Constructing 3D Surfaces from Random Sets of Points by Means of Level Curves

Abstract

This paper proposes an easy approach to obtaining 3D surface models in parametric CAD software products from random sets of points, based on the analogy of level curves from geodesic disciplines. The points could be obtained from measurements on existing mechanical parts, as a stage in reverse engineering processes, or can be defined arbitrary in space, as part of the design process. The present research shows that good approximations of the true surface can be obtained by measuring a relative small group of carefully selected points and constructing level curves, following the same procedure as in the case of topography. The instrument to build level curves is an original application developed for AutoCAD using VB.NET which allows the user to construct the level curves parallel to the xy plane for any number of points in space. We tested the application on more set of points sampling the same surface, obtaining the level curves in AutoCAD and using these to build the final 3D model. The surfaces obtained this way were then compared to draw some conclusions regarding the influence of the number of sampled points on the precision of the model.