JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 114-126.doi: 10.6040/j.issn.1671-9352.0.2019.005

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Construction of the cubic λμ-α-DP curve with two kinds of shape parameters

ZHANG Di, ZHA Dong-dong, LIU Hua-yong*   

  1. School of Sciences and Physics, Anhui Jianzhu University, Hefei 230601, Anhui, China
  • Online:2019-09-20 Published:2019-07-30

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Abstract: This paper constructs a type of cubic λμ-α-DP basic function with two kinds of shape parameters. It can effectively global or locally modify its shape. The properties of the cubic λμ-α-DP basis function and curve are analyzed. Moreover, the effect and modification ability of the basis function and the curve with different parameter values are illustrated through graphics. Smooth continuous conditions of the curve are deduced: they can meet with G2 continuous when certain conditions are met. G1 continuous rotating surfaces are also given. Furthermore, using the singular blending technique, the singular blending cubic λμ-α-DP interpolation curve with shape parameters is constructed. The properties of the curve and the influences of the curve with multiple parameters are presented. By changing the blending parameters, the approximation degree between the singular blending interpolation curve and its control polygon can be adjusted, thus enhancing the shape-control capability of the cubic λμ-α-DP interpolation curves.

Key words: DP curve, smooth continuous, local adjustable, singular blending, blending parameters

CLC Number: 

  • TP391
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