Making clickable hex grids

I try to implement MouseListener by using
public class HexBoard extends Frame implements MouseListenerbut the error message says I need to define the class as a abstract class. After trying that, i still get a error message in main says my class constructor is wrong. can anyone here help me please
import java.awt.*;
import java.awt.event.*;
public class HexBoard extends Frame {
    public static int board_size = 7;
    public static int width = 980;
    public static int height = 600;
    private static int cellSize = width / (board_size + 20);
    public static int radius = (cellSize + cellSize / 4) / 2;
    public static int center_x = width / 2 - radius / 4;
    public static int center_y = (height - radius) / 2;
    public static double[][] grids;
    public HexBoard() {
        grid();
        this.setSize(980, 600);
        this.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent e) {
                System.exit(0);
    public void init() {
        grid();
    //addMouseListener(this);
    private void drawNeck(Graphics g, double x, double y, double r, int n, boolean filled) {
        Polygon p = new Polygon();
        for (int i = 0; i < n; i++) {
            p.addPoint((int) (x + r * Math.cos(i * 2 * Math.PI / n)),
                    (int) (y + r * Math.sin(i * 2 * Math.PI / n)));
        if (filled == true) {
            g.fillPolygon(p);
        } else {
            g.drawPolygon(p);
//Draws a n-Eck polygon with the given parameter
    public void drawNeck(Graphics g, double x, double y, double r, int n) {
        drawNeck(g, x, y, r, n, false);
//Draws a filled n-Eck polygon with the given parameter
    public void fillNeck(Graphics g, double x, double y, double r, int n) {
        drawNeck(g, x, y, r, n, true);
    //Draws oval
    public void draw_oval(Graphics g, double x, double y) {
        x = x - radius * Math.sqrt(2) * 0.5;
        y = y - radius * Math.sqrt(2) * 0.5;
        int x_value = (int) x;
        int y_value = (int) y;
        double r = radius * 1.5;
        int rr = (int) r;
        g.drawOval(x_value, y_value, rr, rr);
    //Draws oval
    public void draw_filloval(Graphics g, double x, double y) {
        x = x - radius * Math.sqrt(2) * 0.5;
        y = y - radius * Math.sqrt(2) * 0.5;
        int x_value = (int) x;
        int y_value = (int) y;
        double r = radius * 1.5;
        int rr = (int) r;
        g.fillOval(x_value, y_value, rr, rr);
//here the paint method which needs to be modificated
    public void paint(Graphics g) {
        for (int i = 0; i < board_size * board_size; i++) {
            //draw_oval(g, grids[0], grids[i][1]);
//draw_filloval(g, grids[i][0], grids[i][1]);
drawNeck(g, grids[i][0], grids[i][1], radius, 6);
// find the center of hexagon grids
public void grid() {
int count = 0;
grids = new double[board_size * board_size][2];
grids[0][1] = center_y;
if (board_size % 2 != 0) {
grids[0][0] = center_x - radius * (board_size + num_odd(board_size) - 1);
} else if (board_size % 2 == 0) {
System.out.printf("even");
grids[0][0] = center_x - radius * (board_size + num_even(board_size) - 1) + radius / 2;
for (int i = 1; i < board_size * board_size; i++) {
count = count + 1;
if (count == board_size) {
count = 0;
grids[i][0] = grids[i - board_size][0] + radius + radius / 2;
grids[i][1] = grids[i - board_size][1] - radius * Math.sqrt(3) * 0.5;
} else {
grids[i][0] = grids[i - 1][0] + radius + radius / 2;
grids[i][1] = grids[i - 1][1] + radius * Math.sqrt(3) * 0.5;
// finds the number of odd numbers smaller than a bigger odd number
public static int num_odd(int size) {
int[] temp = new int[board_size];
int num_odd = 0;
int count = 0;
for (int i = 0; i < size; i++) {
temp[i] = count;
if (temp[i] % 2 != 0) {
num_odd = num_odd + 1;
count = count + 1;
return num_odd;
// finds the number of even numbers smaller than a bigger even number
public static int num_even(int size) {
int[] temp = new int[board_size];
int num_even = 0;
int count = 0;
for (int i = 0; i < size; i++) {
temp[i] = count;
if (temp[i] % 2 == 0) {
num_even = num_even + 1;
count = count + 1;
System.out.printf("dd " + num_even);
return num_even;
public void changeSize(int size) {
board_size = size;
repaint();
public void mouseReleased(MouseEvent e) {
public static void main(String args[]) {
HexBoard hex = new HexBoard();
hex.setSize(width, height);
hex.setVisible(true);
}Edited by: gamewell on Apr 22, 2008 12:16 PM
Edited by: gamewell on Apr 22, 2008 12:17 PM
Edited by: gamewell on Apr 22, 2008 12:18 PM

