/*
 * $Id$
 */

package edu.jas.root;


import java.io.Serializable;

import edu.jas.arith.BigDecimal;
import edu.jas.arith.BigRational;
import edu.jas.arith.Rational;
import edu.jas.poly.Complex;
import edu.jas.poly.ComplexRing;
import edu.jas.structure.ElemFactory;
import edu.jas.structure.RingElem;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.RingFactory;


/**
 * Rectangle. For example isolating rectangle for complex roots.
 * @param  coefficient type.
 * @author Heinz Kredel
 */
public class Rectangle & Rational> implements Serializable {


    /**
     * rectangle corners.
     */
    public final Complex[] corners;


    /**
     * Constructor.
     * @param c array of corners.
     */
    @SuppressWarnings("unchecked")
    /*package*/ Rectangle(Complex[] c) {
        if (c.length < 5) {
            corners = (Complex[]) new Complex[5];
            for (int i = 0; i < 4; i++) {
                corners[i] = c[i];
            }
        } else {
            corners = c;
        }
        if (corners[4] == null) {
            corners[4] = corners[0];
        }
    }


    /**
     * Constructor.
     * @param mid corner.
     */
    @SuppressWarnings("unchecked")
    public Rectangle(Complex mid) {
        this(mid, mid);
    }


    /**
     * Constructor.
     * @param sw corner.
     * @param ne corner.
     */
    @SuppressWarnings("unchecked")
    public Rectangle(Complex sw, Complex ne) {
        this(new Complex(sw.ring, sw.getRe(), ne.getIm()), sw, new Complex(sw.ring, ne.getRe(),
                        sw.getIm()), ne);
    }


    /**
     * Constructor.
     * 
     *  nw|0 ne|3
     *  sw|1 se|2
     * 
     * @param nw corner.
     * @param sw corner.
     * @param se corner.
     * @param ne corner.
     */
    @SuppressWarnings("unchecked")
    public Rectangle(Complex nw, Complex sw, Complex se, Complex ne) {
        this((Complex[]) new Complex[] { nw, sw, se, ne });
    }


    /**
     * String representation of Rectangle.
     * @see java.lang.Object#toString()
     */
    @Override
    public String toString() {
        //return "[" + corners[0] + ", " + corners[1] + ", " + corners[2] + ", " + corners[3] + "]";
        return "[" + corners[1] + ", " + corners[3] + "]";
        //return centerApprox() + " = [" + corners[0] + ", " + corners[1] + ", " + corners[2] + ", " + corners[3] + "]";
    }


    /**
     * Get a scripting compatible string representation.
     * @return script compatible representation for this Rectangle.
     */
    public String toScript() {
        // Python case
        //return "(" + corners[0] + ", " + corners[1] + ", " + corners[2] + ", " + corners[3] + ")";
        return "(" + corners[1].toScript() + ", " + corners[3].toScript() + ")";
    }


    /**
     * Get north west corner.
     * @return north west corner of this rectangle.
     */
    public Complex getNW() {
        return corners[0];
    }


    /**
     * Get south west corner.
     * @return south west corner of this rectangle.
     */
    public Complex getSW() {
        return corners[1];
    }


    /**
     * Get south east corner.
     * @return south east corner of this rectangle.
     */
    public Complex getSE() {
        return corners[2];
    }


    /**
     * Get north east corner.
     * @return north east corner of this rectangle.
     */
    public Complex getNE() {
        return corners[3];
    }


    /**
     * Exchange NW corner.
     * @param c new NW corner.
     * @return rectangle with north west corner c of this rectangle.
     */
    public Rectangle exchangeNW(Complex c) {
        Complex d = getSE();
        Complex sw = new Complex(c.factory(), c.getRe(), d.getIm());
        Complex ne = new Complex(c.factory(), d.getRe(), c.getIm());
        return new Rectangle(c, sw, d, ne);
    }


    /**
     * Exchange SW corner.
     * @param c new SW corner.
     * @return rectangle with south west corner c of this rectangle.
     */
    public Rectangle exchangeSW(Complex c) {
        Complex d = getNE();
        Complex nw = new Complex(c.factory(), c.getRe(), d.getIm());
        Complex se = new Complex(c.factory(), d.getRe(), c.getIm());
        return new Rectangle(nw, c, se, d);
    }


    /**
     * Exchange SE corner.
     * @param c new SE corner.
     * @return rectangle with south east corner c of this rectangle.
     */
    public Rectangle exchangeSE(Complex c) {
        Complex d = getNW();
        Complex sw = new Complex(c.factory(), d.getRe(), c.getIm());
        Complex ne = new Complex(c.factory(), c.getRe(), d.getIm());
        return new Rectangle(d, sw, c, ne);
    }


    /**
     * Exchange NE corner.
     * @param c new NE corner.
     * @return rectangle with north east corner c of this rectangle.
     */
    public Rectangle exchangeNE(Complex c) {
        Complex d = getSW();
        Complex nw = new Complex(c.factory(), d.getRe(), c.getIm());
        Complex se = new Complex(c.factory(), c.getRe(), d.getIm());
        return new Rectangle(nw, d, se, c);
    }


