Optimal Constrained Explicit Multi-degree Reduction Approximation of DP Curves

摘要

DP curves, which possess the shape-preserving property and linear complexity evaluation algorithm, occupy a significantly important place in computer aided geometric design. Thus to do the research on the DP curves algorithms has a positive meaning. Aphirukmatakun et al. presented a degree elevation algorithm of DP curves based on the transformation between the DP basis and power basis. At the same time, Itsariyawanich et al. put forward a degree reduction algorithm. However, up to now, there has been no optimal algorithm for explicit multi-degree reduction of DP curves with endpoints constraints. In this paper, based on the orthogonality of Jacobi basis, we give out an effective algorithm of constrained multi-degree reduction approximation of DP curve. We prove that the approximation is optimal in the L_2 norm. In the end of this paper, we demonstrate the validity and efficiency of our algorithm.