Department of Computer Science Worcester Polytechnic Institute

Objective:	In this assignment, you will learn how to generate a forest of trees using an iterated function system (IFS) called Lindenmayer Systems (a.k.a. L-Systems), and place those trees on a "ground plane." As with Assignment 1, this assignment consists of two parts: a "Preparation" part and a "New Stuff" part.
Preparation:	The aim of this preparation part is for you to create the IFS for generating the strings that will define each tree for the forest. In addition, you will create a PolyCylinder routine to better understand transformations (e.g., translations, rotations) in OpenGL. A drawing pattern is defined by a turtle string made up of command characters that control how the turtle moves, as well as its state. The commands include: Character Meaning F Move forward a step of length len, drawing a line (or cylinder) to the new point. f Move forward a step of length len without drawing. + Apply a positive rotatation about the X-axis of xrot degrees. - Apply a negative rotatation about the X-axis of xrot degrees. & Apply a positive rotatation about the Y-axis of yrot degrees. ^ Apply a negative rotatation about the Y-axis of yrot degrees. \ Apply a positive rotatation about the Z-axis of zrot degrees. / Apply a negative rotatation about the Z-axis of zrot degrees. | Turn around 180 degrees. [ Push the current state of the turtle onto a pushdown stack. ] Pop the state from the top of the turtle stack, and make if the current turtle stack. L-Systems are used to generate a turtle string by iteratively expanding a start token by applying production (or re-writing) rules. Each L-Systems consists of a grammar that defines re-writing rules. Each rule in the grammar consists of a left-hand side (LHS) and a right-hand side (RHS), separated by a colon. A sample grammar looks like this: start: F-F-F-F F: F-F+F+FF-F-F+F In addition to specifying a grammar, we also need to specify the values for len, xrot, yrot, and zrot, as well as a value denoting how many times we want to iterate (i.e., apply the production rule(s)). Similar to the way the Koch curve is created by replacing each segment with a predefined pattern, the turtle string is rewritten by substituting every instance of a LHS by its corresponding RHS. For any token in the string for which there is no matching LHS, the token is simply copied into the new string. For example, given the grammar: start: F+F F: F-F+F-F after one iteration, the resulting turtle string would be: F-F+F-F+F-F+F-F and after two iterations, the resulting turtle string would be: F-F+F-F-F-F+F-F+F-F+F-F-F-F+F-F+F-F+F-F-F-F+F-F+F-F+F-F-F-F+F-F Your system should be able to handle multiple productions rules, each having a unique LHS, for example: start: X X: F-[[X]+X]+F[+FX]-X F: FF Here is an example (in 2D) of some grammars and their corresponding trees. Can you extend these to 3D for use in this project? (The angle specified is the rotation for the "+" and "-" characters.)
Setup:	Copy the Makefile you used in Assignment 1, change the names accordingly for your program, and add in the other modules you have created (e.g., grammar.h grammar.cpp, etc.).
Prep Coding:	L-Systems: Write a program that implements the L-System re-writing scheme described above. Your program should be able to read several grammars from grammar files, store them in appropriate data structures, and then generate the correct turtle strings by applying the rewriting rules as specified. Here is a sample L-System file. A description of the file format is contained in the file itself, and you may assume that all files have the same format. Compile and run your program! The PolyCylinder: We define a PolyCylinder as a polyline in three dimensions. Given a sequence of points in 3-space { (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) }, a polycylinder draws a cylinder from (x1, y1, z1) to (x2, y2, z2), and another one from (x2, y2, z2) to (x3, y3, z3). To avoid "gaps" in the joints of the polycylinder, a sphere of the same diameter as the cylinders is drawn at each point. You need to write some code that: Moves (translates) to the first point, Draws a sphere, Points (rotates) towards the next point, Draws a cylinder to the next point, Moves (translates) to the next point, Draws a sphere, Points (rotates) towards the next point, Draws a cylinder to the next point, Moves (translates) to the next point, And so on, for all the points in the list. HINT 1: This part is an exercise in translating and rotating your coordinate system before drawing your geometry. After you accomplish this, you will understand how transformations are accumulated in OpenGL. HINT 2: You can simplify your life by always drawing your cylinder along the Z axis. To do this, apply your rotations such that you are always "moving" along the Z axis by first rotating yourself to point the current Z direction towards the next point. Using the description of setting up a simple scene given in Hill, Example 5.6.2, set up a view of your scene, draw a checkerboard ground plane, and draw some PolyCylinders in the scene. You can just come up with some (x, y, z) points on your own for this. Be creative! Write your name, or something. Compile and run your program!
