Z³: An Economical Hardware Technique for High-Quality Antialiasing and Transparency

In this paper we present an algorithm for low-cost hardware antialiasing and transparency. This technique keeps a central Z value along with compact floating-point Z gradients in the X and Y dimensions for each fragment within a pixel (hence the name Z³). It uses a small fixed amount of storage per pixel. If the visible complexity of the pixel exceeds the storage space available for the pixel, the minimum number of fragments having the closest Z values are merged. This combines different fragments from the same surface, resulting in both storage and processing efficiency. When operating with opaque surfaces, Z³ can provide superior image quality over sparse supersampling methods that use eight samples per pixel while using storage for only three fragments. Z³ also makes the use of large numbers of samples (e.g., 16) feasible in inexpensive hardware, enabling higher quality images. It is simple to implement because it uses a small fixed number of fragments per pixel. Z³ can also provide order-independent transparency even if many transparent surfaces are present. Moreover, unlike the original A-buffer algorithm it correctly antialiases interpenetrating transparent surfaces because it has three-dimensional Z information within each pixel.