Based on "Craphics Gems" book. All sources from original site

I'm currently working on a project that requires quite a bit of geometry, so I downloaded the source code that goes along with the Graphics Gems book. Thankfully, c syntax is very similar to Javascript, so porting the code is easy. The first archive contains nearestpoint.c, which is the example provided for two concepts from the book - "Solving the Nearest Point-on-Curve Problem" and "A Bezier Curve-Based Root-Finder."

Here's the text from the book: The basic problem can be stated in this manner:
given a parametric curve Q and a point P, both in the plane, find the point on the
curve closest to P (that is, find the parameter value t such that the distance from
P to Q(t) is a minimum). Our approach begins with the geometry observation that the
line segment (whose length we wish to minimize) from P to Q(t) is perpendicular to
the tangent of the curve at Q(t) as shown in Fig. 1. The equation we wish to solve
for t is `[Q(t) - P] * Q'(t) = 0.`