well, i didn't build the tile marix in the end. Instead, I calculated Euclidean distance between the hex grids center and a mouse Cursor point using nearest neighebor algorithm.
    public int CursorToGrid (int x, int y) {
        int grid_index = -1;
        double temp = Integer.MAX_VALUE;
        double distance[] = new double [board_size*board_size];
        // find the nearst neighbor using Euclidean distance
        for (int i = 0; i < board_size * board_size; i++) {
            distance[i] = Math.sqrt(Math.pow(grids[0]-x,2)+Math.pow(grids[i][1]-y,2));
System.out.println(distance[i]);
if (distance[i] < temp) {
temp = distance[i];
grid_index = i;
// check if a click outsite the hex map
if ( distance[grid_index] > radius) {
grid_index = 10000;
System.out.println("the grid " + grid_index);
return grid_index;
works:D

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GJ;AKLDFJG wrote:
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I used the last days and tried several things. I think now I have a quite good working solution (just one bug remains) and it is very performant. To give others a chance to see what I have done I post the source code of the main class (a canvas drawing and implementing scrolling) here. As soon as the sourceforge project is accepted, I will publish the whole sources at there. Enjoy. And if you have some idea for my last bug in getElementAtPixel(Point), then please tell me.
package internetrail.graphics.hexgrid;
import java.awt.Canvas;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Image;
import java.awt.Point;
import java.awt.Polygon;
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import java.awt.event.ComponentListener;
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import java.awt.image.BufferedImage;
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     public final int CONST_Heightdouble;
     /** <p>The steepness of a side of the hex grid element (calculated for the upper left arc).</p> */
     public final double CONST_Steepness;
     /** <p>The model of this hex grid </p> */
     private final IHexGridModel m_Model;
     /** <p>A cache for already created images of the hex map.</p> */
     private final Map<Point, Image> m_Cache = new WeakHashMap<Point, Image>();
     /** <p>The graphical area to draw the selection ring around a hex element.</p> */
     private final Area m_SelectionRing;
     /** <p>The image of the selection ring around a hex element.</p> */
     private final BufferedImage m_SelectionRingImage;
     /** <p>The current position of the hex grid in pixels (top left visible corner).</p> */
     private Point m_ScrollPosition = new Point(0, 0);
     /** <p>Flag to define if a grid is shown ({@code true}) or not ({@code false}).</p> */
     private boolean m_ShowGrid = true;
     /** <p>Flag to define if the selected hex grid element should be highlighted ({@code true}) or not ({@code false}).</p> */
     private boolean m_ShowSelected = true;
     /** <p>The offset of hex grid elements shown on the screen, measured in hex grid elements.</p> */
     private Point m_CurrentOffset = new Point(0, 0);
     /** <p>The offset of the image shown on the screen, measured in pixels.</p> */
     private Point m_PixelOffset = new Point(0, 0);
     /** <p>The index of the currently selected hex grid element.</p> */
     private Point m_CurrentSelected = new Point(0, 0);
     /** <p>The width of a buffered pre-calculated image in pixel.</p> */
     private int m_ImageWidth;
     /** <p>The height of a buffered pre-calculated image in pixel.</p> */
     private int m_ImageHeight;
     /** <p>The maximum number of columns of hex grid elements to be shown at once on the screen.</p> */
     private int m_MaxColumn;
     /** <p>The maximum number of rows of hex grid elements to be shown at once on the screen.</p> */
     private int m_MaxRow;
     /** <p>Create a new hex grid view.</p>
      * <p>The hex grid view is bound to a {@link IHexGridModel} and registers at
      * that model to listen for {@link IHexGridElement} updates.</p>
      * @param Model The model backing this view.
     public CHexGridView(IHexGridModel Model) {
          // Set the model
          m_Model = Model;
          CONST_Width = m_Model.getElementsWidth();
          CONST_Height = m_Model.getElementsHeight();
          CONST_Width1fourth = CONST_Width/4;
          CONST_Width3fourth = CONST_Width*3/4;
          CONST_Width1dot5 = CONST_Width*3/2;
          CONST_Heighthalf = CONST_Height/2;
