Accurate Scanconversion of Triangulated Surfaces

Abstract

Scanconverting a planar face produces depth-values for pixels totally or partly covered by the projection of that face. State-of-the-art hardware-supported scanconversion techniques use sub pixel adjustment and extended precision calculations to achieve an acceptable depth-accuracy despite numeric round-off errors. Unfortunately, this depth-accuracy only holds for the interior pixels of the face. During the scanconversion of the boundaries of polyhedral solids or of the tesselations of curved surfaces, significantly larger depth-errors may occur at pixels traversed by the projection of the bounding edges. These errors are due to the use of the wrong surface equations resulting from an erroneous classification of pixels with respect to the projections of faces. They may lead to logical mistakes of serious consequences for hidden-surface removal and for solid-modeling applications. To address this problem, a new scanconversion technique is presented, which exploits surface data and face/face adjacency information to infer face-projections. For simplicity, the exposition is confined to triangular faces of manifolds, where each edge is adjacent to two triangles. At pixels covered by the projection of an edge, the surface depth computed in the standard manner is compared to the depth of the surface supporting the adjacent triangle. Pixel classification is obtained by taking into account the result of this comparison and the orientations of both faces.