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Open AccessArticle

Designing Developable C-Bézier Surface with Shape Parameters

by Caiyun Li 1 and Chungang Zhu 2,*
1
School of Mathematical and Physical Sciences, Dalian University of Technology, Panjin 124221, China
2
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 402; https://doi.org/10.3390/math8030402
Received: 16 February 2020 / Revised: 8 March 2020 / Accepted: 9 March 2020 / Published: 11 March 2020
(This article belongs to the Special Issue Modern Geometric Modeling: Theory and Applications)
Developable surface plays an important role in geometric design, architectural design, and manufacturing of material. Bézier curve and surface are the main tools in the modeling of curve and surface. Since polynomial representations can not express conics exactly and have few shape handles, one may want to use rational Bézier curves and surfaces whose weights control the shape. If we vary a weight of rational Bézier curve or surface, then all of the rational basis functions will be changed. The derivation and integration of the rational curve will yield a high degree curve, which means that the shape of rational Bézier curve and surface is not easy to control. To solve this problem of shape controlling for a developable surface, we construct C-Bézier developable surfaces with some parameters using a dual geometric method. This yields properties similar to Bézier surfaces so that it is easy to design. Since C-Bézier basis functions have only two parameters in every basis, we can control the shape of the surface locally. Moreover, we derive the conditions for C-Bézier developable surface interpolating a geodesic. View Full-Text
Keywords: developable surface; C-Bézier basis; dual method; geodesic developable surface; C-Bézier basis; dual method; geodesic
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Li, C.; Zhu, C. Designing Developable C-Bézier Surface with Shape Parameters. Mathematics 2020, 8, 402.

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