Computing Non-Crossing Smooth Contours on Triangulated Meshes

Abstract

Contour processing is a fundamental task in many fields, such as Photogrammetry, Meteorology, and Geographic Information Science. Contours, usually extracted from raster images or triangulated meshes, greatly benefit from a smoothing postprocessing phase. In the case of triangulated meshes, unsmoothed contours look angular, and disclose the edges of the underlying mesh. Attempts to smooth contours individually by using splines may cause crossings among nearby contours, clearly misrepresenting the data. To partially reduce this problem, previous studies propose to use the underlying mesh at aiding the contour smoothing process. The algorithm proposed herein builds on previous work to guarantee, for the first time, non-crossing smooth contours that are continuous in the first derivative. We formally prove our claims and present experimental results to show that, in addition, our algorithm outputs less than half the control points produced by previous approaches. Further work is proposed for achieving higher degrees of smoothness.