          CONST_Widthquad = CONST_Width*4;
          CONST_Heightdouble = CONST_Height*2;
          CONST_Steepness = (double)CONST_Heighthalf / CONST_Width1fourth;
          m_ImageWidth = getSize().width+CONST_Widthquad;
          m_ImageHeight = getSize().height+CONST_Heightdouble;
          m_MaxColumn = m_ImageWidth / CONST_Width3fourth;
          m_MaxRow = m_ImageHeight / CONST_Height;
          // Register this canvas for various notifications
          m_Model.addElementListener(this);
          addComponentListener(this);
          // Create the selection ring to highlight hex grid elements
          m_SelectionRing = new Area(new Polygon(new int[]{-1, CONST_Width1fourth-1, CONST_Width3fourth+1, CONST_Width+1, CONST_Width3fourth+1, CONST_Width1fourth-1}, new int[]{CONST_Heighthalf, -1, -1, CONST_Heighthalf, CONST_Height+1, CONST_Height+1}, 6));
          m_SelectionRing.subtract(new Area(new Polygon(new int[]{2, CONST_Width1fourth+2, CONST_Width3fourth-2, CONST_Width-2, CONST_Width3fourth-2, CONST_Width1fourth+2}, new int[]{CONST_Heighthalf, 2, 2, CONST_Heighthalf, CONST_Height-2, CONST_Height-2}, 6)));
          m_SelectionRingImage = new BufferedImage(CONST_Width, CONST_Height, BufferedImage.TYPE_INT_ARGB);
          Graphics2D g = m_SelectionRingImage.createGraphics();
          g.setColor(Color.WHITE);
          g.fill(m_SelectionRing);
     @Override public synchronized void paint(Graphics g2) {
          // Caculate the offset of indexes to show
          int offsetX = 2 * (m_ScrollPosition.x / CONST_Width1dot5) - 2;
          int offsetY = (int)(Math.ceil(m_ScrollPosition.y / CONST_Height) - 1);
          m_CurrentOffset = new Point(offsetX, offsetY);
          // Check if the image is in the cache
          Image drawing = m_Cache.get(m_CurrentOffset);
          if (drawing == null) {
               // The image is not cached, so draw it
               drawing = new BufferedImage(m_ImageWidth, m_ImageHeight, BufferedImage.TYPE_INT_ARGB);
               Graphics2D g = ((BufferedImage)drawing).createGraphics();
               // Draw background
               g.setColor(Color.BLACK);
               g.fillRect(0, 0, m_ImageWidth, m_ImageHeight);
               // Draw the hex grid
               for (int column = 0; column <= m_MaxColumn; column += 2) {
                    for (int row = 0; row <= m_MaxRow; row++) {
                         // Draw even column
                         IHexGridElement element = m_Model.getElementAt(offsetX + column, offsetY + row);
                         if (element != null) { g.drawImage(element.getImage(m_ShowGrid), (int)(column*(CONST_Width3fourth-0.5)), CONST_Height*row, null); }
                         // Draw odd column
                         element = m_Model.getElementAt(offsetX + column+1, offsetY + row);
                         if (element!= null) { g.drawImage(element.getImage(m_ShowGrid), (int)(column*(CONST_Width3fourth-0.5)+CONST_Width3fourth), CONST_Heighthalf*(row*2+1), null); }
               // Put the image into the cache
               m_Cache.put(m_CurrentOffset, drawing);
          // Calculate the position of the image to show
          offsetX = CONST_Width1dot5 + (m_ScrollPosition.x % CONST_Width1dot5);
          offsetY = CONST_Height + (m_ScrollPosition.y % CONST_Height);
          m_PixelOffset = new Point(offsetX, offsetY);
          g2.drawImage(drawing, -offsetX, -offsetY, null);
          // If the selected element should he highlighted, then do so
          if (m_ShowSelected) {
               // Check if the selected element is on screen
               if (isElementOnScreen(m_CurrentSelected)) {
                    // Correct vertical offset for odd columns
                    if ((m_CurrentSelected.x % 2 == 1)) { offsetY -= CONST_Heighthalf; }
                    // Draw the selection circle
                    g2.drawImage(m_SelectionRingImage, (m_CurrentSelected.x - m_CurrentOffset.x) * CONST_Width3fourth - offsetX - ((m_CurrentSelected.x + 1) / 2), (m_CurrentSelected.y - m_CurrentOffset.y) * CONST_Height - offsetY, null);
     @Override public synchronized void update(Graphics g) { paint(g); }
     public synchronized void componentResized(ComponentEvent e) {
          // Upon resizing of the component, adjust several pre-calculated values
          m_ImageWidth = getSize().width+CONST_Widthquad;
          m_ImageHeight = getSize().height+CONST_Heightdouble;
          m_MaxColumn = m_ImageWidth / CONST_Width3fourth;
