Fast display of images of three-dimensional surfaces without aliasing

Abstract

A method and system for generating an anti-aliased image of a three dimensional surface is described. A point of view of the display screen is specified by an azimuth angle and an elevation angle with respect to the three-dimensional surface. The surface is defined as a two-dimensional array of height values. The projection of a point of the surface to the display plane is performed by applying a rotation based on the azimuth and elevation angles, followed by a parallel projection to the display plane so that, the columns of the surface project to the columns of the display screen. The points of the surface are projected in pairs, starting with the nearest points within a column and proceeding to the farthest points of the column. The grey-level shading (or color) values are accumulated in a one-dimensional array of floating-point variables that store the intensities of the pixels of a column of the display screen. The intensities are accumulated by weighting the grey-level shades (or colors) by the distance between the projected pair of points and by the fractional offsets from the integer-valued pixel locations. Because the grey-level shade of every grid point of the surface contributes to the pixel intensities, aliasing effects within columns of pixels are avoided. Aliasing effects across columns are avoided by the use of intermediate scan lines between the columns of pixels.