Contents:

• Collaboration Policy
• Overview
• Rotational Symmetry
• Our Framework
• Technical Requirements
• Grading Standards
• Submitting Your Assignment

Collaboration Policy

For this assignment, you must work individually in regard to the design and implementation of your project.

Please make sure you adhere to the policies on academic integrity in this regard.

Overview

The book's use of the star shape to build a "mandala" had me reading more about true mandalas, which are spiritual patterns that represent the Universe in Hinduism and Buddhism. (Read more on wikipedia.) For this project you are to design and build a mandala pattern of your choosing. The mandala must be centered around the middle of a canvas with your choice of dimensions, with a pattern than demonstrates rotational symmetry on a variety of underlying shapes (more technical requirements below).

For more inspiration, feel free to see:

• Google image search for colorful mandala
• www.dreamstime.com/illustration/mandala.html

Rotational Symmetry

In class, we have demonstrated techniques for drawing regular polygons and stars that demonstrate symmetry about their center. More generally the same principles can be used to make copies of any shape with such rotational symmetry. For this assignment you have two options:

• If you wish to tackle all the mathematics yourself, you are welcome to implement the entire sketch from scratch. (In that case, feel free to ignore the rest of this section.)

• We are offering the following framework that you may choose to use as your starting point. It has a few "magical incantations" that we have not yet explained, but it should make it relatively easy to stamp a pattern around the center at your chosen radius and scale.

  To begin, our code provides the regular polygon and star implementations from class. But the cooler framework that we are providing is a new function with signature:

        void stamp(Pattern model, int number, float radius, float scale, float theta)
        

  This function will place 'number' copies of the model pattern (more about that soon), placed evenly around the origin at distance 'radius'. The images will be drawn with the given scale factor and the images will be placed so that the first one is at angle 'theta' relative to the center.

  We need a little magic for you to be able to define a general pattern to stamp in such a way. As an example, assume that you want to use horses in your mandala. You would do this by using the following syntax:

        class Horse implements Pattern {
          void draw() {
            // give commands here that draw a single horse pattern
            // ...
          }
        }
        

  Note well: for proper use with our framework, such a draw() routine should layout the geometry so that the pattern is drawn relative to the origin (0,0), with the bottom of the pattern as drawn being the side that will be drawn oriented inward toward the center. Our stamp() function will combine other transformations to replicate the pattern.

  Once you have defined a pattern such as Horse, you may use it with the stamp() function using a syntax such as the following:

        stamp(new Horse(), 4, 200, 0.5, QUARTER_PI);
        

  This command would cause 4 horses to be drawn, each at radius 200 from the center and at half-scale relative to the original pattern definition, and such that the first of the four hourses is drawn at angle QUARTER_PI.

Our Framework

If you are interested in using our framework, please use this source code as your starting point for the project.

To better explain usage of this framework, we have designed a sample sketch with this framework (sample source code). It generates the following (not particularly artistic) image

If examining the source code, note well that the Smiley pattern is described so that the center of the face is at (0,0), and that is the reference point that is drawn at precisely the given radius during the stamp() function. Similarly, the Arrow pattern is described with the origin within the middle of the polygon.

Technical Requirements

Your sketch must meet the following technical requirements:

• The canvas must be at least 500 pixels by 500 pixels.
• You must demonstrate rotational symmetry using at least two distinct numbers of objects around the center. (For example, you might use eight-fold symmetry for one object and four-fold symmetry for another.)
• Your mandala must use at least five distinct patterns that are placed at various locations in the figure. (In our example, the smiley face and arrow constitute only two patterns)
• In addition to the stamped patterns, you must use at least one regular polygon and at least one star.

Submitting Your Assignment

Please see details regarding the submission process from the general programming web page, as well as a discussion of the late policy.

For this project, we ask that you submit the following three files:

• The .pde file that contains the actual Processing source code you've written
• A .jpg image of your final mandala. You might create this from within Processing by using the command

        save("mandala.jpg");   // or any other such filename
        

• A separate 'readme' text file, as outlined in the general webpage on programming projects.

Grading Standards

The assignment is worth 70 points, which will be assessed as follows:

• (20 points) Use of at least five distinct (and interesting) patterns.
• (10 points) Non-trivial use of polygon and star
• (10 points) Good program design (e.g., organization, use of variables)
• (10 points) Comments, Naming Conventions, and adherence to submission procedures
• (10 points) Artistic merit
• (10 points) Degree of difficulty