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Explicit Representation and Extension of Definition Interval for Algebraic Trigonometric Twice-Combined Base

Author: ZhangFengWei
Tutor: WangGuoZhao
School: Zhejiang University
Course: Applied Mathematics
Keywords: AT-Bernstein base Group display indicates AT-B -spline basis
CLC: TP391.41
Type: Master's thesis
Year: 2008
Downloads: 14
Quote: 0
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Abstract


Mixing curve is constructed NURBS defects in the new space , a new curve . Such curves can be an accurate representation of a class of widely used beyond the curve . Extensive engineering applications , such as circle involute line A Archimedes spirals , tapered spirals defined in of of span { Sint the cost , TSINT , tcost T n -4 , ..., t , 1 } space. Therefore , in this space on the blend curve study has important significance . wherein the definition of the group interval extension on the one hand can expand the scope of the expression of the curve , such as a full circle , said conical spiral and the Archimedes spiral one cycle representation of the other hand can expand the range of shape parameters to adjust the shape of the curve in the wider base on this space by polynomial and trigonometric quadratic forms , so called algebra triangle second mixed base . This paper studied the expression of mixed base in the second AT-Bernstein based and uniform second-order B-spline - based display and define the interval extension Firstly, the second-order AT-Bernstein -based and uniform second-order B-spline basis the display expression for the second order AT-Bernstein group in more than five bands , its definition interval expand to 2π. then gives the recursive form of the transformation matrix of the base , through a few examples to illustrate the significance interval extensions uniform second-order B-spline basis given the solution to maintain a positive theory given the length of the interval of several specific order .

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