## Computing Visibility Without Depth (Abstract)

**UNC-CH Computer Science Technical Report TR95-047**,
University of North Carolina, October 1995.

**Computing Visibility Without Depth**

*Leonard McMillan*

A fundamental problem in computer graphics is the determination of the
visible subset of surface elements within a scene given the desired
viewpoint. Often, the best method for computing visibility is depends
on the form and properties of the scene's description. This paper presents
a visibility algorithm for a specific type of scene description, called a
*perspective-projected surface*. Surfaces of this type are
commonplace, since they describe nearly all physically-based
image-formation processes. The algorithm establishes a particular
drawing order where the last surface drawn at any image region
corresponds to the visible surface in that region, similar to the classic
painter's algorithm. The unique aspect of the algorithm is that the drawing
order is established independent of the scene's geometry- in particular
the depth values relative to the viewing surface. The paper goes on to
give a formal proof of the algorithm's correctness.

**Figure 1.** All perspective-projected surfaces can be
mapped onto a spherical manifold. Any subsequent re-projection of that
surface to a manifold with a different center of projection induces
an unique coordinate frame for the original surface. In this induced
coordinate system an occlusion compatable ordering for performing the
reprojection can be established independent of the underlying range
function.

**Figure 2.** A selection of images from the paper
that demonstrate the algorithm's application to various projection
manifolds.

**Note:** This paper explains in tedious detail the terse
appendix of the McMillan and Bishop SIGGRAPH '95 paper.