Exact antialiasing of textured terrain models Daniel Cohen-Or Computer Science Department, School of Mathemat- ical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel e-mail: daniel@math.tau.ac.il We introduce a fast area-sampling anti- aliasing technique for textured terrain models. We scan the model in image or- der, averaging the pixel footprint values. The technique samples all, but only, the visible parts. It improves previous texture mapping methods that ignore self- occluded footprints. It is superior to super-sampling. The image quality is as- sessed in both spatial and temporal do- mains. The good precision of the sampling process in the spatial domain provides an alias-free temporal domain. The low com- putational cost of the rendering technique and its high-quality filtering in the spatio- temporal domain offer a tool for real-time rendering of discrete terrain models. Key words: Terrian visualization — Visual simulations — Voxel-based modelling — Ray casting — Antialiasing — Area samp- ling — Supersampling 1 Introduction Images of continuous scenes that contain arbitrarily high spatial frequencies are sample and represented in a finite set of raster pixels. Due to the discrete nature of the image raster, the image is limited to display only a finite range of frequencies. Aliasing is a phenomenon caused by high frequencies sampled at a lower rate. Spatial domain aliasing produces artifacts such as Moire patterns or jagged edges. Spatial aliasing, which can be acceptable in a still image, can cause stronger visual artifacts in a real-time animated sequence of images. An eye-irritating effect caused by spatio-temporal domain aliasing is known as flickering. This is due to the display of high frequencies at falsely spatial locations that are not correlated in time, which causes sudden changes in pixel values. Antialiasing techniques use subpixel accuracy to reduce or eliminate aliasing artifacts. Accurate spatial antialiasing reduces flickering due to the coherency exhibited among the images in the time domain (shown in Sect. 5). Thus, real-time anima- tions of textured models must employ a very accu- rate antialiasing technique to avoid the disturbing flickering. However, embedding accurate anti- aliasing into the rendering process traditionally causes a serious performance degradation, which conflicts with the real-time requirement. The anti- aliasing technique presented in this paper is embedded in an algorithm that renders textured terrains. The paper is structured as follows. In Sect. 2, a brief review of antialiasing methods of textured models is presented In Sect. 3, previous works on terrain rendering are surveyed and the scheme that is implemented in this work is introduced. The new antialiasing technique is introduced in Sect 4. In Sect. 5, it is shown that, by implement- ing exact spatial aliasing, the technique reduces temporal aliasing artifacts. The algorithm’s cost is analyzed in Sect. 6, and in Sect. 7 we show results from a few test cases. We end with conclusions in Sect. 8. 2 Antialiasing techniques Antialiasing methods can be regarded as an ap- proximation of the convolution integral between the continuous image I and a filter kernel H at The Visual Computer (1997) 13 : 184 — 198 184  Springer-Verlag 1997