Abstract: An antialiased rendering algorithm that guarantees that each pixel of the output image is within a user-specified error tolerance of the filtered underlying continuous image wherein an object-space octree is used to cull hidden geometry rapidly, and a quadtree data structure is used to test visibility through image-space regions. When regions are too complex, quadtree subdivision is employed to simplify the geometry. Subdivision stops when the algorithm can either analytically filter the required region or bound the convolution integral appropriately with interval methods.

Abstract: A hierarchical Z-buffer scan-conversion algorithm that does well on both (a) quickly rejecting most of the hidden geometry in a model, and (b) exploiting the spatial and temporal coherence of the images being generated. The method uses two hierarchical data structures, an object-space octree and an image-space Z-pyramid, in order to accelerate scan conversion. The two hierarchical data structures make it possible to reject hidden geometry very rapidly while rendering visible geometry with the speed of scan conversion. For animation purposes, the algorithm is also able to exploit temporal coherence. The resulting method is well suited to models with high depth complexity, achieving significant speedup in some cases compared to ordinary scan conversion.

Abstract: Disclosed are a method and a system for processing patterns such as oriented patterns, to derive constituents which are more useful than the original patterns. For example, an oriented pattern such as a seismic section can be decomposed into a flow field, which is an estimate of a moving accretion boundary which formed the subsurface layers, and a residual pattern, which is an estimate of layer properties, such as acoustic velocity. Similarly, an oriented pattern such as a chart displaying changes in borehole resistivity with depth along its vertical direction and changes in resistivity with angle around the borehole along its horizontal dimension, can be decomposed into a flow field and a residual pattern, where the flow field is an estimate of a moving accretion boundary and the residual pattern is an estimate of resistivity changes with depth and angle independent of the accretion boundary. The flow field can be mapped onto regular, e.g.