Yes, I'd love to do more accurate normals, but the first goal in this thread was to come up with a "quadrangulation" of the surface using planar quadrilaterals _only_ (no triangles). I still don't know how to quadrangulate a sphere such that both the volume & the surface area converge to reasonable values. I'm willing to have crinkles (including non-convexities), so long as they smooth out in the limit, which would also help solve the "normal" problem. At 05:11 PM 1/8/2013, John Aspinall wrote:
For purposes of 3d graphics, a much more obvious property to approximate is the surface normal. The surface normal is used directly in graphic rendering to calculate reflectance for all but 100% "matte" surfaces. This immediately eliminates "crinkly" approximations.
On 01/07/2013 09:05 PM, Henry Baker wrote:
I was thinking today that I need to make more precise my definition of "approximation" to a 3D surface.
In the case of a sphere, I think that 1) the limit of the series should have the same _volume_ as the sphere; and 2) the limit of the series should have the same _surface area_ as the sphere.