Real-Time High Quality Volume Isosurface Rendering

We present a volume format which is capable of representing complex reconstructions as well as a fast isosurface rendering algorithm. Our volume format consists of a set of densely packing tetrahedral polynomials in Bernstein form, each constrained to provide continuity across face boundaries. We define a specific class of tetrahedral partition suitable for our method, along with a least-squares approximation method to generate data in this format as approximations to arbitrary continuous volumes. Our volume format is closed under convolution with scalar volumes, so by representing reconstruction filters in our format we can create convolved volumes easily. We also present a fast rendering algorithm which maintains interactive rates for most volumes up to 128x128x128 resolution. Our results include analytic and observational error for how our format approximate several common volume reconstructions, as well as space requirements and rendering speed