geometry - Rounding Inaccuracies When Combining Areas in Java?

Question

I'm working with Areas in Java.

My test program draws three random triangles and combines them to form one or more polygons. After the Areas are .add()ed together, I use PathIterator to trace the edges.

Sometimes, however, the Area objects will not combine as they should... and as you can see in the last image I posted, extra edges will be drawn.

I think the problem is caused by rounding inaccuracies in Java's Area class (when I debug the test program, the Area shows the gaps before the PathIterator is used), but I don't think Java provides any other way to combine shapes.

Any solutions?

Example code and images:

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.Area;
import java.awt.geom.Line2D;
import java.awt.geom.Path2D;
import java.awt.geom.PathIterator;
import java.util.ArrayList;
import java.util.Random;

import javax.swing.JFrame;

public class AreaTest extends JFrame{
    private static final long serialVersionUID = -2221432546854106311L;


    Area area = new Area();
    ArrayList<Line2D.Double> areaSegments = new ArrayList<Line2D.Double>();

    AreaTest() {
        Path2D.Double triangle = new Path2D.Double();
        Random random = new Random();

        // Draw three random triangles
        for (int i = 0; i < 3; i++) {
            triangle.moveTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
            triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
            triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
            triangle.closePath();
            area.add(new Area(triangle));
        }       

        // Note: we're storing double[] and not Point2D.Double
        ArrayList<double[]> areaPoints = new ArrayList<double[]>();
        double[] coords = new double[6];

        for (PathIterator pi = area.getPathIterator(null); !pi.isDone(); pi.next()) {

            // Because the Area is composed of straight lines
            int type = pi.currentSegment(coords);
            // We record a double array of {segment type, x coord, y coord}
            double[] pathIteratorCoords = {type, coords[0], coords[1]};
            areaPoints.add(pathIteratorCoords);
        }

        double[] start = new double[3]; // To record where each polygon starts
        for (int i = 0; i < areaPoints.size(); i++) {
            // If we're not on the last point, return a line from this point to the next
            double[] currentElement = areaPoints.get(i);

            // We need a default value in case we've reached the end of the ArrayList
            double[] nextElement = {-1, -1, -1};
            if (i < areaPoints.size() - 1) {
                nextElement = areaPoints.get(i + 1);
            }

            // Make the lines
            if (currentElement[0] == PathIterator.SEG_MOVETO) {
                start = currentElement; // Record where the polygon started to close it later
            } 

            if (nextElement[0] == PathIterator.SEG_LINETO) {
                areaSegments.add(
                        new Line2D.Double(
                            currentElement[1], currentElement[2],
                            nextElement[1], nextElement[2]
                        )
                    );
            } else if (nextElement[0] == PathIterator.SEG_CLOSE) {
                areaSegments.add(
                        new Line2D.Double(
                            currentElement[1], currentElement[2],
                            start[1], start[2]
                        )
                    );
            }
        }

        setSize(new Dimension(500, 500));
        setLocationRelativeTo(null); // To center the JFrame on screen
        setDefaultCloseOperation(EXIT_ON_CLOSE);
        setResizable(false);
        setVisible(true);
    }

    public void paint(Graphics g) {
        // Fill the area
        Graphics2D g2d = (Graphics2D) g;
        g.setColor(Color.lightGray);
        g2d.fill(area);

        // Draw the border line by line
        g.setColor(Color.black);
        for (Line2D.Double line : areaSegments) {
            g2d.draw(line);
        }
    }

    public static void main(String[] args) {
        new AreaTest();
    }
}

A successful case:

A failing case:

Answer 1

Here:

    for (int i = 0; i < 3; i++) {
        triangle.moveTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.closePath();
        area.add(new Area(triangle));
    }       

you are adding in fact 1 triangle in the first loop 2 triangles in the second loop 3 triangles in the third loop

This is where your inaccuracies come from. Try this and see if your problem still persists.

    for (int i = 0; i < 3; i++) {
        triangle.moveTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.lineTo(random.nextInt(400) + 50, random.nextInt(400) + 50);
        triangle.closePath();
        area.add(new Area(triangle));
        triangle.reset();
    }    

Note the path reset after each loop.

EDIT: to explain more where the inaccuracies come from here the three paths you try to combine. Which makes it obvious where errors might arise.