Polygon Morphing and Its Application in Orebody Modeling

Abstract

Three different polygon morphing methods are examined. The first one is based on the utilization of the trimmed skeleton of the symmetric difference of the source and target polygons as an intermediate polygon. The second one reduces the problem to the problem of morphing compatible planar triangulations and utilizes the representation of planar triangulations as a matrix constructed using barycentric coordinates of the planar triangulation's vertices relative to their neighbors. The third and last one describes the polygon by the parametric curve representation based on estimated Fourier parameters and thus transfers the morphing process to Fourier parametric space. The different features and comparative results of these methods are shown by the tests with different examples. These methods are used for generating a set of polygonal sections from two nonplanar polygonal sections which are nearly planar in 3D before constructing a three-dimensional object from these nonplanar sections.