A Fast Rubber-Sheeting Transformation Using Simplicial Coordinates

Abstract

A computationally efficient piecewise-linear rubber-sheet map transformation is derived by analyzing geometrical relationships of areas, linear equations and inequalities, and simplicial coordinates. The use of simplicial coordinates permits a representation of the rubber-sheet transformation, which is completely independent of the image points. The geometric analysis used in deriving the simplicial coordinates leads to special point-in-polygon algorithms for the rubber-sheeting, which may be employed in more general situations. The geometric analysis also leads to convenient formulas for areas of triangulated regions.