/*

RepRap
------

The Replicating Rapid Prototyper Project


Copyright (C) 2005
Adrian Bowyer & The University of Bath

http://reprap.org

Principal author:

Adrian Bowyer
Department of Mechanical Engineering
Faculty of Engineering and Design
University of Bath
Bath BA2 7AY
U.K.

e-mail: A.Bowyer@bath.ac.uk

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For this purpose the words "software" and "library" in the GNU Library
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=====================================================================

rr_line: 2D parametric line

First version 20 May 2005
This version: 2 October 2005 (translation to Java)

*/

// Teeny class to hold bisectors of line pairs

class rr_bisector
{
	public rr_line b;      // The bisecting line
	public double s_angle; // The sine of the angle 
	
	public rr_bisector(rr_line l, double a)
	{
		b = l;
		s_angle = a;
	}
}


// Exception for when trying to intersect parallel lines

class rr_ParallelLineException extends Exception
{
    public rr_ParallelLineException(String s)
    {
	super(s);
    }
}

// Class to hold and manipulate linear half-planes

class rr_half_plane
{

    // The half-plane is normal*(x, y) + offset < 0

    public rr_2point normal; 
    public double offset;


    // Convert a parametric line

    public rr_half_plane(rr_line l)
    {
	double rsq = 1/(l.direction.mul(l.direction));
	normal = new rr_2point(-l.direction.y*rsq, l.direction.x*rsq);
	rr_2point p = l.origin.add(l.direction);
	offset = rsq*l.origin.op(p);
    }


    // Make one from two points on its edge

    public rr_half_plane(rr_2point a, rr_2point b)
    {
	this(new rr_line(a, b));
    }   

    // Deep copy

    public rr_half_plane(rr_half_plane a)
    {
	normal = new rr_2point(a.normal);
	offset = a.offset;
    }


    // Convert to a string

    public String toString()
    {
	return "|" + normal.toString() + ", " + Double.toString(offset) + "|";
    } 


    // Change the sense

    public rr_half_plane complement()
    {
	rr_half_plane r = new rr_half_plane(this);
	r.normal.x = -r.normal.x;
	r.normal.y = -r.normal.y;
	r.offset = -r.offset;
	return r;
    }


    // Find the potential value of a point

    public double value(rr_2point p)
    {
	return offset + normal.mul(p);
    }


    // Find the potential interval of a box

    public rr_interval value(rr_box b)
    {
	return ((b.x.mul(normal.x)).add(b.y.mul(normal.y))).add(offset);
    }


    // The point where another line crosses

    public rr_2point cross_point(rr_half_plane a) throws rr_ParallelLineException
    {
	double det = normal.op(a.normal);
	if(det == 0)
	    throw new rr_ParallelLineException("cross_point: parallel lines.");
	det = 1/det;
	double x = normal.y*a.offset - a.normal.y*offset;
	double y = a.normal.x*offset - normal.x*a.offset;
	return new rr_2point(x*det, y*det);
    }

    public double cross_t(rr_line a) throws rr_ParallelLineException 
    {
	double det = a.direction.mul(normal);
        if (det == 0)
	    throw new rr_ParallelLineException("cross_t: parallel lines.");  
	return value(a.origin)/det;
    }

    public rr_2point cross_point(rr_line a) throws rr_ParallelLineException
    {
	return a.point(cross_t(a));
    }

}


// Class to hold and manipulate parametric lines

class rr_line
{
    public rr_2point direction;
    public rr_2point origin;

    public rr_line(rr_2point a, rr_2point b)
    {
	origin = new rr_2point(a);
	direction = b.sub(a);
    }

    public rr_line(rr_line r)
    {
	origin = new rr_2point(r.origin);
	direction = new rr_2point(r.direction);
    }

    // Convert to a string

    public String toString()
    {
	return "<" + origin.toString() + ", " + direction.toString() + ">";
    }


    // The point at a given parameter value

    public rr_2point point(double t)
    {
	return origin.add(direction.mul(t));
    }


    // Normalise the direction vector

    public void norm()
    {
	direction = direction.norm();
    }


    // Arithmetic

    public rr_line neg()
    {
	rr_line a = new rr_line(this);
	a.direction = direction.neg();
	return a;
    }

    public rr_line add(rr_2point b)
    {
	rr_2point a = origin.add(b);
	rr_line r = new rr_line(a, a.add(direction));
	return r;
    }

    public rr_line sub(rr_2point b)
    {
	rr_2point a = origin.sub(b);
	rr_line r = new rr_line(a, a.add(direction));
	return r;
    }

    /*
    public rr_line add(rr_line a)
    {
	a.origin = a.origin.add(origin);
	return a;
    }
    */

    //public rr_line sub(rr_line a, rr_line b)
    //{
    //	return add(a, b.neg());
    //}

    // The parameter value where another line crosses

    public double cross_t(rr_line a) throws rr_ParallelLineException 
    {
	double det = a.direction.op(direction);
        if (det == 0)
	    throw new rr_ParallelLineException("cross_t: parallel lines.");  
        rr_2point d = a.origin.sub(origin);
	return a.direction.op(d)/det;
    }


    // The point where another line crosses

    public rr_2point cross_point(rr_line a) throws rr_ParallelLineException
    {
	return point(cross_t(a));
    }


    // The squared distance of a point from a line

    public rr_2point d_2(rr_2point p)
    {
        double fsq = direction.x*direction.x;
        double gsq = direction.y*direction.y;
        double finv = 1.0/(fsq + gsq);
        rr_2point j0 = p.sub(origin);
        double fg = direction.x*direction.y;
        double dx = gsq*j0.x - fg*j0.y;
        double dy = fsq*j0.y - fg*j0.x;
        double d2 = (dx*dx + dy*dy)*finv*finv;
        double t = direction.mul(j0)*finv;
        return new rr_2point(d2, t);
    }

    // Normalised line that bisects the angle between 
    // two others joining points a, b, and c and the sine
    // of the angle it makes with them.
    
    static public rr_bisector bisect(rr_2point a, rr_2point b, rr_2point c)
    {
    	rr_2point ab = (a.sub(b)).norm();
    	rr_2point cb = (c.sub(b)).norm();
    	rr_2point d = (ab.add(cb)).norm();
    	double ang = ab.op(d);
    	rr_line r = new rr_line(b, b.add(d));
    	return new rr_bisector(r, ang);
    }
}