Test if a point is "near" a segment specified by 2 points

RoadSegment.java

// See: www.exaflop.org/docs/cgafaq/cga1.html
// Let the point be C (Cx,Cy) and the line be AB (Ax,Ay) to (Bx,By).
// Let P be the point of perpendicular projection of C on AB.  The parameter
// r, which indicates P's position along AB, is computed by the dot product 
// of AC and AB divided by the square of the length of AB:
//     AC dot AB
// r = ---------  
//     ||AB||^2
//
// r has the following meaning:
//
//	r=0      P = A
//	r=1      P = B
//	r<0      P is on the backward extension of AB
//	r>1      P is on the forward extension of AB
//	0<r<1    P is interior to AB
//  
// L = sqrt((Bx-Ax)^2 + (By-Ay)^2)
//
//         (Cx-Ax)(Bx-Ax) + (Cy-Ay)(By-Ay)
// => r = --------------------------------
//                     L^2
// 
//         (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
// Let s = -----------------------------
//                 L^2
// => d = |s * L|
public class RoadSegment {

	private double Ax, Ay;
	private double Bx, By;
	private double ABx, ABy;
	private double sqAB;
	
	private double length;
	private double width;
	
	public RoadSegment(double lon1, double lat1, double lon2, double lat2, double roadWidth) {
		Ax = lat1; Ay = lon1;		
		Bx = lat2; By = lon2;
		ABx = Bx - Ax;
		ABy = By - Ay;
		sqAB = ABx * ABx + ABy * ABy;
		length = Math.sqrt(sqAB);
		width = roadWidth;
	}
	
	public boolean isNear(double lon, double lat) {
		double Cx = lat, Cy = lon;
		double ACx = Cx - Ax, ACy = Cy - Ay;
		double r = (ACx * ABx + ACy * ABy) / sqAB;
		if (r < 0 || r > 1) {
			return false;
		}
		double d = Math.abs((-ACy * ABx + ACx * ABy) / length);
		return (d < width);
	}
	
	public double getLength() {
		return length;
	}
}