Geometric Continuity Conditions for H-Bézier Curves of Degree n

With the aim to tackle the problem that the complex composite curves can not be constructed by using a single curve, the geometric continuity conditions for H-Bézier curves of degree n with shape parameter are investigated. The H-Bézier curves of degree n not only inherit the major properties of the classical Bézier curve of degree n, but also have a prominent performance on adjusting their shapes by changing shape parameter. Based on the analysis of the basis functions and terminal properties, the necessary and sufficient conditions of G1 and G2 geometric continuity between two adjacent H-Bézier curves of degree n are proposed. Modeling examples provided show that the derived continuity conditions are effective and hence can greatly enhances problem-solving abilities in complex curves design by using H-Bézier curves.