          m_MaxRow = m_ImageHeight / CONST_Height;
          // And flush the cache
          m_Cache.clear();
     public void componentMoved(ComponentEvent e) { /* do nothing */ }
     public void componentShown(ComponentEvent e) { /* do nothing */ }
     public void componentHidden(ComponentEvent e) { /* do nothing */ }
     public synchronized void elementUpdated(IHexGridElement Element) {
          // Clear cache where the element may be contained at
          for (Point p : m_Cache.keySet()) { if (isElementInScope(Element.getIndex(), p, new Point(p.x + m_MaxColumn, p.y + m_MaxRow))) { m_Cache.remove(p); } }
          // Update the currently shown image if the update element is shown, too
          if (isElementOnScreen(Element.getIndex())) { repaint(); }
     /** <p>Returns the model visualized by this grid view.</p>
      * @return The model visualized by this grid view.
     public IHexGridModel getModel() { return m_Model; }
     /** <p>Returns the current selected hex grid element.</p>
      * @return The current selected hex grid element.
     public IHexGridElement getSelected() { return m_Model.getElementAt(m_CurrentSelected.x, m_CurrentSelected.y); }
     /** <p>Sets the current selected hex grid element by its index.</p>
      * <p>If the selected hex grid element should be highlighted and is currently
      * shown on the screen, then this method will {@link #repaint() redraw} this
      * component automatically.</p>
      * @param Index The index of the hex grid element to become the selected one.
      * @throws IllegalArgumentException If the index refers to a non-existing hex
      * grid element.
     public synchronized void setSelected(Point Index) throws IllegalArgumentException {
          // Check that the index is valid
          if ((Index.x < 0) || (Index.y < 0) || (Index.x > m_Model.getXElements()) || (Index.y > m_Model.getYElements())) { throw new IllegalArgumentException("There is no hex grid element with such index."); }
          m_CurrentSelected = Index;
          // If the element is on screen and should be highlighted, then repaint
          if (m_ShowSelected && isElementOnScreen(m_CurrentSelected)) { repaint(); }
     /** <p>Moves the visible elements to the left by the number of pixels.</p>
      * <p>To move the visible elements to the left by one hex grid element, pass
      * {@link #CONST_Width3fourth} as the parameter. The component will
      * automatically {@link #repaint()}.</p>
      * @param Pixels The number of pixels to move to the left.
      * @return The number of pixels moved to the left. This is always between 0
      * and {@code abs(Pixels)}.
     public synchronized int moveLeft(int Pixels) {
          int delta = m_ScrollPosition.x - Math.max(0, m_ScrollPosition.x - Math.max(0, Pixels));
          if (delta != 0) {
               m_ScrollPosition.x -= delta;
               repaint();
          return delta;
     /** <p>Moves the visible elements up by the number of pixels.</p>
      * <p>To move the visible elements up by one hex grid element, pass {@link
      * #CONST_Height} as the parameter. The component will automatically {@link
      * #repaint()}.</p>
      * @param Pixels The number of pixels to move up.
      * @return The number of pixels moved up. This is always between 0 and {@code
      * abs(Pixels)}.
     public synchronized int moveUp(int Pixels) {
          int delta = m_ScrollPosition.y - Math.max(0, m_ScrollPosition.y - Math.max(0, Pixels));
          if (delta != 0) {
               m_ScrollPosition.y -= delta;
               repaint();
          return delta;
     /** <p>Moves the visible elements to the right by the number of pixels.</p>
      * <p>To move the visible elements to the right by one hex grid element, pass
      * {@link #CONST_Width3fourth} as the parameter. The component will
      * automatically {@link #repaint()}.</p>
      * @param Pixels The number of pixels to move to the right.
      * @return The number of pixels moved to the right. This is always between 0
      * and {@code abs(Pixels)}.
     public synchronized int moveRight(int Pixels) {
          int delta = Math.min(m_Model.getXElements() * CONST_Width3fourth + CONST_Width1fourth - getSize().width, m_ScrollPosition.x + Math.max(0, Pixels)) - m_ScrollPosition.x;
          if (delta != 0) {
               m_ScrollPosition.x += delta;
               repaint();
          return delta;
     /** <p>Moves the visible elements down by the number of pixels.</p>