New Stuff:	Now we need to put it all together. Using the code you wrote in the preparation section, your program should read in five L-System files, "lsys1.txt," "lsys2.txt," "lsys3.txt," "lsys4.txt," and ONE OF YOUR OWN, and store them in instances of your grammar class. You should then apply the re-writing rules for each grammar according to the values specified for this in each grammar file. Choose a random location on the ground plane to start drawing one of the randomly selected tress, using a random color, and draw it. HINT: You should apply a translation and a rotation to move to the correct start location. Repeat Step 2 (at least) 10 times in order to draw your forest. (If you REALLY want to test your program, try this input file. This is from p. 20 of the reference book listed at the bottom of this page and is PURELY OPTIONAL!)
Extra Credit:	The extra credit for this assignment allows you to generate more-realistic tress. Implement a variation on L-Systems, called Stochastic L-Systems, whereby a production rule can have a probability associated with it, and there can be multiple production rules that have the same LHS. For example, the grammar: start: F F(0.33): F+F F(0.33): F-F F(0.34): F+F-F would choose how to replace each "F" it encounters according to the probabilities associated with each rule. (The probabilities for each unique LHS should sum to 1.) This adds better variation to the trees that are created. A sample stochastic L-System file can be found in "lsysStochastic.txt." After getting this to work, you must create 2 additional stochastic grammars that show some interesting trees. Add leaves to the end of your branches by drawing the appropriate geometry. You don't have to get too fancy, but choose a different color for them. Reduce the diameter and length of each tree segment, depending on how far "up the tree" or how far "away from the trunk" the segment is. This will give a tapering effect to the tree.
Attacking the Problem:	For the L-System part, start out by creating several classes that will help you manage the different things you will need to keep straight. For example, you might want to have a turtle class consisting of a position, orientation, length when drawing, and a string representing the turtle string. You might want to have a rule class that has strings for the lhs and rhs. A grammar class would consist of a list of rules, along with a method (addRule) to add a new rule to the grammar. The main method for the grammar class might be something like a rewrite method that takes in a turtle and a number of iterations, and returns a new string after applying the rules to the turtle string for the desired number of iterations. The functionality for implementing '[' and ']' can be greatly simplified by using the built-in OpenGL functions glPushMatrix and glPopMatrix. This will save and return you to the proper state. Another thing that will help you greatly is to use the Standard Template Library (STL) that is available with C++. There are a number of classes that you will find very useful, such as "string," "hash_map," "multimap," and/or "list." If you have never used these before, this is a good opportunity for you to "get out of your comfort zone," as these tools will serve you well in most future endeavors, both in this class and well beyond. Some good links to C++ help include the SGI site and also CPP Reference.
Documentation:	You must create adequate documentation, both internal and external, along with your assignment. The best way to produce internal documentation is by including inline comments. The preferred way to do this is to write the comments as you code. Get in the habit of writing comments as you type in your code. A good rule of thumb is that all code that does something non-trivial should have comments describing what you are doing. This is as much for others who might have to maintain your code, as for you (imagine you have to go back and maintain code you have not looked at for six months -- this WILL happen to you in the future!). I use these file and function (method) headers, in my code. Please adopt these (or the official CS ones) for all your assignments. The file header should be used for both ".h" and ".c" (or ".cpp") files. Create external documentation for your program and submit it along with the project. The documentation does not have to be unnecessarily long, but should explain briefly what each part of your program does, and how your filenames tie in. Most importantly, tell the TA how to compile and run your program.
What to Turn in:	Submit everything you need to compile and run your program (source files, data files, etc.) BEFORE YOU SUBMIT YOUR ASSIGNMENT, put everything in one directory on ccc.wpi.edu, compile it, and make sure it runs. Then tar everything up into a single archive file. The command to tar everything, assuming your code is in a directory "ass2", is: tar cvf FirstName_LastName_ass2.tar ass2
Academic Honesty:	Remember the policy on Academic Honesty: You may discuss the assignment with others, but you are to do your own work. The official WPI statement for Academic Honesty can be accessed HERE.
References:	Most of the motivation for my interest in this work comes from the book "The Algorithmic Beauty of Plants," by Prezmyslaw Prusinkiewicz and Arstid Lindenmayer, Springer Verlag, New York, 1990, ISBN 0-387-97297-8, ISBN 3-540-97297-8. The whole book has been put online by the author. In addition, there are links to other interesting works on this page. You can also find it on Amazon. Back to course page.