A fast wireframe display algorithm for hidden surface removal in constructive solid geometry

A fast algorithm for rendering three dimensional geometry as wireframes is developed. The algorithm employs a constructive solid geometry (CSG) model as its underlying geometric representation scheme, set membership classification for the removal of non-boundary lines, and a finite-point backward ray tracing method for hidden line removal. By eliminating conventional polygon surface approximation and its associated surface topology representation, requiring high information overhead, the algorithm demonstrates speed and simplicity. The primary purpose of the algorithm is for expeditious real-time graphical simulation, particularly for interactive design. The algorithm demonstrates overall time complexity of O(n² h ^{* 2} ), where n denotes the total number of geometric primitives, and h denotes the total number of boundary edge segments. Desirable side effects associated with the use of set membership classification include the ability to generate NC machine instructions and the detection of object interference for collision avoidance during the simulation of manufacturing processes. Examples demonstrating the visualization of 3-D mechanical components are included.