Geometric interpolants with different degrees of smoothness

Abstract

Geometric interpolation is a basic task in geometric modelling. In this paper, the geometric interpolant with different degrees of smoothness is introduced. The method provides the lower degree, flexile interpolation curves and construction is simple. Moreover, convexity, regularity and the construction of some special geometric interpolants are also discussed.

Keywords:

• geometric continuity
• implicit algebraic curves
• interpolation
• curve/surface modelling
• spline

2000 AMS Subject Classification :

• 65D17

Acknowledgements

The authors would like to thank the referees for the comments and suggestions, which improved the clarity of the manuscript. The research is supported partially by the National Natural Science Foundation of China (grant nos 60373093, 60533060, 10726068, 10801024), the Research Project of Liaoning Educational Committee of China (grant no. 2005085) and the Innovation Foundation of the Key Laboratory of High-Temperature Gas Dynamics of CAS, China.