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Optimal Multi-degree Reduction of a New Curve That Has Shape Preserving and Linear Evaluation Properties

Author: ZhuangChengMing
Tutor: WangGuoZuo
School: Zhejiang University
Course: Mathematics and Applied Mathematics
Keywords: Computer Aided Geometric Design A standard wholly positive group DP-NTP curve Multi-degree reduction Corner cutting algorithm
CLC: TP391.7
Type: Master's thesis
Year: 2008
Downloads: 18
Quote: 0
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Abstract


2003 Delgado and Pe ( ? ) Propose a new class of generalized Ball curve , the this curve both conformal and rapid evaluated two functions , and pointed out a reform ideas for the exterior design The basic idea is to construct a kinds of standard all-positive ( normalized totally positive (NTP )) base , at the same time makes the number of basis functions by serial number was two high and low in the middle of the canyon -shaped distribution , thus overcoming the Wang-Ball group has linear computation time complexity , but not NTP group, and Said-Ball curve NTP , but does not have the limitations of linear complexity of computing time . Such a parameter curve is named DP-NTP curve , and its base is referred to as a single parameter DP-NTP group . In view of the above the superiority of DP-NTP curve there is an urgent need for research and development of various effective algorithm , including the order reduction algorithm has an important role in data communications and data compression . To this end, according to the characteristics and frequency of the basic structure of the single parameter DP-NTP - attenuation characteristics , designed DP-NTP curve L 2 norm constraints , explicit , once down multi-stage the two approximation algorithms : One is application the liter -order matrix generalized inverse preserving and curve endpoints multi-degree reduction . The second is into the DP-NTP - Jacobi basis to achieve multi-degree reduction curve constraints ; given error analysis instance verify , to the engineering staff to provide a reliable reference , and the results of computer-aided design system optimization important role.

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