Nancy, On Thu, 22 Jun 2000, nancy collins wrote:
>sorry if i've been missing the point. Absolutely no need to apologize; you're doing ME the favor! :-) > can you explain to me if this is the >approximation you are talking about? take N identical 2D sheets >of quads, and stack them into a 3D volume of cubes so the data values >are constant along the stacking axis, and then warp that volume into >a sphere or torus. or something different? Something different. Rather than describing coordinates and coordinate systems, let's try something visceral. Imagine a doughnut or bagle. Boy this is tough to describe in words! Set the bagle flat on the table and in order to share it with a friend cut it vertically in half in two places. (not very good for putting cream chease on it, but I prefer mine plain.) Now looking at the cut ends we see a solid circular cross section of bagle. Now for various reasons, instead of it being round (say hand rolled) make it square in cross section (machine extruded). Now put the two halves back together again. What we have is square in cross section and forming a circle. This is the real representation of my data. It is constant inside of this cylindrically symmetric, square cross sectioned, ring. Since it is constant I only need one number to describe it's value. The hard part is that if I pick four cross sectional points say (1,1) (1,2) (2,1) and (2,2) they are not only connected to one another but to an infinite set of points which form the corners or edges of my square ring. Mathematically, Take a cartesian coordinate system (x,y,z) and a cylindrical coordinate system (r,phi,z). A 1-1 transformation between these coordinates systems is given by x = r * cos(phi) and y = r * sin(phi) Take the volume interior to the bounding surfaces: r=1; r=2; z=1; z=2; This gives a square cross sectioned ring. I would like to describe this geometry to DX and ask it to fill this volume with a value. A picture is really worth a thousand words! Tom
