I. Simple Display Model-No two objects overlap on the display, so it is
	ok to update an object by erasing its old image and displaying its
	new one

    1. XOR can provide a way to quickly draw feedback objects without
       going through the display manager

    2. Many windowing systems provide a way to specify the color with
       which we wish to draw an xor object against a normal background.
       The system then computes the color that needs to be xor'ed to
       achieve the desired color. Formally, if C is the color than
       C = XOR(D,B) and D is the color the system computes.

    3. xor.java illustrates the
       use of xor in java. The below applet shows xor.java in action. You
       should click on the applet to get the two xor'ed red rectangles to
       appear and disappear. Note that the code specifies that an xor'ed
       rectangle should appear red when drawn over a white background. When
       it is drawn over the black and yellow backgrounds, the resulting
       color is unpredictable.

II. More Realistic Model-Objects can overlap on the display A. Problems with simple erase and redraw 1. If you erase an object's old image, it may erase parts of other objects as well 2. If you redraw an object it will appear on top of all other objects--perhaps it should be covered by other objects in its new location B. Need a more sophisticated algorithm which redraws parts of other objects which are erased and draws the object in the proper covering order C. Solutions 1. Redraw all objects using appropriate covering order--too expensive when hundreds or thousands of objects 2. Only redraw damaged parts of screen--must keep data structures that keep track of damaged objects III. Incremental Redisplay A. Rationale-Updating the whole screen when there are hundreds or thousands of objects is too expensive B. Definitions 1. Bounding Box--The small rectangle that encloses a set of objects C. Strategy 1. Keep track of all objects that have a changed visual property, such as position, size, color, or stacking order a. As objects are changed, merge their old position into an "old" bounding box. This bounding box keeps track of the original locations of the changed objects 2. When an update command is issued a. Compute the new bounding box of the changed objects b. For each displayed object, determine whether the displayed object intersects either the new or old bounding box. i. Redraw the objects that intersect either the new or old bounding box in the appropriate stacking order ii. Only redraw the portion of the object that changes--most windowing systems provide a clip region that facilitates redrawing only a portion of the object. 3. Optimization--For composite objects, check the composite object's bounding box before checking its individual children. If the composite object doesn't intersect either of the bounding boxes, then none of its children can, so none of its children must be checked. 4. Algorithm a. Data structures and Variables i. For each window you should maintain the following variables a. objs_changed: The set of objects that have changed b. old_bbox: The bounding box for the changed objects' old positions c. new_bbox: The bounding box for the changed objects' new positions b. Update algorithm -all variables prefixed by self refer to instance variables -if a variable is not prefixed by self then it is a local variable Win::Update() new_bbox = empty old_bbox = self.old_bbox for each obj in self.objs_changed do new_bbox = new_bbox U obj's position for each obj in self.children do if intersect(obj, old_bbox) or intersect(obj, new_bbox) obj.update(old_bbox, new_bbox) self.old_bbox = empty Container::Update(old_bbox, new_bbox) for each obj in self.children do if intersect(obj, old_bbox) or intersect(obj, new_bbox) obj.update(old_bbox, new_bbox) Primitive_Obj::Update(old_bbox, new_bbox) self.draw(old_bbox, new_bbox) c. Notification algorithm Win::notifyChange(obj) self.objs_changed_objs = self.objs_changed U obj self.old_bbox = self.old_bbox U obj's position D. Java Notes 1. Java's repaint method merges bounding boxes so you cannot use an old and a new bounding box--you must change the above update procedure so that it uses a single bounding box instead 2. If you really want to use an old and new bounding box, then call paintImmediately. paintImmediately will immediately queue a paint event rather than aggregating a number of repaint calls and then generating a single paint event. However, you must be careful about calling paintImmediately because if there are several changes to the display, you could end up calling it several times. One scheme that could work with a display manager would be to add a second notification procedure called UpdatesCompleted. UpdatesCompleted would call paintImmediately twice, once with the old bounding box and once with the new bounding box. IV. Separation of display manager from windows: The previous algorithm hard-codes the display algorithm into the window. A better approach is to allow display managers to be attached to windows so that different display algorithms can be used depending on the application. A. Interface: Use the observer pattern interface DisplayManager { public: void update(); void addObject(GraphicalObject); void removeObject(GraphicalObject); void notifyChange(GraphicalObject, PropertyName); } B. Variables: Each window and container should maintain a pointer to a display manager object C. Methods: Win::update() displayManager.update(); Container::update() displayManger.update(); /* Methods for implementing the above display algorithm */ DisplayManager::Update() new_bbox = empty old_bbox = self.old_bbox for each obj in self.objs_changed do new_bbox = new_bbox U obj's position for each obj in registeredObjects do if intersect(obj, old_bbox) or intersect(obj, new_bbox) obj.update(old_bbox, new_bbox) self.old_bbox = empty V. Quadtrees: Quadtrees provide a way of dividing a region into quadrants. Each quadrant contains a list of all the objects that intersect its bounding box. Each node of a quadtree has four children, corresponding to a northeast, northwest, southeast, and southwest quadrant. A. Splitting a quadrant: When the number of objects in a quadrant exceeds a threshold, the quadrant is subdivided into four quadrants. B. Alternative Quadtree implementations: 1. Only leaf nodes contain a list of objects. Objects can appear in multiple leaf nodes if they overlap multiple quadrants. 2. All nodes contain a list of objects. An object appears in the topmost quadrant that is large enough to completely contain that object.