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July 15th, 2011, 09:43 PM   #1
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Projecting 2D onto 3D Surface

Hi!

I was wondering if there's a formula that would allow one to project something 2D (e.g., text) onto a 3D cylinder. I'm not sure if this can be done with Linear Algebra or not, with Orthogonal Projections and whatnot, or if this fits under a different math topic.

Thanks!
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August 12th, 2011, 05:57 AM   #2
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Re: Projecting 2D onto 3D Surface

Strictly speaking, what you are asking doesn't make sense. You "project" something of dimension n onto a subspace of lower dimension. What you are really talking about is "mapping" a two dimensional figure onto a two dimensional surface of a three dimensional object.

That can be done in a number of ways, depending on exactly what you want to do. For example, if you have a two dimensional figure in a three dimensional coordinate system, you can imagine the cylinder to have the z-axis as its axis. From each point on the figure, draw the line from (0, 0, z) (where "z" is the z-coordinate of the point on the figure) to that point. The point is mapped to the point at which that line crosses the surface of the cylinder. Another way, that will give a different mapping is to draw the line from (0, 0, 0) (or any othe single point on the axis) to the point on the figure and again map that point to the point where the line crosses the cylinder.
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