I would like to construct a sphere by gluing unit cubes together. I'm only attempting to approximate the shape of a sphere as closely as is possible with unit cubes.

Before I get out the glue, how would I go about creating a spreadsheet that would show me the quantity and placement of cubes in each cross-sectional layer? (think of an MRI scan cross-section)

For input, the spreadsheet should ask for the radius of the sphere to be built, as well as which layer of that sphere should be displayed.

There may be more than one way to accomplish this. Any spreadsheet that will allow me to build a sphere by displaying each layer of a sphere for a given radius is considered valid.

Here is an example of output:

Hint: The formula for distance in 3 dimensions is:

d=√[(x2-x1)2+(y2-y1)2+(z2-z1)2]

Bonus question! Adjust your algorithm to display a hollow sphere (think of a ping pong ball, or a beach ball). Note: All cubes must be connected into one contiguous piece.

(In reply to Excel implementation of Specific Algorithm by Steve Herman)

Great Steve.  That is exactly what I would have been looking for had I been Dustin.

You will note in Dustin's comment (preceding this) that he always used the same cell for all of his centres irrespective of radius (N12 in the images presented).

In my attempt of the solid layers I similarly maintained a static cell as my centre; admittedly I was guided by a sheet Dustin offered when we first discussed this proposal.

I shall offer my solution a little later.

Posted by brianjn on 2012-02-26 17:56:25