Vapor trails emanating from a jet or a missile can be rendered using methods similar to the painting technique described in Section 8.3. A circular, wispy 2D image such as that used in the preceding section is used to generate the vapor pattern over some unit interval by rendering it as a billboard. A texture image consisting only of alpha values is used to modulate the alpha values of a white billboard polygon. The trajectory of the airborne object is painted using multiple overlapping copies of the billboard as shown in Figure 92. Over time the individual billboards gradually enlarge and fade. The program for rendering a trail is largely an exercise in maintaining an active list of the position, orientation and time since creation for each billboard used to paint the trail. As each billboard polygon exceeds a threshold transparency value it can be discarded from the list.