Shape Preserving For Curves And Surfaces Modeling Via Blending

Shape preserving is an essential research in curves and surfaces modeling, which is widely discussed. But less results on shape-preserving in blending-based curves and surfaces modeling are reported, this paper gives more attention to the above-absented problem. This paper discusses the following problem:the construction of monotonicity-preserving blending curve, the construction of convexity-preserving blending curve, the construction of shape preserving single direction surface and the construction of shape preserving two directions surface.Firstly, we discuss shape preserving for blending curve, and give the conditions of monotonicity-preserving and convexity-preserving for generalized conic curve using rational first-order blending scheme. Then we propose some conditions of convexity-preserving for one-direction blending surface with shape parameters. Then we discuss the conditions of convexity-preserving for two-direction surface. The shape parameters in the conditions that we give have locality, so it's very convenient in practical applications. Numerical experiments show our approach is effective.Finally, main works, highlights of innovations and realistic values in this paper are summarized and the outlook research works are mentioned.