Geometry.pde

public static class Geometry {

    public static boolean inLine(PVector p, PVector a, PVector b) {
        final float EPSILON = 0.001f;
        PVector ap = PVector.sub(p, a);
        PVector ab = PVector.sub(b, a);
        return PVector.angleBetween(ap, ab) <= EPSILON && ap.mag() < ab.mag();
    }

    public static PVector scalarProjection(PVector p, PVector a, PVector b) {
        PVector ap = PVector.sub(p, a);
        PVector ab = PVector.sub(b, a).normalize();
        ab.mult(ap.dot(ab));
        return PVector.add(a, ab);
    }
    
    
    public static PVector closerLinePoint(PVector p, PVector a, PVector b) {
        PVector projection = scalarProjection(p, a, b);
        float lineLength = a.dist(b);
        if(projection.dist(b) > lineLength) return a;
        if(projection.dist(a) > lineLength) return b;
        return projection;
    }
    
    
    public static boolean inTriangle(PVector p, PVector t1, PVector t2, PVector t3) {
        boolean b1 = Sign(p, t1, t2) < 0.0f;
        boolean b2 = Sign(p, t2, t3) < 0.0f;
        boolean b3 = Sign(p, t3, t1) < 0.0f;
        return ((b1 == b2) && (b2 == b3));
    }
    
    
    private static float Sign(PVector p1, PVector p2, PVector p3) {
        return (p1.x - p3.x) * (p2.y - p3.y) - (p2.x - p3.x) * (p1.y - p3.y);
    }
    
    
    private static PVector linesIntersection(PVector p1, PVector p2, PVector p3, PVector p4) {
        float d = (p2.x - p1.x) * (p4.y - p3.y) - (p2.y - p1.y) * (p4.x - p3.x);
        if(d == 0) return null;
        float a = ((p3.x - p1.x) * (p4.y - p3.y) - (p3.y - p1.y) * (p4.x - p3.x)) / d;
        return new PVector(p1.x + a * (p2.x - p1.x), p1.y + a * (p2.y - p1.y));
    }
    
}