Lets say I have a single curve segment with a known height (difference between the lowest points of the curve and the highest point of the curve) and length (difference between the leftmost and rightmost sides). How do I find out the diameter of the circle or ellipse that would align to that curve for it's entire length? Also how would I determine the distance from the center of that circle to the top of the curve? I do not know any calculus but I am pretty good with linear algebra.
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Just in case, this could help, but probably you already read it. http://en.wikipedia.org/wiki/Curvature#Local_expressions, http://en.wikipedia.org/wiki/Convex_function, http://en.wikipedia.org/wiki/Concave_function – iadvd Apr 03 '15 at 04:12
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I know not the first thing about any of this so thanks. – LinkReincarnate Apr 03 '15 at 04:13
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Not every curve can be aligned with a circle. Unless what you're really asking is "given the width/height of a circular arc, how can I determine how big the circle it's from is?". – Jack M Apr 03 '15 at 04:14
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@LinkReincarnate it is funny because I asked something related to curvature some days ago and it was answered today... about the point of maximum curvature... http://math.stackexchange.com/questions/1215196/what-is-the-name-of-the-most-locally-convex-concave-point-of-a-fx-function – iadvd Apr 03 '15 at 04:15
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Yes exactly Jack. That is what I want. – LinkReincarnate Apr 03 '15 at 04:16
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I found the answer I was looking for http://www.mathopenref.com/arcradius.html
The Arc Radius is what I wanted. How do I determine the distance from the center of the circle to the bottom of the curve? Is it just the Arc Radius minus the height of the curve?
LinkReincarnate
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