Abstract
Digital shape reconstruction (DSR) deals with creating CAD models of physical objects using 3D scanned data. Our primary interest is to reconstruct mechanical engineering objects that are usually composed of a hierarchy of surfaces – primary surfaces, connecting features (fillets) and vertex blends – and are structured by well-defined topological rules. After an overview of segmenting large polygonal meshes by the functional decomposition paradigm, we focus on the reconstruction of vertex blends using setbacks. This topic was thoroughly studied more than a decade ago in the context of constructive CAD; now the concept is revisited for DSR. A new method is presented to locate the optimal cross-sectional termination of fillets and construct the boundary curves of vertex blends on the mesh. These will correspond to the vertex blend boundaries of the final CAD model, as well. Finally, we discuss special cases of self-intersecting segmenting curve networks, and show how these problems can be resolved by setback vertex blends.
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References
Marks, P.: Capturing a Competitive Edge through Digital Shape Sampling & Processing (DSSP). Blue Book Series. Society of Manufacturing Engineers (2005)
Botsch, M., Pauly, M., Kobbelt, L., Alliez, P., Lévy, B., Bischoff, S., Rössl, C.: Geometric modeling based on polygonal meshes. In: Eurographics Tutorial Notes, Prague, Czech Republic, Eurographics (2007)
Várady, T., Martin, R.R., Cox, J.: Reverse engineering of geometric models – an introduction. Comput. Aided Des. 29(4), 225–268 (1997)
Braid, I.C.: Non-local blending of boundary models. Comput. Aided Des. 29(2), 89–100 (1997)
Várady, T., Hoffmann, C.M.: Vertex blending: Problems and solutions. In: Dælen, M., Lyche, T., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces II, Vanderbilt, pp. 501–527. University Press, Nashville (1998)
Besl, P.J., Jain, R.C.: Segmentation through variable-order surface fitting. IEEE Trans. Pattern Anal. Mach. Intell. 10(2), 167–192 (1988)
Sapidis, N.S., Besl, P.J.: Direct construction of polynomial surfaces from dense range images through region growing. ACM Trans. Graph. 14, 171–200 (1995)
Vieira, M., Shimada, K.: Surface mesh segmentation and smooth surface extraction through region growing. Comput. Aided Geom. Des. 22(8), 771–792 (2005)
Lai, Y.K., Zhou, Q.Y., Hu, S.M., Wallner, J., Pottmann, H.: Robust feature classification and editing. IEEE Trans. Vis. Comp. Graphics 13(1), 34–45 (2007)
Benkö, P., Martin, R.R., Várady, T.: Algorithms for reverse engineering boundary representation models. Comput. Aided Des. 33, 839–851 (2001)
Fitzgibbon, A.W., Eggert, D.W., Fisher, R.B.: High-level CAD model acquisition from range images. Comput. Aided Des. 29, 321–330 (1997)
Petitjean, S.: A survey of methods for recovering quadrics in triangle meshes. ACM Comput. Surv. 34(2), 211–262 (2002)
Benkö, P., Kós, G., Várady, T., Andor, L., Martin, R.R.: Constrained fitting in reverse engineering. Comput. Aided Geom. Des. 19(3), 173–205 (2002)
Eck, M., Hoppe, H.: Automatic reconstruction of B-spline surfaces of arbitrary topological type. In: Computer Graphics. SIGGRAPH, pp. 325–334 (1996)
Heckbert, P.S., Garland, M.: Survey of polygonal surface simplification algorithms. In: Multiresolution Surface Modeling Course. SIGGRAPH (1997)
Várady, T.: Automatic procedures to create CAD models from measured data. Computer-Aided Design and Applications 5(5), 577–588 (2008)
Várady, T., Facello, M.A., Terék, Z.: Automatic extraction of surface structures in digital shape reconstruction. Comput. Aided Des. 39(5), 379–388 (2007)
Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511–533 (2002)
Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom. 30, 87–107 (2003)
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Terék, Z., Várady, T. (2009). Setback Vertex Blends in Digital Shape Reconstruction. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_21
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DOI: https://doi.org/10.1007/978-3-642-03596-8_21
Publisher Name: Springer, Berlin, Heidelberg
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