Clipping Using Homogeneous Coordinates

  • Jim Blinn
  • Martin Newell

Siggraph 1978 |

Published by Association for Computing Machinery, Inc.

Clipping is the process of determining how much of a given line segment lies within the boundaries of the display screen. Homogeneous coordinates are a convenient mathematical device for representing and transforming objects. The space represented by homogeneous coordinates is not, however, a simple Euclidean 3-space. It is, in fact, analogous to a topological shape called a “projective plane”. The clipping problem is usually solved without consideration for the differences between Euclidean space and the space represented by homogeneous coordinates. For some constructions, this leads to errors in picture generation that show up as lines marked invisible when they should be visible. This paper will examine these cases and present techniques for correctly clipping the line segments.