Object-order Rendering of Discrete Objects

This dissertation gives accurate and efficient methods for the object-order rendering of discrete objects. Discrete objects are typically represented with a volume raster and rendered with a volume rendering algorithm. However, current object-order volume rendering algorithms suffer from several problems. First, they require that the volume raster be traversed in a strict visibility order, but existing visibility ordering methods do not always correctly order perspective projections of volume rasters. Second, both perspective and orthographic renderings of volume rasters can contain aliasing artifacts, but current object-order techniques have no method for addressing these artifacts. Third, computergenerated animations suffer from temporal aliasing artifacts, which can be addressed by adding motion blur. But currently the only motion-blur method for object-order techniques is super-sampling, which is very expensive. This dissertation presents three new techniques for the object-order rendering of discrete objects which address these shortcomings. First, it gives and proves the correctness of a new method for traversing a rectilinear volume raster in an order that guarantees correct visibility under a perspective projection. Second, it introduces an innovative technique for eliminating the aliasing artifacts that occur when rendering a discrete object. Third, it gives a new technique for adding motion blur to renderings of discrete objects which is much more efficient than super-sampling. It uses the common object-order volume rendering method of splatting as a testbed for realizing these new techniques. This dissertation gives examples of the new techniques applied to volume rendering confocal data, texture-mapping discrete polygons, and rendering terrain datasets. In particular, the terrain representation is innovative compared to traditional object-order methods, which typically represent the terrain with triangular surface patches.