Surface Constructions on Irregular Grids
“Big” surfaces defined on domains that can not be modeled on a single regular grid is typically made by joining several surfaces together with the aid of fillet surfaces or by intersecting the surfaces and joining them after trimming.
In computations on geometry and geometric modeling in general surface modeling is a key issue. The most important type of surfaces are tensor product spline surfaces. They are in general based on regular griding, i.e. knot vectors are the same for all “lines” or “columns”. Examples are B-spline surfaces, Hermite-spline surfaces and Expo-rational B-spline surfaces. Surfaces constructions that in some way handle “irregular grids” has been developed. We find them in for example T-splines, LR B-splines, Truncated Hierarchical B-splines and PHT-splines. In general, surfaces based on irregular grids can be regarded as a collection of surfaces on regular grids that are connected at the edges and the corners in a smooth, but irregular way. This involves T-junctions and star-junctions.
To investigate a surface construction based on blending of local “small” patches into a “big” surface with arbitrary topology also requires that we can deal with T-junctions and star-junctions.
Here we investigate use of blending technique at T- and star-junctions. We look at special blending surfaces between regular patches, and re-parametrization to obtain a correct orientation and a better mapping in the parameter plane. The focus is on smoothness of the resulting surface.
KeywordsSurface Spline Junction Blending
- 1.Mäntylä, M.: An Introduction to Solid Modeling, vol. 13. Computer Science Press, Incorporated, New York (1988) Google Scholar
- 2.Hoffmann, C.M.: Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc., San Francisco (1989). ISBN 1-55860-067-1 Google Scholar
- 8.Lakså, A., Bang, B., Dechevsky, L.T.: Exploring expo-rational B-splines for curves and surfaces. In: Dæhlen, M., Mørken, K., Schumaker, L. (eds.) Mathematical Methods for Curves and Surfaces, pp. 253–262. Nashboro Press, Brentwood (2005)Google Scholar
- 9.Lakså, A.: Basic properties of Expo-Rational B-splines and practical use in computer aided geometric design. unipubavhandlinger 606, Unipub, Oslo (2007)Google Scholar
- 10.Lakså, A.: ERBS-surface construction on irregular grids. In: Pasheva, V., Venkov, G. (eds.) 39th International Conference Applications of Mathematics in Engineering and Economics AMEE13, pp. 113–120. American Institute of Physics (AIP) (2013)Google Scholar