1. A method to generate, by one or more processing units programmed to perform a partial display update in a windowing system having a plurality of display layers, comprising: using one or more general purpose central processing units to perform the programmed acts of— identifying an output region associated with a top-most display layer, the output region having an associated output size and location; identifying a buffer having a size and location corresponding to the output size and location; identifying the top-most display layer as a current display layer; determining if a filter is associated with the current display layer and, if there is— determining an input region for the filter, said input region having an associated size and location, and adjusting the buffer size and location to correspond to the union of the input region's size and location and the buffer's size and location; setting the display layer immediately lower than the current display layer to the current display layer; repeating the act of determining for each relevant display layer in the windowing system; establishing an output buffer, in a memory, having a size and location to accommodate the size and location of the buffer; and using a graphics processing unit to perform the programmed act of causing that portion of each display layer that overlaps the output buffer's location to be composited into the established output buffer through an application programming interface function.