Hello everyone! First thread here! I'm struggling to determine which approach is the best to face this problem: I need to find the closest pair of points between a plane and a circle in 3D! There are so many optimization methods out there and I don't know which one is the best for this case.
Closest pair of points between plane and circle in 3D?
- Thread starter PacaPaw
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lev888
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I would start with exact formulation of the problem. Are you looking for 2 points between(?!) a plane and a circle? I doubt it. Please clarify.
I suspect you are looking for a pair of points, one on the given plane, the other on the given circle, such that the distance between them is the shortest among all possible pairs.
If this is the case I doubt you need an optimization method.
Thank you for the quick reply!! And sorry for not clarifying! Yes, the points i'm looking for are the ones on the given plane and circle.
Using the parametric equations of each, I can determine a general formula for the distance between any point in the plane and any point in the circle. I was thinking about optimizing this equation. How do you suggest I face this problem instead?
Using the parametric equations of each, I can determine a general formula for the distance between any point in the plane and any point in the circle. I was thinking about optimizing this equation. How do you suggest I face this problem instead?
pka
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As posted the question is completely meaningless. In \(\Re^3\) a plane and a circle can have \(0,~1,~2, \text{ all }\)points of the plane in common.
Please state the exact wording of your question.
Dr.Peterson
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I'd probably use the normal vectors to the plane and to the plane containing the circle. A little work with vector products, or maybe something simpler, and I could find the points on the circle that are nearest or furthest from the plane. Of course if the circle intersects the plane, the closest points are the points of intersection, so that would be a special case.