Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter
PAN Yong-juan, WANG Guo-jin
Department of Mathematics, Zhejiang University, Hangzhou 310027, China; Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
Abstract In computer aided geometric design (CAGD), it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However, most existing pertinent methods cannot generate convexity-preserving interpolating transcendental curves; even constructing convexity-preserving interpolating polynomial curves, it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above drawbacks. The basic idea is: first to construct a kind of trigonometric polynomial curves with a shape parameter, and interpolating trigonometric polynomial parametric curves with C2 (or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then, the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast, and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
PAN Yong-juan, WANG Guo-jin. Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(8): 1199-1209.
WANG Wen-tao, WANG Guo-zhao. B¨|zier curves with shape parameter[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 6): 4-.
