Smooth shading of objects on display devices

Abstract

A method for defining a color gradient across a region in a display space that includes defining a bi-cubic patch enclosing the region. The bi-cubic patch includes four corners having a color associated therewith and four curves connecting pairs of the corners forming a closed loop. The four curves define the color gradient across the bi-cubic patch as a function of the four colors associated with the four corners of the bi-cubic patch. The method includes defining a unit square in parameter space including a mapping function from the unit square to the bi-cubic patch such that the corners of the bi-cubic patch map to the corners of the unit square. The color of every point in the unit square is a bi-cubic interpolation of the four colors associated with the four corners of the bi-cubic patch. The method includes clipping the bi-cubic patch for display of the region. In another aspect, the invention provides a method of accurately rendering color gradients across a bi-cubic patch that includes subdividing the bi-cubic patch into sub-patches until each side of a given sub-patch is a good approximation of a line and checking to determine if for all points inside of a given sub-patch the color associated with each point is sufficiently accurate. If not, the sub-patch is further subdivided until the color associated with each point inside a given sub-patch is sufficiently accurate. The method includes dividing the sub-patches into polygons and rendering the polygons.