Simple Method for Constructing NURBS Surfacesfrom Unorganized Points
Nallig Leal, Esmeide Leal, John William Branch
Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.161-176, October 3-6 2010
19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010
Universidad AutÛnoma del Caribe
Calle 90 No 46 - 112
Barranquilla - Colombia - SuramÈrica
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.
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