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Research Papers

Automatic Fairing of Two-Parameter Rational B-Spline Motion

[+] Author and Article Information
Anurag Purwar

Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300anurag.purwar@stonybrook.edu

Xiaoyi Chi

Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300

Qiaode Jeffrey Ge

Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300qiaode.ge@stonybrook.edu

In this paper, quaternion surfaces are visualized by projecting them in E3.

J. Mech. Des 130(1), 011003 (Dec 07, 2007) (7 pages) doi:10.1115/1.2803253 History: Received October 11, 2006; Revised January 16, 2007; Published December 07, 2007

This paper deals with the problem of automatic fairing (or fine-tuning) of two-parameter rational B-spline spherical and spatial motions. The results presented in this paper extend the previous results on fine-tuning of one-parameter rational B-spline motions. A dual quaternion representation of spatial displacements is employed and the problem of fairing two-parameter motions is studied as a surface fairing problem in the space of dual quaternions. By combining surface fairing techniques from the field of computer aided geometric design with the computer aided synthesis of freeform rational motions, smoother (C3 continuous) two-parameter rational B-spline motions are generated. Several examples are presented to illustrate the effectiveness of the proposed method. Techniques for motion smoothing have important applications in the Cartesian motion planning, camera motion synthesis, and spatial navigation in virtual reality systems. In particular, smoother two-parameter freeform motions have applications in the development of a kinematic based approach to geometric shape design and in five-axis NC tool path planning.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

15×15 Control net projected in E3 for two-parameter bicubic B-spline spherical motion

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Figure 2

Quaternion surface with isophote for two-parameter bicubic B-spline spherical motion

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Figure 3

Isophote details on the quaternion surface for two-parameter bicubic B-spline spherical motion

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Figure 4

Trajectory under two-parameter bicubic rational B-spline spherical motion

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Figure 5

15×15 Control net projected in E3 for dual part under two-parameter bicubic B-spline spatial motion

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Figure 6

Trajectory under two-parameter bicubic rational B-spline spatial motion

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