Approximate merging of B-spline curves and surfaces |
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Authors: | Jun Chen Guo-jin Wang |
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Affiliation: | (1) Department of Industrial Engineering, Chosun University, 501-759 Gwangju, South Korea |
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Abstract: | Applying the distance function between two B-spline curves with respect to the L
2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one
B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and
of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem
can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly
in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate
merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the
algorithm. |
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Keywords: | Computer aided geometric design approximate merging B-spline curves and surfaces |
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