Distance as a tool for surface definition

Abstract

It is often impossible to study a geometric surface that lacks an analytic description. However, using computer graphics techniques it is now feasible to visualize such implicitly defined surfaces; hence initiate their study. A typical example of such surfaces is the ones defined as “the locus of points that satisfy a set of conditions”. These conditions are usually distance relationships between geometric entities such as a point, a line, a plane etc. For example, a paraboloid is defined as “the locus of points in 3‐D that are equi‐distant from a plane and a given point”. In this work, we present a way for modelling and visualizing implicit surfaces. We demonstrate our approach with the construction and subsequent visualization of generalized weighted Voronoi tessellation using as control points simple geometric objects.

Citation

Tsoubelis, D. (1998), "Distance as a tool for surface definition", Kybernetes, Vol. 27 No. 3, pp. 273-282. https://doi.org/10.1108/03684929810209487