Efficient algorithm

Question

Give me an efficient algorithm to find out the points in the arc.

Answer 1

import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.text.NumberFormat;
import javax.swing.*;
import javax.swing.event.MouseInputAdapter;
public class ArcPoints extends JPanel
    Arc2D arc;
    Line2D radial;
    Point2D curveLoc;
    boolean showConstruction;
    JLabel label;
    NumberFormat nf;
    public ArcPoints()
        showConstruction = false;
        nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(1);
        Pointer pointer = new Pointer(this);
        addMouseListener(pointer);
        addMouseMotionListener(pointer);
    protected void paintComponent(Graphics g)
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                            RenderingHints.VALUE_ANTIALIAS_ON);
        if(arc == null)
            initArc();
        g2.draw(arc);
        g2.setPaint(Color.blue);
        g2.draw(radial);
        drawPoint(g2, Color.red, curveLoc.getX(), curveLoc.getY());
        if(showConstruction)
            showConstructionMarkers(g2);
    protected void setRadial(Point p, double theta)
        double cx = arc.getCenterX();
        double cy = arc.getCenterY();
        double x = cx + (arc.getWidth()/2)  * Math.cos(theta);
        double y = cy + (arc.getHeight()/2) * Math.sin(theta);
        radial.setLine(cx, cy, x, y);
        curveLoc.setLocation(x, y);
        label.setText("x = " + nf.format(x) + "    y = " + nf.format(y));
        repaint();
    private void initArc()
        double w = getWidth();
        double h = getHeight();
        double x = w/6;
        double y = h/8;
        double width  = w*2/3;
        double height = h*5/8;
        double start  = 0.0;
        double extent = 300.0;
        int type = Arc2D.OPEN;
        arc = new Arc2D.Double(x, y, width, height, start, extent, type);
        radial = new Line2D.Double();
        curveLoc = new Point2D.Double();
    private void showConstructionMarkers(Graphics2D g2)
        g2.setPaint(Color.orange);
        Rectangle2D r = arc.getFrame();
        g2.draw(r);
        g2.setPaint(Color.green.darker());
        double theta = Math.toRadians(arc.getAngleStart() - arc.getAngleExtent());
        g2.draw(getRadialMarker(theta));
        theta = Math.toRadians(arc.getAngleStart());
        g2.draw(getRadialMarker(theta));
    private void drawPoint(Graphics2D g2, Color color, double x, double y)
        g2.setPaint(color);
        g2.fill(new Ellipse2D.Double(x-2, y-2, 4, 4));
    private Line2D getRadialMarker(double theta)
        Rectangle2D r = arc.getFrame();
        double x = r.getCenterX() + (r.getWidth()/2) * Math.cos(theta);
        double y = r.getCenterY() + (r.getHeight()/2) * Math.sin(theta);
        return new Line2D.Double(r.getCenterX(), r.getCenterY(), x, y);
    private JLabel getLabel()
        label = new JLabel("curve x and y", JLabel.CENTER);
        Dimension d = label.getPreferredSize();
        d.height = 25;
        label.setPreferredSize(d);
        return label;
    public static void main(String[] args)
        ArcPoints arcPoints = new ArcPoints();
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(arcPoints);
        f.add(arcPoints.getLabel(), "South");
        f.setSize(400,400);
        f.setLocation(200,200);
        f.setVisible(true);
class Pointer extends MouseInputAdapter
    ArcPoints ap;
    public Pointer(ArcPoints ap)
        this.ap = ap;
    public void mousePressed(MouseEvent e)
        ap.showConstruction = !ap.showConstruction;
        ap.repaint();
    public void mouseMoved(MouseEvent e)
        Point p = e.getPoint();
        // if point is within arc show radial from frame center to arc
        if(ap.arc.contains(p))
            Rectangle2D r = ap.arc.getFrame();
            double dy = p.y - r.getCenterY();
            double dx = p.x - r.getCenterX();
            double theta = Math.atan2(dy, dx);
            double degrees = Math.toDegrees(theta);
            if(degrees < 0.0)
                degrees += 360.0;
            if(containsAngle(degrees))
                ap.setRadial(p, theta);           
     * Arc2D counts angles as increasing counter-clockwise
     * the Math class and the rest of the java.awt.geom
     *     package count angles as increasing clockwise
     * this method tries to bridge the difference
    private boolean containsAngle(double degrees)
        Arc2D arc = ap.arc;
        double start, extend, end;
        double extent = arc.getAngleExtent();
        if(extent > 0.0)
            start = -arc.getAngleExtent();
            end = start + arc.getAngleExtent();
            degrees -= 360.0;
        else
            start = arc.getAngleStart();
            end = start - arc.getAngleExtent();
        return start <= degrees && degrees <= end;
}