Tutorial on Gedit This is a structured tutorial demonstrating the features of the GEdit system. The tutorial guides the designer through three structured examples. Background GEdit is a program that allows a designer to construct shape grammar rules using 2-d shapes. A labeled shape is a finite arrangement of finite lines of non-zero length together with a finite set of labeled points. Each line consists of two endpoints which do not coincide. The shapes are composed of lines and labels. the first and third examples use unlabeled shapes, while the second uses labeled shapes to define the rules. A rule consists of a left hand side (the pattern) and a right hand side (the replacement). Each rule specifies a possible replacement operation. Whenever a Euclidean transformation makes the pattern part of a given shape U, the rule can be applied, replacing the transformed pattern by the replacement shape suitably transformed. The shape grammar web page at www.shapegrammar.org contains more detailed information on shape grammars including articles, bibliographies, and the use of shape grammars, For a more detailed overview of the GEdit system and some of the ideas of shape grammars see the document paper.pdf (the pdf format of the document) that is accessible at the same level as this document. Launching the Program First, launch the application with a GEdit file. Double-click on the file abcd in the Examples folder. This will launch the GEdit program and read the grammar in the abcd file.
The screen after double-clicking on the file abcd in the Examples folder The abcd window is a grammar window containing several rules; the Current Shape window is empty. The menubar after launching GEdit. To see the current shape, go to the pulldown menu in the abcd window and pulldown the menu starting with Possible in it and select Current Shape. You can also select Current Shape from the Views menu.
The rule strip at the top of the abcd window. Each rule appears in a separate cell. There are four rules displayed in the rule strip. Rules with both a pattern and replacement shape contain an orange marker on the left and right hand sides of the rule serving as a reference point. Only the first two rules have both pattern and replacement shapes; the last two rules erase the shape. The first rule replaces a square by two squares arranged so that one corresponds to the pattern and the other to an identical square arranged so that its bottom left hand corner is at the center of the other square. The second rule reverses the roles of the pattern and replacement, effectively erasing one of two squares arranged in that way. Select the first rule in the rule strip by holding the mouse button down. Continue holding the button down, while keeping the mouse relatively steady. A marking menu will pop up. The menu items are arranged in a circular pattern around a circular, central hole. The menu items appear in black lettering on a white background. There are four menu items: Inspect, Remove, Copy and Rules. The first last two items have a small shadowed circle to their left indicating that they are menus. When a menu item is selected it will appear as white lettering on a black background. To avoid making a selection return to the central hole and release the mouse button. Position the mouse over the replacement shape (left hand side) of the first rule. To select the Inspect menu item, continue holding the mouse button down and move until the Inspect menu item is highlighted (becomes white lettering on a black ground). Then release the mouse button. The menu will disappear and the action will be performed.
The Shapes window will appear, allowing you to examine the replacement shape of the first rule at the default 1x scale. You can increase or decrease the scale by invoking a marking menu inside the window. Experiment with the various options: Enlarge, Reduce, and Normal. Notice that Normal is dimmed since the view is already at normal (1x) scale. You can enlarge or reduce the shape by a factor of 8 (1x, 2x, 4x, 8x,1/2x, 1/4x, and 1/8x) Select the Copy submenu, by moving the mouse while keeping the button pressed until the Copy item is highlighted, pause for a moment as soon as it is highlighted while keeping the mouse button pressed. A new menu will appear. Continue keeping the button pressed, select the Rule menu item by keeping the mouse button pressed down, moving the mouse until the item is highlighted, then release the button. To avoid making a Copy selection, return to the center of the Copy menu while keeping the mouse button depressed. Release the mouse button, the menu will disappear and the previous menu will appear. To avoid making any selection, return to the center of the original menu and release the mouse button.
A copy of the rule will appear in the working rule area at the bottom of the abcd window. There are separate menus for the two shaded regions and for the white region in between. In the white region near the arrow, invoke the marking menu. Select the Animate menu item. The Alternatives window appears showing the four ways in which the rule allows the pattern a square to be replaced. The gray lines indicate portions of the original lines retained by the rule, blue lines the added line segments, and orange lines the deleted portions of line segments. From the rule strip, select the replacement shape of the first rule and use the marking menu to select first the Copy submenu and then to select the Current shape menu item. The system will copy the replacement shape into the current shape window. In the current shape window invoke the Rules submenu and select the Possibilities menu item. The animate item animates the rule, retract retracts the rule (in this case it would return the current shape to its previous empty state).
While your system may not show this possibility as the first one, it will appear as one of them. There are 12 possibilities in total including several that leave the shape unchanged. The current shape window allows you to examine them one at a time. To go to the next shape, use the marking menu to select Next or press the right arrow or page down keys; to go the previous shape, use the marking menu to select Previous, or press the left arrow or page up keys. To go to the first shape, press the Home key; to go to the last shape press the End key. You can also examine the possibilities in an array. To view the possibilities window, either select possible from the pulldown menu on the abcd window, or select Possibilities from the views menu. The possibilities window allows you to see more possibilities at the same time. You can increase or decrease the size of the cells by using a marking menu to
select Reduce or Enlarge, trading screen space for detail. To select a particular rule application, invoke the marking menu over the cell containing the desired shape and from the Rules submenu choose select. The current shape window reflect the fact that the rule has changed the current shape If you want to find where the pattern appears in the shape from the Rules menu in the menubar, select Show Pattern. The menu item will be checked when it is on and otherwise will be unchecked. With Show Pattern in effect, selecting Rules and then Possibilities shows the three instances of the square in the shape. Choosing Select from the Rules submenu will now have the effect of selecting the pattern, and displaying the four resulting shapes. Choosing select again will make that shape the current shape.