      * <p>To move the visible elements down by one hex grid element, pass {@link
      * #CONST_Height} as the parameter. The component will automatically {@link
      * #repaint()}.</p>
      * @param Pixels The number of pixels to move down.
      * @return The number of pixels moved down. This is always between 0 and
      * {@code abs(Pixels)}.
     public synchronized int moveDown(int Pixels) {
          int delta = Math.min(m_Model.getYElements() * CONST_Height + CONST_Heighthalf - getSize().height, m_ScrollPosition.y + Math.max(0, Pixels)) - m_ScrollPosition.y;
          if (delta != 0) {
               m_ScrollPosition.y += delta;
               repaint();
          return delta;
     /** <p>Checks if the hex grid element of the given index is currently
      * displayed on the screen (even just one pixel).</p>
      * <p>The intention of this method is to check if a {@link #repaint()} is
      * necessary or not.</p>
      * @param ElementIndex The index of the element to check.
      * @return {@code true} if the hex grid element of the given index is
      * displayed on the screen, {@code false} if not.
     public synchronized boolean isElementOnScreen(Point ElementIndex) { return isElementInScope(ElementIndex, m_CurrentOffset, new Point(m_CurrentOffset.x + m_MaxColumn, m_CurrentOffset.y + m_MaxRow)); }
     /** <p>Checks if the hex grid element of the given index is within the given
      * indexes.</p>
      * <p>The intention of this method is to check if a {@link #repaint()} is
      * necessary or not.</p>
      * @param ElementIndex The index of the element to check.
      * @param ReferenceIndexLeftTop The left top index of the area to check.
      * @param ReferenceIndexRightBottom The right bottom index of the area to check.
      * @return {@code true} if the hex grid element of the given index is within
      * the given area, {@code false} if not.
     public synchronized boolean isElementInScope(Point ElementIndex, Point ReferenceIndexLeftTop, Point ReferenceIndexRightBottom) { if ((ElementIndex.x >= ReferenceIndexLeftTop.x) && (ElementIndex.x <= ReferenceIndexRightBottom.x) && (ElementIndex.y >= ReferenceIndexLeftTop.y) && (ElementIndex.y <= (ReferenceIndexRightBottom.y))) { return true; } else { return false; } }
     /** <p>Return the {@link IHexGridElement hex grid element} shown at the given
      * pixel on the screen.</p>
      * <p><b>Remark: There seems to be a bug in retrieving the proper element,
      * propably caused by rounding errors and unprecise pixel calculations.</p>
      * @param P The pixel on the screen.
      * @return The {@link IHexGridElement hex grid element} shown at the pixel.
     public synchronized IHexGridElement getElementAtPixel(Point P) {
          // @FIXME Here seems to be some bugs remaining
          int dummy = 0; // Variable for warning to indicate that there is something to do :)
          // Calculate the pixel on the image, not on the screen
          int px = P.x + m_PixelOffset.x;
          int py = P.y + m_PixelOffset.y;
          // Determine the x-index of the column (is maybe decreased by one)
          int x = px / CONST_Width3fourth + m_CurrentOffset.x;
          // If the column is odd, then shift the y-pixel by half element height
          if ((x % 2) == 1) { py -= CONST_Heighthalf; }
          // Determine the y-index of the row (is maybe decreased by one)
          int y = py / CONST_Height + m_CurrentOffset.y;
          // Normative coordinates to a single element
          px -= (x - m_CurrentOffset.x) * CONST_Width3fourth;
          py -= (y - m_CurrentOffset.y) * CONST_Height;
          // Check if the normative pixel is in the first quarter of a column
          if (px < CONST_Width1fourth) {
               // Adjustments to the index may be necessary
               if (py < CONST_Heighthalf) {
                    // We are in the upper half of a hex-element
                    double ty = CONST_Heighthalf - CONST_Steepness * px;
                    if (py < ty) { x--; }
               } else {
                    // We are in the lower half of a hex-element
                    double ty = CONST_Heighthalf + CONST_Steepness * px;
                    if (py > ty) {
                         x--;
                         y++;
          return m_Model.getElementAt(x, y);
}Ah, just to give you some idea: I use this component to visualize a hex grid map with more than 1 million grid elements. And it works, really fast, and requires less than 10 MByte of memory.

