Efficient Parallel Gouraud Shading and Linear Interpolation over Triangles

Abstract

A parallel raster algorithm to draw Gouraud shaded triangles is presented. At the heart of the algorithm is a new constrained parallel edge-traversal technique. This parallel traversal represents an increased level of parallelism compared to the existing solutions. Next, traditional algorithms take different amounts of time to advance from one horizontal span to another for the left edge and the right edge of the triangle when the slope of one of the edges is more than one and that of the other edge is less than one. This causes one processor to wait for another processor. The parallel constrained edge traversal technique removes this problem by directly jumping from one span to the next. It also ensures that adjacent triangles that share an edge do not share any pixels. Moreover, no cracks occur between adjacent polygons. Unlike some existing algorithms whose complexity depends on the size of the bounding box of the triangle, the complexity of our algorithm is solely dependenton the perimeter and area of the triangle.Due to the above features, the algorithm presented here exposes a greater degree of parallelism at considerably lesser cost and achieves better processor utilization, compared to existing algorithms for this problem1, 2, 3, 4, 5, 6. The algorithm is well suited for hardware implementation.