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Subject: is a point 'inside' a bezier?



Hi,

I have learned about the implicit equation of a line, which is where P
is a point on the line, N is the normal, and d stays constant as P
moves around on the line:

P (dot) N = d

The useful part of that is that you can dot N with a point that is not
on the line, and instantly tell whether the point is on the normal or
not-normal side by comparing the result to d.

I'm playing with quadratic beziers in two-dimensional BSPs. I have
figured out how to find the point where a line crosses a bezier, and
also how to find where a bezier crosses a bezier (that took a lot
longer to get). Those are kind of slow, though, so I'd like to use
those algorithms as deeper tests.

I was wondering if anyone knew of a technique for testing which side of
a quadratic bezier a point is on, which is as simple as checking a
sign. Hopefully it won't involve a square root operation, too.

Thanks in advance.
Dan


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