Summary

We have designed a high-quality isosurface rendering algorithm that uses an underlying continuous-space representation of the image (quadratic spline). The computation of the 3D isosurface and of its normal is exact.

Main Contribution

We have designed a new 3D rendering algorithm by ray tracing the isosurface of a high-quality continuous model of volumetric discrete and regular data. Based on first principles, we have identified the quadratic B-spline as the best model for our purpose. The nonnegativity of this basis function has allowed us to confine the potential location of the isosurface within a binary shell. We have also showed how to use the space-embedding property of splines to further shrink this shell to essentially a single voxel width. Not all rays traced through a given shell voxel will intersect the isosurface; many may only graze it, especially when the ray-tracing vantage point is close or within the volume to render. We have therefore proposed an efficient heuristic to detect those cases and presented experiments to support our claims. We believe that this algorithm is one of the best isosurface rendering method available to date. It is less artifact-prone than others because (1) the isosurface is continuously-defined, and this, independently of the viewing geometry; (2) it is continuously differentiable everywhere with a well-defined gradient; and, (3) the method takes great care in detecting all rays intersecting the isosurface.