Importing text file into 2D char array

Hey folks. I've aged a few years trying to figure this project out. Im trying to make a crossword puzzle and am having problems importing the answer letters into a 2D array of 15*15. The text file would look something like this:
LAPSE TAP RAH
AVAIL OLE ODE
BARGE PARADOX
etc
I have JTextFields that the user will answer and a button the user can press to see if the answers are right by comparing the 2D array answer with what the user inputted.-the user input would be scanned and put into a 2D array also.
How should i go about inserting each letter into an array? The spaces i would later need to make code to grey out the text field. This is what i have so far. Forgive me if its sloppy.
     class gridPanel extends JPanel
          //----Setting Grid variables
          private static final int ROWS = 15;
          private static final int COLS = 15;
          String[] letters = { "A", "B", "C", "D", "E" };// To test entering strings into array
           gridPanel()
             this.setBackground(Color.BLUE);
             //.......Making my JTextField grid for user input
             JTextField[][] grid = new JTextField[ROWS][COLS];
             for(int ROWS = 0; ROWS<grid.length; ROWS++)
                 for(int COLS = 0; COLS<grid.length; COLS++)
                     grid[ROWS][COLS] = new JTextField(1);
                     add(grid[ROWS][COLS]);
                 //grid[ROWS][COLS].setText("" + letters[0]);
             String an = null;
             StringTokenizer tokenizer = null;
             Character[][] answer = new Character[ROWS][COLS];
          try{
             BufferedReader bufAns = new BufferedReader( new FileReader("C:\\xwordanswers.txt"));
             for (int rowCurrent = 0; rowCurrent < ROWS; rowCurrent++)
          an = bufAns.readLine();
          tokenizer = new StringTokenizer(an);
          for (int colCurrent = 0; colCurrent < COLS; colCurrent++) {
          char currentValue = tokenizer.nextToken().charAt(0);//Needs to be changed to reflect each letter
                    answer[rowCurrent][colCurrent] = currentValue;
                System.out.println(currentValue);
          }catch (IOException ioex)
                    System.err.println(ioex);
                    System.exit(1);
        }//xword graphics end
      This obviously prints the first char of each word, it also gives me an "Exception in thread "main" java.util.NoSuchElementException" error for some reason.
Any help is greatly appreciated.
John

If the file format is stored as follows:
APPLE
L A
PARSE
N E
PEAR then we can parse this into a 2D char array:
char[][] readMap(String fileName) {
    char[][] ret = new char[ROWS][COLS];
    FileInputStream FIS = new FIleInputStream(fileName);
    int i, j;
    for(i = 0; i < ROWS; i++)
        for(j = 0; j < COLS; j++)
            ret[i][j] = FIS.read();
    FIS.close();
    return ret;
}Then you can use the resulting 2D char array in your answer checking mechanism.
Hope this helps~
Alex Lam S.L.

How to add one column for entry in the TLB screen?

Hi all,
Does anybody know how to add a customised column for free text in the TLB header screen? The reason is user needs to add ship or container no. This info will be later on interfaced via CIF exit to R/3.
I think many of you have the same requirement.
Thanks heaps!

Thanks Digambar,
Can you help to work out more detail on how to customize the code in the TLB screen?
Are you thinking of adding one field in the table and making the ALV grid control editable? If you have any reference doc/link to do it, it would great!
Cheers,

Making clickable hex grids

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