Abstract
Many applications within computer aided engineering require the support of a triangulation to gain geometrical and structural insight into the original surface being approximated. Therefore, downstream applications such as computer numerically controlled (CNC) machine path generation, finite element analysis (FEA) and flattening are triangulation dependant processes. However, despite the importance of triangulation in these applications, very little work has been focused on the downstream effects of triangulation. This paper investigates these effects on the application of surface flattening and demonstrates how subtle, but important changes in the triangulation can have a major impact on the flattening results.
Keywords
- Computer Numerically Control
- Delaunay Triangulation
- Original Surface
- Developable Surface
- Computer Numerically Control Machine
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Cader, R.A., Ball, A.A., Cripps, R.J.: Pattern shape design for ceramic ware: an integrated solution. International Journal of Computer Integrated Manufacturing 19(3), 287–293 (2005)
Kumar, G.V.V.R., Srinivasan, P., Shastry, K.G., Prakash, B.G.: Geometry based triangulation of multiple trimmed NURBS surfaces. Computer-Aided Design 33, 439–454 (2001)
Kumar, S., Manocha, D.: Interactive Display of Large Scale NURBS models. IEEE Transactions on Visualisation and Computer Graphics 2(4), 323–336 (1996)
Luken, W.L.: Tessellation of trimmed NURB surfaces. Computer-Aided Geometric Design 13, 163–177 (1996)
McCartney, J., Hinds, B.K., Seow, B.L.: The flattening of triangulated surfaces incorporating darts and gussets. Computer-Aided Design 31, 249–260 (1999)
O’Rourke, J.: Computational Geometry in C, 2nd edn. Cambridge University, Cambridge (2001)
Peterson, J.W.: Tessellation of NURBS surfaces. In: Graphics Gems IV, pp. 286–320. Academic Press, London (1994)
Piegl, L.A., Tiller, W.: Geometry based triangulation of trimmed NURBS surfaces. Computer-Aided Design 30(1), 11–18 (1998)
Rockwood, A., Heaton, K., Davis, T.: Real-time rendering of trimmed surfaces. ACM Computer Graphics 23(3), 107–116 (1989)
Sadoyan, H., Zakarian, A., Avagyan, V., Mohanty, P.: Robust uniform triangulation algorithm for computer aided design. Computer-Aided Design 38, 1134–1144 (2006)
Schneider, P.J., Eberly, D.H.: Geometric Tools for Computer Graphics. Morgan Kaufmann, San Francisco (2003)
Shimada, K., Gossard, D.C.: Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis. Computer Aided Geometric Design 15, 199–222 (1998)
Sugihara, K., Inagaki, H.: Why is the 3D Delaunay triangulation difficult to construct? Information Processing Letters 54, 275–280 (1995)
Wang, C.C.L., Smith, S.S.-F., Yuen, M.M.F.: Surface flattening based on energy model. Computer-Aided Design 34, 823–833 (2002)
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© 2009 Springer-Verlag Berlin Heidelberg
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Parwana, S.S., Cripps, R.J. (2009). Surface Triangulation and the Downstream Effects on Flattening. 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_17
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DOI: https://doi.org/10.1007/978-3-642-03596-8_17
Publisher Name: Springer, Berlin, Heidelberg
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