DukeW123 pointed out a simpler algorithm than mine.
Another idea for your "interior point algorithm"...the sum of the areas of the three triangles formed by any two points of the original triangle and the test point is the area of the "big" triangle. This will not be true for points outside the triangle...this would also be a lot easier to implement...you could essentially do it in one long line of code, using Hero's [a.k.a. Heron's] formula.
A problem with this algorithm is that it depends on testing equality of floating point numbers, which in computers is not very reliable due to rounding error. Another problem is this algorithm doesn't distinguish between a point being on the triangle from being in the interior of the triangle. Still, it's an interesting contribution. Thanks, DukeW123.
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Heron's Formula -- The area of triangle ABC (whose side lengths are a, b, and c, and whose semiperimeter is s=(a+b+c)/2) is sqrt((s)(s-a)(s-b)(s-c))
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