What is the maximum distance from an anchor point to a bezier curve?

Posted by drawnonward on Stack Overflow See other posts from Stack Overflow or by drawnonward
Published on 2010-04-22T18:49:30Z Indexed on 2010/04/23 3:03 UTC
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bezier

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distance

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geometry

Given a cubic bezier curve P0,P1,P2,P3 with the following properties:

• Both P1 and P2 are on the same side of the line formed by P0 and P3.
• P2 can be projected onto the line segment formed by P0 and P3 but P1 cannot.

What is the T value for the point on the curve farthest from P3?

Here is an image with an example curve. The curve bulges on the left, so there is a point on the curve farther from P3 than P0.

I found this reference for finding the minimum distance from an arbitrary point to a curve. Is trial and error the only way to solve for maximum distance as well? Does it make any difference that the point is an anchor on the curve?

Thanks

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