Algorithms on cone spline surfaces and spatial osculating arc splines |
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Affiliation: | 1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300350, China;2. School of Engineering, The University of Warwick, Coventry CV4 7AL, UK;1. Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan;2. College of Engineering, Oregon State University, 219A Dearborn Hall, Corvallis, Oregon, 97331, USA |
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Abstract: | Developable surfaces are of considerable importance to many industrial applications, e.g., sheet metal forming processes. The objective of this paper is to provide algorithms on the approximation of developable surfaces with pieces of right circular cones. Special emphasis is devoted to practical choices of free parameters and to error estimation. Furthermore, a new algorithm for the approximation of spatial curves with a circular arc spline is presented which stands in close relation to above algorithms on developable surfaces. The proposed arc spline has contact of order 2 to the given curve in a series of curve points. The investigation includes a segmentation algorithm and error estimation. |
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