Painter's algorithm

The painter's algorithm, also known as a priority fill, is one of the simplest solutions to the visibility problem in 3D computer graphics. When projecting a 3D scene onto a 2D plane, it is necessary at some point to decide which polygons are visible, and which are hidden.

The name "painter's algorithm" refers to the technique employed by many painters of painting distant parts of a scene before parts which are nearer thereby covering some areas of distant parts. The painter's algorithm sorts all the polygons in a scene by their depth and then paints them in this order, farthest to closest. It will paint over the parts that are normally not visible — thus solving the visibility problem — at the cost of having painted invisible areas of distant objects. The ordering used by the algorithm is called a 'depth order', and does not have to respect the numerical distances to the parts of the scene: the essential property of this ordering is, rather, that if one object obscures part of another then the first object is painted after the object that it obscures. Thus, a valid ordering can be described as a topological ordering of a directed acyclic graph representing occlusions between objects.

The algorithm can fail in some cases, including cyclic overlap or piercing polygons. In the case of cyclic overlap, as shown in the figure to the right, Polygons A, B, and C overlap each other in such a way that it is impossible to determine which polygon is above the others. In this case, the offending polygons must be cut to allow sorting. Newell's algorithm, proposed in 1972, provides a method for cutting such polygons. Numerous methods have also been proposed in the field of computational geometry.

The case of piercing polygons arises when one polygon intersects another. As with cyclic overlap, this problem may be resolved by cutting the offending polygons.

In basic implementations, the painter's algorithm can be inefficient. It forces the system to render each point on every polygon in the visible set, even if that polygon is occluded in the finished scene. This means that, for detailed scenes, the painter's algorithm can overly tax the computer hardware.

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