四边形上一种线性双有理映射构造方法

A Method for Constructing Linear Birational Mappings in Quadrilaterals

作为一种特殊的有理映射,双有理映射可应用于图像变形、等几何分析中区域参数化中。针对文献[1]通过几何方法构造四边形上的双有理映射,需要先确定权值再构造的问题,提出一种基于动直线的方法,可直接构造四边形上的双有理映射。此外,通过选择不同的参数,可以得到四边形上不同的双有理映射。验证可知,该方法满足文献[1]提出的权值比例关系,并通过实例说明了其有效性。

As a special kind of rational mapping,birational mapping can be applied to image warping and domain parametrization of Isogeometric Analysis.By geometric methods,reference[1]constructed a birational mapping on a quadrilateral,but this method needs to compute the weights first and then construct a birational mapping.By the technique of moving lines,a method for the construction of birational map on quadrilateral is proposed.Hence,the computation of weights is not needed here,our method can generate birational map directly.In addition,by choosing different parameter,different birational mappings are calculated.It is easy to verify that the weights of the mapping generated by our method satisfy the weight proportional relation proposed by reference[1].An example is also provided to illustrate our method.