### A class of trigonometric Bézier curve and surface which satisfy G2 continuity

LIU Hua-yong, XIE Xin-ping, LI Lu, ZHANG Da-ming, WANG Huan-bao

1. School of Mathematic &
Physics, Anhui Jianzhu University, Hefei 230601, Anhui, China
• Received:2015-09-04 Online:2016-10-20 Published:2016-10-17

Abstract: In order to meet the relatively high smooth jointing in relatively simple conditions, at the same time we can also modify the shape of curve and surface under without changing the control points, and then a group of low order trigonometric Bézier basis function with two shape parameters was constructed. Based on the group of basic functions, a class of curve and surface of arbitrary order trigonometric Bézier is defined by trigonometric function. The basic properties of the curves are discussed, and the conditions of the smooth blending of curves and surfaces are also discussed. According to the blending condition, the combination curves and surfaces of the piecewise smooth curves can be constructed. The blending curves and surfaces will not be changed the continuity of curve and surface by modifying the control points and parameters of the method and automatically meet with the G2 continuity and simple calculation. The results of numerical examples show the effectiveness of this method.

CLC Number:

• TP391
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