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 case anyone needs help visualizing, here's an example of a sphere I built using my hollow sphere spreadsheet. (It is filled with water to help you see its hollowness)

I built it in a video game called MineCraft.  Needing the ability to construct spheres in this game is the reason I designed my spreadsheet in the first place.  It was quite fun to design the algorithm a year ago, hence this problem on perplexus.

Posted by Dustin on 2012-02-27 03:51:25