Distance as a tool for surface definition

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.