We address the task of rendering by ray tracing the isosurface of a high-quality continuous model of volumetric discrete and regular data. Based on first principles, we identify the quadratic B-spline as the best model for our purpose. The nonnegativity of this basis function allows us to confine the potential location of the isosurface within a binary shell. We then show 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 intersect the isosurface; many may only graze it, especially when the ray-tracing vantage point is close to or within the volume to be rendered. We propose an efficient heuristic to detect those cases. We present experiments to support our claims.