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I'm looking for a deterministic algorithm to obtain the best fitting rhombus out of a set of user-drawn points. It need not necessarily be optimal (simple would be better).

Thanks.

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    A number of points greater than 4 is provided (the user draws the shape using a digital stylus). The rhombus does not necessarily have sides parallel to the main axes. There is no specification for the error, one of the usual metrics such as least squares can be used.2012-08-14

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Well a rhombus is well defined by two slopes and three intercepts, so you have five unknowns to solve for. The problem is of course that your inputs (i.e. the matrix coefficients) are not exact. In this case, least squares leads to:

$x = (A^T A)^{-1} A^T b$

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    To whomever downvoted, mind adding an explanation on why you think this won't work / or where I'm wrong? It's an interesting problem to me, and if you have a better solution, I'll be the first to upvote it.2012-08-16