Project 2: Fractal Plants
CS354 Computer Graphics
Due: ***NEW*** October 16, 11:59pm ***END NEW***

This project is focused on drawing two-dimensional fractal plants. Part of the project is implementing and using your own transformation matrices; this way you'll understand how they are used in OpenGL and other graphics systems. The basic project described below is worth 85%. To get 100% or more, you'll need to implement some additional features.

Project Specifications
Carefully read the lecture notes on L-systems.  Next understand the purpose and use of the MODELVIEW and PROJECTION matrices in OpenGL.  You may refer to the reference book mentioned below or to some online OpenGL tutorial.

Your plant should be defined using recursive functions corresponding to a simple L-system. Consult the lecture notes on L-systems for detailed instructions. Your L-system should include at least branching, turning and scaling. The plant should include at least leaves and branches (other primitives like flowers and fruits are optional). So your L-system should include at least two character symbols, such as `F' for branch and `L' for leaf, and use branching (brackets '[' and ']') and turning (`+' and `-'). Give the definition of your L-system in your documentation.

You must specify the transformations used by your L-system by specifying your own matrices, and loading them into the OpenGL MODELVIEW matrix. The OpenGL commands you may NOT use this time are glRotate, glScale, glTranslate, glMultMatrix, glPushMatrix and glPopMatrix. Instead, you should keep track of your own 2D version of the MODELVIEW matrix, and modify it by left-multiplying it by translation matrices, rotation matrices, etc. You can use the function load2DMatrix() in the starter code to put a 2D matrix into the OpenGL MODELVIEW matrix.  ***NEW*** You will also need to write a more generalized version of this function where you can set additional elements in the 3rd row and 3rd column of the matrix.  Name this more general function load3DMatrix(). ***END NEW***  Your program should be able to take depth of the L-system as an input parameter. You should include this in your user interface.  Set the default depth be 1, and set 'a' to increase the depth of your L-system and 's' to decrease the depth of the L-system.  Naturally, make sure the depth cannot be negative.

The starter code contains 2-D versions of the branch and leaf drawing primitives, but you will extend these to 3-D.  Using the 2-D version of the leaf (this will be like the silhouette of the leaf in x and y coordinates), create a 3-D extrusion by giving the 2-D silhouette a uniform thickness in the z dimension.  GL_QUADS and GL_TRIANGLES may be helpful when you are creating the extrusion.  Do the same with the 2-D branch.

When your 3-D plant has been completed, assign the following key bindings to the user interface:

'/' - rotates the plant about its y-axis counterclockwise (i.e. when you are looking at the trunk of the plant from the top down, the plant rotates counterclockwise).
'?' - rotates the plant about its y-axis clockwise.

Note that to implement these full-plant rotations, you should only need to perform one matrix multiply and one matrix load before you begin drawing the plant.

Your code should also be able to switch between using a perspective projection matrix and an orthographic projection matrix.  Assign 'p' to toggle between these two projection modes, and make sure you print to stdout the projection mode that is currently in use.  You may use the built-in OpenGL matrix functions for this part of the assignment and this part only.  Some helpful functions to look at: glFrustum(), glOrtho() and gluPerspective().  Use reasonable parameters.

Finally, answer the 2 questions for report.txt that are listed in the "What and How to Submit" section.

Additional Features
If you successfully complete everything up to this point, your score for the project will be an 85%.  Select some additional features from the following list to receive 100% or more.

Look at some of the cool images from previous semester to get further inspired!  Note that you can get up to 120% credit for this project, but any extra credit can only be applied to your overall Project grade average, which cannot exceed 100%.

Getting Started

Here is the starter code which brings up a window and draws a leaf and branch. It includes a function to load a 2D transformation matrix into the 3D OpenGL MODELVIEW matrix properly. To compile it, type "make" on the Dell Linux machines in Taylor/Painter basement labs. This will produce an executable "plant".  If you would like to build a version with the .ppm reader, type "make plant2" and run the executable "plant".

Look here for some suggestions about getting started.

Written Questions for Each Team Member (20% of the project grade)

1.  What is the difference an orthographic projection and a perspective projection?  What is the difference between glFrustum() and glOrtho()?  Between glFrustum() and gluPerspective()?  If you were given the parameters to glFrustum(), how would you make an equivalent call using gluPerspective()?  ***NEW*** For the last question, you may assume that in the call to glFrustum(), top == -bottom and right == -left. ***END NEW***

2. ***NEW*** What changes would be needed in order to express and then draw a leaf as a fractal? ***END NEW***  Provide some pseudocode and mention any changes that would be needed in the L-system.

3. If you know a 3-D fruit has rotational symmetry about an axis and you were given a triangulation of the 2-D cross-section (this cross section is spanned by the axis of symmetry), how would you go about creating a triangulation for the surface of the 3-D fruit?  Provide pseudocode.  ***NEW*** Assume that the triangulation of the 2-D cross-section is itself symmetric about the axis of symmetry and has one top and one bottom vertex that lies on the axis of symmetry.***END NEW***

What and How to Submit
Your program should compile and run on the Taylor or Painter basement machines. Then submit the following files:

The README file should be a plain text file, it should clearly mention: your name(s), what the submitted files contain (e.g. which is the executable, which contain the source code etc.), any unusual steps needed to get your program to run, and a short description of the user interface.

The report (report.txt) should also be a plain text file which should contain the description of the L-system you implemented (in the form of rules and the initial axiom). In the report, please mention all the extra features that you have implemented or else we may fail to notice and hence credit them.  As a group, answer the following two questions in the report:

How does the plant change visually when you switch between a perspective projection and an orthographic projection?
2) Why is this?

Also, in report.txt, you may write about what new ideas you came up with, what design decisions you took etc; please keep such a  discussion short and to the point.

You should grab the image of the best plant you generated by using  xv command on Taylor/Painter basement machines.  Save it as gif or jpeg file. Here is a note on how to grab a window using xv.

Each group member also needs to turn in his or her own version of the answers to the 3 written questions.  Put the answers to these questions in a file called project2.txt.

Use the turnin program to submit your files. Just like in Project 1, you have to turnin to:
djeu cs354_project2_code per group for all code-related files and
djeu cs354_project2_written per person for each person's project2.txt.

Here is a short note on how to use the turnin program.

Start early, and good luck!

A great coffee table book is The Algorithmic Beauty of Plants, by Przemyslaw Prusinkiewicz, Aristid Lindenmayer. Also you can learn more advanced concepts from this tutorial.

OpenGl Reference book.
Neider, Davis and Woo, "OpenGL Programming Guide" Second Edition, Addison-Wesley