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This demo is for Windows only. Readme File for PathDemo ------------------------ Bryan Stout PathDemo was developed as a means of visually illustrating how different pathfinding algorithms work. This file explains the basics of how PathDemo and its components work, since it has no help file yet. PathDemo was developed in Delphi 2.0, and so needs Win95 or Windows NT to run. This version of PathDemo may be distributed freely, as long as this unaltered ReadMe file accompanies it. Overview -------- In PathDemo, one can edit a square grid map, select a search algorithm, and observe how the search functions in the map. Functions available include: - Map Edit: lay out terrain of varying cost, assign start/goal nodes. - Search Control: start, pause, continue, clear search; change display speed; zoom in or out. - Algorithm Selection: choose search algorithm, assign appropriate parameters. - Heuristic Selection: assign heuristic weight, choose distance approximation function. Map Editor Panel and Map Display --------------------------------- The Map Display shows a square grid which is the map used for searching paths. The map begins at the largest magnification, and all the squares begin with clear terrain. The grid's full size is 40 columns by 32 rows. The Map Editor panel contains a set of radio buttons showing the different terrains that can be assigned to the map tiles -- with their relative costs -- including blocked terrain, and the start and goal nodes. - To show different parts of the map grid, use the scroll bars beside the grid. - To zoom the map grid out or in, use the "Map Size" track bar in Search Control panel in the upper right corner. - To place a start node in the map, click the Start radio button, and then click on any square in the map. Clicking in other squares will move the start to that location -- there can be only one start square. The Goal node placement works in exactly the same way. The location of the start and goal nodes has no effect on the terrain cost, and vice versa. - To change the terrain cost of map squares, click on the terrain you want to paint on the map. Every individual square you click on will change to that terrain. Clicking and dragging will paint every square in the rectangle which has the the click and current squares as corners. To correct mistakes, you will have to paint them back to the way you want them. Search Algorithm Panel ---------------------- In this panel, you can select the search algorithm, and alter parameters affecting them. These are the algorithm choices available: First, there are unplanned searches, which simply head towards the goal, and deal with obstacles as they come up (for details on the algorithms, see the article "Smart Moves"): - Random Bounce. If an obstacle is detected, head in a random direction for one square, and try again. - Simple Trace. Trace around obstacles until one is heading in the same direction again. - Robust Trace. Compute the line segment joining the blocking spot and the goal. Trace until that line is crossed again. All the other searches plan the whole route ahead. Some of them use a recursive stack to keep track of the search's progress: - Depth-First Search (DFS). This simply tries all paths out to a given depth, as specified in the "Search Depth" spin control. - Iterative-Deepening Depth-First Search (IDDF). This does the DFS search at increasing depths, until a path is found. - Iterative-Deepening A-Star Search (IDA*). This is like IDDF, but it keeps track of the cost of the path from home, and estimates the distance to the goal. If their sum is too great, the search cuts off (but this cutoff depth keeps increasing until the path is found). The remaining searches keep a couple of lists of the squares visited -- Open, for those not examined yet, and Closed, for those which have been. When each node is examined, its neighbors are put on Open: - Breadth-First Search. Open is just a FIFO queue, so all the nodes are expanded in the order they are place on Open. - Dijkstra's Algorithm. Similar to breadth-first, but it keeps track of the distance from the goal of all the squares. Open is kept sorted in order by this distance, and nodes can be re-ordered in the lists (and even moved from Closed back to Open) if a shorter path to the square is found. - Best-First Search. This sorts nodes in Open according to the shortest estimated distance to the goal. This makes the search very fast, but it ignores the cost of terrain. - A-Star Search (A*). The nodes in Open are sorted by the sum (f) of the distance from start (g) and the estimate to the goal (h). All around, the most robust of these search algorithms, hence it is the focus of the Gem. - To view the algorithm choices, click on the up or down arrows at the right end of the list box at the top of the panel. - To select an algorithm, click on the choise that is visible; the selected choice is colored blue. The seach won't run if an algorithm is not chosen. - To specify a bi-directional search for Open list-based searches, click the "Bidirectional Search" check box. Note: this does not yet work perfectly, as it takes the first solution found which joins both ends, rather than waiting for the best one. The remaining controls affect stack-based searches (DFS, IDDF, IDA*): - To save, at each square, the shortest path discovered to that square, click the "Save Min Path Length" check box. With this unchecked, the stack-based searches are horribly inefficient, retreading old ground frequently (try it!). - To have the search always aim first towards the goal, check the "Aim to Goal First" check box. Also a big help. - To set the depth for DFS, click on the arrows of the "Search Depth" spin control, or enter a value into the box directly. Heuristic Estimate Panel ------------------------ The controls here control how the Best-First and A* searches make estimates of the distance remaining to the goal. This estimate can vary depending on one's application; PathDemo always computes it by multiplying a constant weight times the estimated distance to goal. Both of these factors can be altered. - To change the constant weight, move the slider in the Heuristic Weight track bar. Note that if the terrain is all clear, '1' is the correct value. If there is much terrain of higher cost, other values may give a better approximation. A '0' yields the same as Dijkstra's search; a value higher than all the terrain cost yields the same as Best-first search. - To choose a different distance function, view the different entries in the Distance Function list box, and click the one desired. The different distance functions are: - The maximum of the differences in the X and Y coordinates (max(dx,dy)). - The Euclidean distance (square root of sum of squares of dx, dy). - The diagonal shortcut. A diagonal route is followed until one is directly up, down, or across from the goal, and an orthogonal distance is used for the remainder of the way. PathDemo uses 1.4 as an estimate of the diagonal distance of sqrt(2). - The Manhattan distance (dx + dy). If the start were at [1,1], and the goal at [5,4], then dx=4, dy=3, and the different distance functions would give us 4, 5, 6.2, and 7 respectively. In PathDemo's map (squares, with diagonal moves allowed), the diagonal shortcut gives the true distance between two squares as the crow flies; the first two give underestimates, the last one an overestimate. Search Control Panel -------------------- This panel has controls over starting, stopping, and clearing the search, and over the search speed and map size. When the search runs, its visual display depends on the type of search being done: - Unplanned searches sh