Algebraic and Geometric Characterizations of Double-Cross Matrices of Polylines

作者：Kuijpers Bart^*; Moelans Bart

来源：ISPRS International Journal of Geo-Information, 2016, 5(9): 152.

DOI：10.3390/ijgi5090152

• double-cross matrix
• qualitative calculus
• polyline
• qualitative descriptions of polylines
• trajectory and moving object bata

We study the double-cross matrix descriptions of polylines in the two-dimensional plane. The double-cross matrix is a qualitative description of polylines in which exact, quantitative information is given up in favour of directional information. First, we give an algebraic characterization of the double-cross matrix of a polyline and derive some properties of double-cross matrices from this characterisation. Next, we give a geometric characterization of double-cross similarity of two polylines, using the technique of local carrier orders of polylines. We also identify the transformations of the plane that leave the double-cross matrix of all polylines in the two-dimensional plane invariant.

• 出版日期2016-9