/*
 
 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
 
 RepRap is free; you can redistribute it and/or
 modify it under the terms of the GNU Library General Public
 Licence as published by the Free Software Foundation; either
 version 2 of the Licence, or (at your option) any later version.
 
 RepRap is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 Library General Public Licence for more details.
 
 For this purpose the words "software" and "library" in the GNU Library
 General Public Licence are taken to mean any and all computer programs
 computer files data results documents and other copyright information
 available from the RepRap project.
 
 You should have received a copy of the GNU Library General Public
 Licence along with RepRap; if not, write to the Free
 Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA,
 or see
 
 http://www.gnu.org/
 
 =====================================================================
 
 RrHalfPlane: 2D planar half-spaces
 
 First version 20 May 2005
 This version: 9 March 2006
 
 */

package org.reprap.geometry.polygons;

/**
 * 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
 */
public class RrHalfPlane
{
	
	// The half-plane is normal*(x, y) + offset <= 0
	
	private Rr2Point normal; 
	private double offset;
	
	
	/**
	 * Convert a parametric line
	 * @param l
	 */
	public RrHalfPlane(RrLine l)
	{
		double rsq = 1/l.direction().mod();
		normal = new Rr2Point(-l.direction().y()*rsq, l.direction().x()*rsq);
		offset = -Rr2Point.mul(l.origin(), normal());
	}
	
	
	/**
	 * Make one from two points on its edge
	 * @param a
	 * @param b
	 */
	public RrHalfPlane(Rr2Point a, Rr2Point b)
	{
		this(new RrLine(a, b));
	}   
	
	/**
	 * Deep copy
	 * @param a
	 */
	public RrHalfPlane(RrHalfPlane a)
	{
		normal = new Rr2Point(a.normal);
		offset = a.offset;
	}
	
	
	public String toString()
	{
		return "|" + normal.toString() + ", " + Double.toString(offset) + "|";
	} 
	
	// Get the components
	
	public Rr2Point normal() { return normal; }
	public double offset() { return offset; }
	
	/**
	 * Is another line the same within a tolerance?
	 * @param a
	 * @param b
	 * @param tolerance
	 * @return
	 */
	public static boolean same(RrHalfPlane a, RrHalfPlane b, double tolerance)
	{
		if(Math.abs(a.normal.x() - b.normal.x()) > tolerance)
			return false;
		if(Math.abs(a.normal.y() - b.normal.y()) > tolerance)
			return false;
		double rms = Math.sqrt((a.offset*a.offset + b.offset*b.offset)*0.5);
		if(Math.abs(a.offset - b.offset) > tolerance*rms)
			return false;
		
		return true;
	}
	
	
	/**
	 * Change the sense
	 * @return
	 */
	public RrHalfPlane complement()
	{
		RrHalfPlane r = new RrHalfPlane(this);
		r.normal = r.normal.neg();
		r.offset = -r.offset;
		return r;
	}
	
	/**
	 * Move
	 * @param d
	 * @return
	 */
	public RrHalfPlane offset(double d)
	{
		RrHalfPlane r = new RrHalfPlane(this);
		r.offset = r.offset - d;
		return r;
	}
	
	
	/**
	 * Find the potential value of a point
	 * @param p
	 * @return
	 */
	public double value(Rr2Point p)
	{
		return offset + Rr2Point.mul(normal, p);
	}
	
	
	/**
	 * Find the potential interval of a box
	 * @param b
	 * @return
	 */
	public RrInterval value(RrBox b)
	{
		return RrInterval.add(RrInterval.add((RrInterval.mul(b.x(), normal.x())), 
				(RrInterval.mul(b.y(), normal.y()))), offset);
	}
	
	
	/**
	 * The point where another line crosses
	 * @param a
	 * @return
	 * @throws rr_ParallelLineException
	 */
	public Rr2Point cross_point(RrHalfPlane a) throws rr_ParallelLineException
	{
		double det = Rr2Point.op(normal, 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 Rr2Point(x*det, y*det);
	}
	
	/**
	 * Parameter value where a line crosses
	 * @param a
	 * @return
	 * @throws rr_ParallelLineException
	 */
	public double cross_t(RrLine a) throws rr_ParallelLineException 
	{
		double det = Rr2Point.mul(a.direction(), normal);
		if (det == 0)
			throw new rr_ParallelLineException("cross_t: parallel lines.");  
		return -value(a.origin())/det;
	}
	
	/**
	 * Point where a parametric line crosses
	 * @param a
	 * @return
	 * @throws rr_ParallelLineException
	 */
	public Rr2Point cross_point(RrLine a) throws rr_ParallelLineException
	{
		return a.point(cross_t(a));
	}
	
	/**
	 * Take a range of parameter values and a line, and find
	 * the intersection of that range with the part of the line
	 * (if any) on the solid side of the half-plane.
	 * @param a
	 * @param range
	 * @return
	 */
	public RrInterval wipe(RrLine a, RrInterval range)
	{
		if(range.empty()) return range;
		
		// Which way is the line pointing relative to our normal?
		
		boolean wipe_down = (Rr2Point.mul(a.direction(), normal) >= 0);
		
		double t;
		
		try
		{
			t = cross_t(a);
			if (t >= range.high())
			{
				if(wipe_down)
					return range;
				else
					return new RrInterval();
			} else if (t <= range.low())
			{
				if(wipe_down)
					return new RrInterval();
				else
					return range;                
			} else
			{
				if(wipe_down)
					return new RrInterval(range.low(), t);
				else
					return new RrInterval(t, range.high());                 
			}
		} catch (rr_ParallelLineException ple)
		{
			t = value(a.origin());
			if(t <= 0)
				return range;
			else
				return new RrInterval();  
		}
	}
	
}