Summary
In this paper, a new method for constructing NURBS surfaces from scattered and unorganized points is presented. The method is easy to implement and allows fitting a NURBS surface to a scattered point cloud without constructing either NURBS patches networks or polygon meshes. Based on the projection of the points onto the regression plane of the cloud, the method detects both regions where the cloud lacks points, and regions where the cloud is too dense. Then, by inserting and removing points, the point cloud is regularized and approximated by a NURBS surface. In order to reduce the approximation error, an evolutionary strategy obtains the weights of the NURBS surface so that the distance between the point cloud and the NURBS is minimal. Finally, the points inserted outside the bounds of the point cloud are removed by trimming the NURBS surface. Numerical and graphical results are provided, demonstrating that the method produces valid surfaces with low fitting error.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Myers, A.: Introductory literature review surface reconstruction from three dimensional range data. Technical report, The University of Adelaide, Department of Computer Science (1999)
Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1995)
Ristic, M.: Efficient fitting of Non-Uniform Rational B-Spline surfaces using non-organized 3D data. In: SPIE’S, vol. 11(1) (December 2000)
Park, I., Yun, I., Lee, S.: Constructing NURBS Surface Model from Scattered and Unorganized Range Data. In: Second International Conference on 3-D Digital Imaging and Modeling (1999)
Gregorski, B., Hamann, B., Joy, K.: Reconstruction of B-spline Surfaces From Scattered Data Points. In: Proceedings of Computer Graphics International (2000)
Eck, M., Hoppe, H.: Automatic Reconstruction of B-Spine Surfaces of Arbitrary Topological Type. In: Proceedings of the 23rd annual conference on Computer Graphics and Interactive Techniques, ACM Press, New York (1996)
Krishnamurthy, V., Levoy, M.: Fitting smooth surfaces to dense polygon meshes. In: SIGGRAPH 1996 Conference Proceedings. ACM SIGGRAPH, Addison Wesley, Reading (1996)
Bertram, M., Tricoche, X., Hagen, H.: Adaptive Smooth Scattered-data Approximation for Large-scale Terrain Visualization. In: EUROGRAPHICS - IEEE TCVG Symposium on Visualization (2003)
Shi, X., Wang, T., Wu, P., Liu, F.: Reconstruction of convergent g 1 smooth b-spline surfaces. In: Computer Aided Geometric Design, vol. 21 (November 2004)
Yvart, A., Hahmann, S., Bonneau, G.: Smooth Adaptive Fitting of 3D models using hierarchical triangular splines. In: Shape Modeling International (2005)
Cordero, J., Parejo, J.: Curvas y Superficies para Modelado Geométrico, 1st edn., Alfa Omega, España (2002)
De Boor, C.: On Calculating With B-Splines. J. Approximation Theory 6(1), 50–62 (1972)
Bäck, T., Schwefel, H.: Genetic Algorithms in Engineering and Computer Science. John Wiley & Sons Ltd., Chichester (1995)
Tenenbaum, J., De Silva, V., Langford, D.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290 (5500), 2319–2323 (2000)
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
Leal, N., Leal, E., Branch, J.W. (2010). Simple Method for Constructing NURBS Surfaces from Unorganized Points. In: Shontz, S. (eds) Proceedings of the 19th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15414-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-15414-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15413-3
Online ISBN: 978-3-642-15414-0
eBook Packages: EngineeringEngineering (R0)