    /**
     * Contains a point.
     * @param c point.
     * @return true if c is contained in this rectangle, else false.
     */
    public boolean contains(Complex c) {
        Complex ll = getSW();
        Complex ur = getNE(); // ?? Fix ?? getSW();
        C cre = c.getRe();
        C cim = c.getIm();
        return    cre.compareTo(ll.getRe()) >= 0 && cim.compareTo(ll.getIm()) >= 0
               && cre.compareTo(ur.getRe()) <= 0 && cim.compareTo(ur.getIm()) <= 0;
    }


    /**
     * Contains a rectangle.
     * @param r rectangle.
     * @return true if r is contained in this rectangle, else false.
     */
    public boolean contains(Rectangle r) {
        return contains(r.getSW()) && contains(r.getNE()); // && contains(r.getSE()) && contains(r.getNW())
    }


    /**
     * Random point of recatangle.
     * @return a random point contained in this rectangle.
     */
    public Complex randomPoint() {
        Complex sw = getSW();
        Complex se = getSE();
        Complex nw = getNW();
        Complex r = sw.factory().random(13);
        C dr = se.getRe().subtract(sw.getRe()); // >= 0
        C di = nw.getIm().subtract(sw.getIm()); // >= 0
        C rr = r.getRe().abs();
        C ri = r.getIm().abs();
        C one = ((RingFactory) dr.factory()).getONE();
        if (!rr.isZERO()) {
            if (rr.compareTo(one) > 0) {
                rr = rr.inverse();
            }
        }
        if (!ri.isZERO()) {
            if (ri.compareTo(one) > 0) {
                ri = ri.inverse();
            }
        }
        // 0 <= rr, ri <= 1
        rr = rr.multiply(dr);
        ri = ri.multiply(di);
        Complex rp = new Complex(sw.factory(), rr, ri);
        //System.out.println("rp = " + rp);
        rp = sw.sum(rp);
        return rp;
    }


    /**
     * Copy this.
     * @return a copy of this.
     */
    public Rectangle copy() {
        return new Rectangle(corners);
    }


    /**
     * Comparison with any other object.
     * @see java.lang.Object#equals(java.lang.Object)
     */
    @Override
    @SuppressWarnings("unchecked")
    public boolean equals(Object b) {
        if (!(b instanceof Rectangle)) {
            return false;
        }
        Rectangle a = null;
        try {
            a = (Rectangle) b;
        } catch (ClassCastException e) {
        }
        for (int i = 0; i < 4; i++) {
            if (!corners[i].equals(a.corners[i])) {
                return false;
            }
        }
        return true;
    }


    /**
     * Hash code for this Rectangle.
     * @see java.lang.Object#hashCode()
     */
    @Override
    public int hashCode() {
        int hc = 0;
        for (int i = 0; i < 3; i++) {
            hc += 37 * corners[i].hashCode();
        }
        return 37 * hc + corners[3].hashCode();
    }


    /**
     * Complex center.
     * @return r + i m of the center.
     */
    public Complex getCenter() {
        C r = corners[2].getRe().subtract(corners[1].getRe());
        C m = corners[0].getIm().subtract(corners[1].getIm());
        ElemFactory rf = r.factory();
        C two = rf.fromInteger(2);
        r = r.divide(two);
        m = m.divide(two);
        r = corners[1].getRe().sum(r);
        m = corners[1].getIm().sum(m);
        return new Complex(corners[0].factory(), r, m);
    }


    /**
     * Complex of BigRational approximation of center.
     * @return r + i m as rational approximation of the center.
     */
    public Complex getRationalCenter() {
        Complex cm = getCenter();
        BigRational rs = cm.getRe().getRational();
        BigRational ms = cm.getIm().getRational();
        ComplexRing cf = new ComplexRing(rs.factory());
        Complex c = new Complex(cf, rs, ms);
        return c;
    }


    /**
     * Complex of BigDecimal approximation of center.
     * @return r + i m as decimal approximation of the center.
     */
    public Complex getDecimalCenter() {
        Complex rc = getRationalCenter();
        BigDecimal rd = new BigDecimal(rc.getRe());
        BigDecimal md = new BigDecimal(rc.getIm());
        ComplexRing cf = new ComplexRing(rd.factory());
        Complex c = new Complex(cf, rd, md);
        return c;
    }


    /**
     * Approximation of center.
     * @return r + i m as string of decimal approximation of the center.
     */
    public String centerApprox() {
        Complex c = getDecimalCenter();
        StringBuffer s = new StringBuffer();
        s.append("[ ");
        s.append(c.getRe().toString());
        s.append(" i ");
        s.append(c.getIm().toString());
        s.append(" ]");
        return s.toString();
    }


    /**
     * Length.
     * @return |ne-sw|**2;
     */
    public C length() {
        Complex m = corners[3].subtract(corners[1]);
        return m.norm().getRe();
    }


    /**
     * Rational Length.
     * @return rational(|ne-sw|**2);
     */
    public BigRational rationalLength() {
        //BigRational r = new BigRational(length().toString());
        return length().getRational();
    }


    /**
     * Length real side.
     * @return |re(ne)-re(sw)|;
     */
    public C lengthReal() {
        C m = corners[3].getRe().subtract(corners[1].getRe());
        return m.abs();
    }


    /**
     * Length imaginary side.
     * @return |im(ne)-im(sw)|;
     */
    public C lengthImag() {
        C m = corners[3].getIm().subtract(corners[1].getIm());
        return m.abs();
    }

}