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Constructing a Sphere (Posted on 2012-02-25) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Dustin    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Bonus thoughts | Comment 12 of 16 |
(In reply to Bonus thoughts by Steve Herman)

I am not concerned about a maximally hollow sphere.  It should be basically completely hollow, but the degree of hollowness is not important.


Your formula in a) should do it!

b) sounds potentially difficult to implement in spreadsheet form, but I love a challenge!  I'll get right to work on this.  Perhaps I shall forfeit the contiguity of the cubes in favor of maximum hollowness.

  Posted by Dustin on 2012-02-27 04:00:18
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