Abstract: A system for avoiding overflow and underflow of image variables by clamping image gradients. The method is described with respect to a triangular polygon to be rendered, and a function for that polygon such as color. First the delta x and delta y values between each of the vertices of the triangle are computed. Using the delta x and delta y values, the area of the triangle is computed. The sign of the triangle area is used to determine whether the triangle is visible. If the triangle is visible then the method determines whether the width of the triangle in the x-direction, dx_min, is at least equal to a minimum threshold. To make this determination, first the vector with the largest delta y is selected. Using the largest delta y value, dx_min is computed. If dx_min is less than the threshold value, then a correction value is computed. The position of the vertex that is not part of the vector with the largest delta y is then corrected using the correction value.

Abstract: The present invention simulates the effect of non-homogenous fog in computer graphics images. The non-homogenous fog visibility equation includes four parameters. A distance scaling parameter K1. A variable fog parameter K2. A normalization constant K3, and a scaling constant K4. The visibility at a sample point can be determined using the visibility equation: ##EQU1## where Z.sub.ns is a normalized and scaled image distance which is equal to (K4*K1*Z)+(K4*K2). To improve computational efficiency the visibility function can be evaluated using a lookup table. The lookup table of the present invention has an efficient addressing scheme and a minimum number of output steps. The visibility function can be expressed as a function of a fog ratio and a fog distance. The fog distance is a distance from the viewpoint to the point where the visibility is reduced to 37% of full visibility. The fog ratio is the square root of the ratio of "near fog" density to "far fog" density.

Abstract: A flight simulator combines flight data and polygon face terrain data to provide a CRT display at each window of the simulated aircraft. The data base specifies the relative position of each vertex of each polygon face therein. Only those terrain faces currently appearing within the pyramid of vision defined by the pilots eye and the edges of the pilots window need be displayed at any given time. As the orientation of the pyramid of vision changes in response to flight data, the displayed faces are correspondingly displaced, eventually moving out of the pyramid of vision. Faces which are currently not visible (outside the pyramid of vision) are clipped from the data flow. In addition, faces which are only partially outside of pyramid of vision are reconstructed to eliminate the outside portion. Window coordinates are generated defining the distance between each vertex and each of the boundary planes forming the pyramid of vision.