The computer (86) executes interactive software preparing B-spline descriptions of the surface and its piecewise-linear trimming curves. The graphics accelerator (19) performs the trimming by traversing separate segments in sequence to find points of intersection in parameter space between the curve and subspan boundaries. Such points are classified as new verticesm entrances, exits or intermediate points of the subspan for use with its remaining vertices in description of a trimmed polygon for display by colour monitor (94).