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#Actualjjd

Posted 15 January 2014 - 09:59 AM

Let's say I have some coplanar points in R^3. I want to describe these points by coordinates on the plane they share, in R^2. This way I can do some tests faster. How should I do this? 

 

Take any 3 distinct points A, B, and C. Take the cross product of (B - A) and (C - A) to get the normal, N, of the plane. Let (B - A) be one of your axes (normalize it). Take the cross product of N and (B - A) to get another orthogonal vector in the plane as the other axes (normalize it). Then project your points (relative to A) in your new axes.

 

-Josh


#1jjd

Posted 15 January 2014 - 09:53 AM

Let's say I have some coplanar points in R^3. I want to describe these points by coordinates on the plane they share, in R^2. This way I can do some tests faster. How should I do this? 

 

Take any 3 distinct points A, B, and C. Take the cross product of (B - A) and (C - A) to get the normal, N, of the plane. Let (B - A) be one of your axes (normalize it). Take the cross product of N and (B - A) to get another orthogonal vector in the plane as the other axes (normalize it).

 

-Josh


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