3-D graphic display of discrete spatial data by prism maps

Abstract

An efficient algorithm for displaying 3-D scenes showing a discrete spatially varying surface is described. Given a 2-D map or planar graph composed of polygons where each polygon has a positive real number attribute, a prism is erected on each polygon with height proportional to that attribute. The resulting 3-D scene is plotted with shading and hidden lines removed. Thus the spatial variation of the attribute may be quickly and intuitively grasped by the nontechnical observer. This has applications to areas such as geography if the map is a cartographic map, or to physics if the map diagrams the periodic table. The algorithm takes time O(N log(N)) where N is the number of edges in the map. Most of the calculations can be done without knowing the prism heights so extra plots with different attributes for the prisms can be produced quickly. This algorithm has been implemented and tested on maps of up to 12000 edges.