// Arup Guha
// 12/16/2014
// Implementation of some 2d geometry routines

public class Test2DGeo {

    public static void main(String[] args) {

        pt2D a = new pt2D(3.0, 7.0);
        pt2D b = new pt2D(-4.0, 6.0);
        pt2D c = new pt2D(10.0, 2.0);
        pt2D d = new pt2D(1.0, -5.0);

        // find area of triangle abc, via vectors.
        vect2D v1 = new vect2D(a, b);
        vect2D v2 = new vect2D(a, c);
        System.out.printf("The area of triangle ABC is %.3f.\n", v1.crossMag(v2)/2);

        // Find the angle between the two vectors.
        System.out.printf("The angle between the vectors is %.3f radians.\n", v1.angle(v2));

        // Test typical line intersection.
        line first = new line(a, b);
        line second = new line(c, d);
        pt2D meet = first.intersect(second);
        System.out.printf("The two lines meet at point (%.3f, %.3f).\n", meet.x, meet.y);

        // Test parallel line intersection call.
        pt2D e = new pt2D(24.0, 4.0);
        line third = new line(c, e);
        pt2D never = first.intersect(third);
        if (never == null) System.out.println("These lines never meet.");
    }
}

class vect2D {

    public double x;
    public double y;

    public vect2D(double myx, double myy) {
        x = myx;
        y = myy;
    }

    public vect2D(pt2D start, pt2D end) {
        x = end.x - start.x;
        y = end.y - start.y;
    }

    public double dot(vect2D other) {
        return this.x*other.x + this.y*other.y;
    }

    public double mag() {
        return Math.sqrt(x*x+y*y);
    }

    // Thjs formula comes from using the relationship between the dot product and
    // the cosine of the included angle.
    public double angle(vect2D other) {
        return Math.acos(this.dot(other)/mag()/other.mag());
    }

    public double signedCrossMag(vect2D other) {
        return this.x*other.y-other.x*this.y;
    }

    public double crossMag(vect2D other) {
        return Math.abs(signedCrossMag(other));
    }
}

class line {

    final public static double EPSILON = 1e-9;

    public pt2D p;
    public vect2D dir;

    public line(pt2D start, pt2D end) {
        p = start;
        dir = new vect2D(start, end);
    }

    public pt2D intersect(line other) {

        // This is the denominator we get when setting up our system of equations for
        // our two parametric line parameters.
        double den = det(dir.x, -other.dir.x, dir.y, -other.dir.y);
        if (Math.abs(den) < EPSILON) return null;

        // We already have the denominator, now solve for the numerator for lambda, the
        // parameter for this line. Then return the resultant point.
        double numLambda = det(other.p.x-p.x, -other.dir.x, other.p.y-p.y, -other.dir.y);
        return eval(numLambda/den);
    }

    // Returns the shortest distance from other to this line. Sets a vector from the starting
    // point of this line to other and uses the cross product with that vector and the direction
    // vector of the line.
    public double distance(pt2D other) {
        vect2D toPt = new vect2D(p, other);
        return dir.crossMag(toPt)/dir.mag();
    }

    // Returns the point on this line corresponding to parameter lambda.
    public pt2D eval(double lambda) {
        return new pt2D(p.x+lambda*dir.x, p.y+lambda*dir.y);
    }

    public static double det(double a, double b, double c, double d) {
        return a*d - b*c;
    }
}

class pt2D {

    public double x;
    public double y;

    public pt2D(double myx, double myy) {
        x = myx;
        y = myy;
    }
}