Shape Analysis of Triangles Through Directional Techniques
研究了三角形形状变量在球面上的分布，发现Bookstein模型下的形状分布近似于Fisher分布，并通过地理数据重新检验了中心地理论假设。
SUMMARY Kendall has shown how the shape variables of a labelled triangle can be mapped to a point on a sphere. Using Mardia and Dryden's method, we obtain the shape distribution of triangles under Bookstein's model. Various properties are discussed and in particular we show that this distribution, transformed to the sphere, is approximately the Fisher distribution. In particular, we examine the reduction of this distribution when the shape space is reduced to a subset of the sphere. Some practical examples are given, and the hypothesis of central place theory for a geographical data set is reassessed.