions on Graphics 25(3), 549–559 (2006)
Xu, K., Zhang, H., Tagliasacchi, A., Liu, L., Li, G., Meng, M., Xiong, Y.: Partial Intrinsic Reflectional Symmetry of 3D Shapes. In: ACM Transactions on Graphics (SIGGRAPH Asia 2009) (2009) (to appear)
Liu, S., Martin, R.R., Langbein, F.C., Rosin, P.L.: Segmenting Periodic Reliefs on Triangle Meshes. In: Martin, R., Sabin, M.A., Winkler, J.R. (eds.) Mathematics of Surfaces 2007. LNCS, vol. 4647, pp. 290–306. Springer, Heidelberg (2007)
Pauly, M., Mitra, N.J., Wallner, J., Pottmann, H., Guibas, L.: Discovering structural regularity in 3D geometry. ACM Transaction on Graphics 27(3), 43 (2008)
Mizoguchi, T., Date, H., Kanai, S., Kishinami, T.: Quasi-optimal mesh segmentation via region growing/merging. In: Proc. ASME/DETC-35171 (2007)
Vieira, M., Shimada, K.: Surface mesh segmentation and smooth surface extraction through region growing. Computer-Aided Geometric Design 22(8), 771–792 (2005)
Besl, P., McKay, N.: A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(2), 239–256 (1992)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992)
Geomagic, http://www.geomagic.com
Lorensen, W.E., Harvey, E.C.: Marching cubes: A high resolution 3D surface construction algorithm. ACM SIGGRAPH Computer Graphics 21(4), 163–169 (1987)
Kondo, D., Mizoguchi, T., Kanai, S.: Recognizing Periodicities on 3D Scanned Meshes Based on Indexed-ICP Algorithm. In: Integrated Design and Manufacturing in Mechanical Engineering, Springer, Heidelberg (to appear, 2010)
Li, M., Langbein, F.C., Martin, R.R.: Detecting approximate symmetries of discrete point subsets. Computer-Aided Design 40(1), 76–93 (2008)
Li, M., Langbein, F.C., Martin, R.R.: Detecting design intent in approximate CAD models using symmetry. Computer-Aided Design 42(3), 183–201 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mizoguchi, T., Kanai, S. (2010). Decomposing Scanned Assembly Meshes Based on Periodicity Recognition and Its Application to Kinematic Simulation Modeling. In: Mourrain, B., Schaefer, S., Xu, G. (eds) Advances in Geometric Modeling and Processing. GMP 2010. Lecture Notes in Computer Science, vol 6130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13411-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-13411-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13410-4
Online ISBN: 978-3-642-13411-1
eBook Packages: Computer ScienceComputer Science (R0)