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Research Papers

Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

[+] Author and Article Information
Yuan Yuan

Department of Industrial and Systems Engineering,  The University of Wisconsin, Madison, Wisconsin, 53706szhou@engr.wisc.edu

Shiyu Zhou1

Department of Industrial and Systems Engineering,  The University of Wisconsin, Madison, Wisconsin, 53706szhou@engr.wisc.edu

1

Corresponding author.

J. Comput. Inf. Sci. Eng 12(2), 021008 (May 14, 2012) (12 pages) doi:10.1115/1.4006000 History: Received September 27, 2011; Revised January 27, 2012; Published May 14, 2012; Online May 14, 2012

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 6

Final fitting of the proposed method

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Figure 7

Smooth surface. “ + ” symbols stand for initial noisy measurement data.

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Figure 8

Initial fitting of two methods: proposed method (left), De Boor’s method (right)

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Figure 9

Final fitting of two methods: proposed method (left), De Boor’s method (right)

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Figure 10

Initial error surface (left) and final error surface (right) of proposed method

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Figure 11

Initial error surface (left) and final error surface (right) of De Boor’s method

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Figure 12

The sinc surface. “ + ” symbols stand for initial noisy measurement data.

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Figure 13

Initial fitting of two methods: proposed method (left), De Boor’s method (right)

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Figure 14

Final fitting of two methods: proposed method (left), De Boor’s method (right)

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Figure 2

Franke’s function. “ + ” symbols stand for initial noisy measurement data.

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Figure 3

Initial fitting surface (left) and initial fitting error surface (right)

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Figure 4

Final approximation surfaces after 20 iterations, proposed method (left), Huang’s method (right)

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Figure 5

True surface and noisy initial sample (represented as “ + ” symbols) (left), top view of the surface (right)

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Figure 1

Basic flow of the sequential B-spline surface construction

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