A Grammar for Brick Patterns Next open another grammar containing two rules for generating brick patterns. The rules uses labels to restrict the application of a rule. From the Files menu in the menubar select Open and then open the brick file in the list. Any of the files with orange squares in their icons are GEdit files that correspond to grammars. You used the file abcd in the previous example. More examples may be added to the list This grammar contains two rules, one that creates an infinite pattern and another that ultimately creates one of four shapes. The two rules both use a single label a circle with an empty fill pattern. The figure below shows an enlarged version of a label filled with a pattern. There is one point associated with the label the point p corresponding to the top left hand corner of the rectangle. The other four points denote the corners of the bounding rectangle for the circle. Even when the circle becomes an ellipse, the top left corner is still the point associated with the label.
P In both rules the label is placed in the same relative position that it appears in the pattern within the rightmost rectangle in the replacement shape. In many programs this is the perceived location of the circle. How the abcd window appears after copying the first rule to the rule area.
The Alternatives window shows the result of animating the rule. Colors serve to distinguish the changed portions of the shape: gray indicates the retained portion the four lines, orange the deleted portions of the shape the label associated with the pattern, and blue the portions added the three line segments at the right and the label. The Current Shape window after copying the pattern to the current shape. After applying the rule two times, this is the single possibility. The design continues to grow down and to the right.
The current shape window after copying the pattern of the second rule to the current shape. After applying the rule two times, this is the single possibility. The design continues to grow around the central square. Importing Pictures There are two ways to incorporate a rule or shape into the system: copying a picture onto the clipboard and then pasting it into the system or reading an entire file in pict format. In both cases, you must create the picture using a standard application (e.g. MiniCad) with the line and circle tools. The simplest way to demonstrate the feature is to go to the rule area and select either the pattern or replacement shapes.
This is the rule area before the cut. This is the rule area after the cut. To show the contents of the clipboard, go to the Finder and select Show Clipboard from the Edit menu. The contents of the clipboard is displayed after the Show Clipboard commands. The pattern has been transferred to the clipboard. Return to the GEdit program and paste the contents of the clipboard back into the pattern. The rule will now look just as it did just before the cut. Next we will convert a file containing a picture containing a rule. The system can interpret any file that has been saved as a picture. It will place the rule in the rule area at the bottom of the grammar window. Draw the lines using the
line tool and labels using the oval tool. The fill pattern of the circle distinguishes labels, allowing a wide variety of labels. Remember to draw the pattern and replacement shapes together to ensure that the rule will perform as expected. Use the default solid black pattern to draw the lines and the ovals. Select the brick window. From the File menu on the menubar select Convert pict Select the closed.pict file. The rotated.pict file corresponds to the rule in the next example. The rule area after the picture has been interpreted. Next, add the rule to rule strip. Select the rule by clicking on it once (clicking it twice brings up pictures of the pattern and replacement). Press the mouse button down in-between the pattern and replacement, and select Add rule from the marking menu that appears. The rule will disappear from the rule area and then reappear at the end of the rule strip.
The rule strip after moving the rule from the rule area. Animate the rule, using Animate from the Rules submenu. This shows that rule erases the pattern and replaces it with a new shape. The result after applying the rule several times A final example - roundoff errors The final example shows a simple grammar that rotates very simple grammar to rotate a square around its center by 45. From the File menu select Open
and select the Rotated Square file in the Examples folder. The file rotated.pict contains the first rule in the grammar. The grammar demonstrates that the square can be rotated twice in succession to return to its original size and position. The rule strip of the window after opening the rotated square file. The alternatives window shows the result of animating the first rule. The rule effectively rotates the square.
Set the current shape to the third shape in the rule strip by selecting that shape and the choosing the Current shape menu item from the copy menu. Then select the first rule. Next generate the rule possibilities by selecting Possibilities from the Rules menu item. Journey through the alternatives, selecting the following one, by choosing Select from the Rules menu. Choose rule possibilities again (from the rules menu select possibilities) The screen image below shows that the square returns to its original position.. If you select this rule application and then apply the rule again, the system will recognize the lower left square within the blue square and not any of the other
three squares. This suggests that there is a problem with roundoff. The system uses rational transformations to approximate an irrational transformation. The result is a roundoff error that creates the problem just described. Exiting from the Program To exit from the program, select Quit from the File menu The system will then ask you three times to restart the shape computation, once for abcd, once for brick, and once for rotated square. Press Yes each time. Sometimes this message appears. Press Yes.
Press Discard to leave the brick file unchanged.