I'm confused as to why there are still visible hard edges after switching to continuous D. On the smooth side walls that recede away from the camera, D seems to vary very smoothly, but on the tops of the arches and on the columns there are very apparent triangles. Based on that, it probably has something to do with those more complex shapes being represented using tessellations of triangles, but I'm not sure how exactly it happens.
I'm also wondering the same thing, and I think it could be because of the representation of complex shapes using tessellations like you said. What's strange is on the first column closest to the viewer, the bottom two circular supports have triangles in this visualization of continuous D, but do not have triangles in the original visualization of D rounded to the nearest integer. Perhaps this may be because the original visualization rounded to integers, but this involves linear interpolation of the two bilinear interpolation results by averaging the two values. However there is still aliasing (triangles) because the trilinear method is still a rough approximation.