Perspective projection of non‐convex polyhedra

An algorithm is presented for removing hidden lines for isometric and perspective projections of three‐dimensional objects. An object can be regarded as being made up of a number of planes, and the whole picture can therefore be visualized as only a collection of planes. Considering planes as the basic element of a picture, non‐convex polyhedra can be displayed directly without prior subdivisions into convex ones. Lines connecting nodal points are first retrieved from the model to be plotted by a simple but efficient technique. On the picture planes, each unique line is examined in turn to see if it is totally or partially hidden. The intersections between a unique line and a projected plane (with or without openings) are determined by a new method which, even in the presence of numerical errors, will always give correct intersection information. Unlike many classical algorithms, intersections are determined by a single formula without tedious case subdivisions. With little additional calculations, object penetrations can also be tackled.