Distance from points to a parabola

Projects a set of points onto a parabola and returns the nearest points on the parabola

This is an adaptation of the projecting method for ellipse introduced by D. Eberly.
Internet publication: "Distance from a point to an ellipse in 2D" (2004) Geometric Tools, LLC, www.geometrictools.com
Book publication: "3D Game Engine Design", 2nd edition.
Morgan Kaufmann Publishers, San Francisco, CA, 2007.
(see Section 14.13.1)

Usage: [RSS, XYproj] = Residuals_parabola(XY,ParG)
Input: XY(n,2) is the array of coordinates of n points
x(i)=XY(i,1), y(i)=XY(i,2)
ParG is a vector 4x1 of the ellipse parameters
ParG = [Vertex(1:2), p, Angle]'
Vertex - the coordinates of the parabola's vertex
p - distance from the focus to the directrix
Angle - the angle of tilt of the parabola

Output: RSS is the Residual Sum of Squares (the sum of squares of the distances)
XYproj is the array of coordinates of projections

The algorithm is proven to converge and reaches an accuracy of 8-9 significant digits. It takes 5-6 iterations per point, on average.