# Detect mouse click on a bezier curve's neighborhood

I'm developing a game in HTML5 and JavaScript using Canvas API for drawing graphics. I want to detect if the user has clicked on a bezier curve which has the line width of 20 pixels (something like this one on the picture). I need to validate if the user has clicked on the area drawn by the curve (red and black).

I implemented such an algorithm for lines, but could not adapt it to quadratic and cubic bezier curves. So I need an algorithm that will compare the position of a point relative to a bezier curve which has the form of

$$B(t) = P_0 (1-t)^2 + P_1 (1-t)t + P_2t^2$$

$$B(t) = P_0 (1-t)^3 + 3P_1 (1-t)t + 3P_2(1-t)t^2 + P_3t^3$$

for cubic bezier curves, and check if it is in the neighborhood of the bezier curve's path, I mean on the black drawn area.

[Red: Bezier curve's path; Black: Bezier curve's drawn area]