On Chebychev fits for pairs of lines and polygons with specified internal angles

摘要

This paper addresses the problems of determining pairs of lines and polygons that best fit a finite set of datapoints. We have determined the best-fit (substitute) feature by minimizing the maximum normal deviation of the datapoints from the substitute feature. In other words, we have the Chebychev or the minimum zone solution. The substitute features show specific geometric characteristics with respect to the location of a subset of data-points. Algorithms are formulated to identify this subset in a given set of datapoints. This paper addresses the problems of determining pairs of lines and polygons that best fit a finite set of datapoints. We have determined the best-fit (substitute) feature by minimizing the maximum normal deviation of the datapoints from the substitute feature. In other words, we have the Chebychev or the minimum zone solution. The substitute features show specific geometric characteristics with respect to the location of a subset of data-points. Algorithms are formulated to identify this subset in a given set of datapoints. # 1997 Elsevier Science Inc.