# The Painters Algorithm

The painter’s algorithm is a common technique used for visible surface determination in 3D computer graphics. It works on the basis of a polygon-by–polygon basis. Other Hidden Surface Removal algorithms work at a pixel by pixel basis. In practice, this method is quite complex, and some of the techniques may be more effective than others. Learn more about this algorithm by reading the following. This article will provide a brief overview of the algorithm used by painter and its main features.

## Problems with the painter’s algorithm

While it is possible to use a painter’s algorithm in some cases, it is not always feasible. In certain cases, it may result in incorrect results. In the classic case of cyclic overflow, for example, the polygons won’t be ordered in one way. The painter’s method still applies in this instance. The same applies for polygon splitting operations. In this case, the order of the polygons is z-order.

The painter’s algorithm is also inefficient. The painter’s algorithm forces the system to paint every point of every polygon in the visible sets, overloading the computer. The painter’s algorithm is unable to deal with intersecting geometry and can fail correctly to render ‘X” shapes. O(nlog n + *n) is the painter’s worst case complexity.

Another problem with the algorithm of the painter is its tendency to paint objects closest to the viewer. This makes the algorithm more efficient in computer graphics. Unlike the standard painter’s algorithm, it doesn’t need to calculate colors for distant scenes. However, it suffers from many of the same problems. The algorithm must paint the nearest area to the viewer before it can draw a background scene.

## Z-buffer techniques

The z buffer technique is a technique to store the closest depth for each pixel. The case of cyclic overlap is not possible to handle with a simple painter’s algorithm. This problem can only be solved by using the depth buffer. The highlighted polygon will be drawn behind or infront of the static pyramid. This is called depth buffering. This technique aids in sorting the problem in the painters algorithm.

The Z-buffer class provides two methods to manipulate the Z-buffer. The first method sets a depth at a given offset. The other checks if the value has increased beyond the current depth. These two methods are used for determining if a pixels is close to an object or hidden behind another. The second method is used to draw the pixel to its position. The third method updates the z-buffer.

A zbuffer can be used to enhance the quality of the scene. This technique interpolates values for z’ across the screen space. A z-buffer that is 16 bits wide may cause a lot of stitching, which can ruin the overall quality of the scene. Modern z-buffers are better at handling 32-bit and 24-bit data. A 8-bit buffer is not suitable for painting because it has too low precision.

## Topological ordering

One of the many algorithms that can be used for computer graphics generation is the painters algorithm. These algorithms are often inefficient and force the system to render each point on every polygon that is part of the visible set, and occluded by the finished scene. This process is inefficient and overburdens computer hardware. Instead of using the painter’s algorithm, computer graphics programs use a different, less time-consuming approach: depth order.

Another method, depth-first, is similar in concept to the painters algorithm. However, it does not deal well with transparency, and so has several issues. It is also unable to separate polygons located in close proximity. It also tends to overrender, creating gaps and overlaps at polygon edges. It is still better than any algorithm for creating complex scenes.

Graph theory defines topological sort as “the depth-first search of a directed graph.” Each box is a directed graph, and each edge has directed edges to boxes behind it. The method produces an ordered list of boxes, and mathematicians recognize this as a partially ordered set. Topological sorting is a powerful method for creating images. A more detailed explanation of the algorithms and its application can be found in the links below.