What preparation do I need before beginning this assignment? Read Sections 2.1–2.3 of the textbook.

The API expects the angles to be in degrees but Java's trigonometric functions assume the arguments are in radians. How do I convert between the two? Use Math.toRadians() to convert from degrees to radians.

What is the purpose of the copy() function in Transform2D? As noted in the assignment, the transformation methods mutate a given polygon. This means that the parallel arrays representing the polygon are altered by the transformation methods. It is often useful to save a copy of the polygon before applying a transform. For example:

// Set the x- and y-scale
StdDraw.setScale(-5.0, 5.0);

// Original polygon
double[] x = { 0, 1, 1, 0 };
double[] y = { 0, 0, 2, 1 };

// Copy of original polygon
double[] cx = Transform2D.copy(x);
double[] cy = Transform2D.copy(y);

// Rotate, translate and draw the copy
Transform2D.rotate(cx, cy, -45.0);
Transform2D.translate(cx, cy, 1.0, 2.0);
StdDraw.polygon(cx, cy);

// Draw the original polygon
StdDraw.polygon(x, y);
copy and polygon

Does a polygon have to be located at the origin in order to rotate it? No. You can rotate any polygon about the origin. For example:

// Original polygon
double[] x = { 1, 2, 2, 1 };
double[] y = { 1, 1, 3, 2 };
StdDraw.polygon(x, y);

// Rotate polygon
// 90 degrees counterclockwise
Transform2D.rotate(x, y, 90.0);
StdDraw.polygon(x, y);
rotate any polygon

Does our code have to account for invalid arguments? No. You can assume:

Frequently Asked Questions:  Sierpinski

What is the formula for the height of an equilateral triangle of side length s? The height is \(s \sqrt{3} / 2 \).

height of an equilateral triangle

What is the layout of the initial equilateral triangle? The top vertex lies at \((1/2, \sqrt{3} / 2)\) You can use this diagram as a reference.

Sierpinski triangle geometry

How do I draw a filled equilateral triangle? Call the method StdDraw.filledPolygon() with appropriate arguments.

I get a StackOverflowError message even when n is a very small number like 3. What could be wrong? This means you are running out of space to store the function-call stack. Often, this error is caused by an infinite recursive loop. Have you correctly defined the base case and reduction step?

May I use different colors to draw the triangles? Yes, you may use any colors that you like to draw either the outline triangle or the filled triangles, provided it contrasts with the white background.

Frequently Asked Questions:  Art

The API checker says that I need to make my methods private. How do I do that? Use the access modifier private instead of public in the method signature. A public method can be called directly by a method in another class; a private method cannot. The only public method that you should have in Art is main().

How should I approach the artistic part of the assignment? This part is meant to be fun, but here are some guidelines in case you're not so artistic. A very good approach is to first choose a self-referential pattern as a target output. Check out the graphics exercises in Section 2.3. Here are some of our favorite student submissions from a previous year. See also the Famous Fractals in Fractals Unleashed for some ideas. Here is a list of fractals, by Hausdorff dimension. Some pictures are harder to generate than others (and some require trigonometry); consult your preceptor for advice if you're unsure.

What will cause me to lose points on the artistic part? We consider three things: the structure of the code; the structure of the recursive function-call tree; and the art itself.

For example, the Quadricross looks very different from the in-class examples, but the code to generate it looks extremely similar to HTree, so it is a bad choice. On the other hand, even though the Sierpinski curve eventually generates something that looks like the Sierpinski triangle, the code is very different (probably including an "angle" argument in the recursive method) and so it would earn full marks.

You must do at least two of these things to get full credit on

Contrast this with the examples Htree, Sierpinski, and NestedCircles which have very similar structures to one another.

You will also lose points if your artwork can be created just as easily without recursion (such as If the recursive function-call tree for your method is a straight line, it probably falls under this category.

May I use GIF, JPG, or PNG files in my artistic creation? Yes. If so, be sure to submit them along with your other files. Make it clear in your readme.txt what part of the design is yours and what part is borrowed from the image file.

How can I call the Transform2D methods inside You must fully qualify each method name with the Transform2D library. For example:

Transform2D.rotate(x, y, 45);

My function for takes several parameters, but the assignment says that I can only read in one command-line argument n. What should I do? Choose a few of the best parameter values and do something like the following:

if      (n == 1) { x = 0.55; y = 0.75; }
else if (n == 2) { x = 0.55; y = 0.75; }
else if (n == 3) { x = 0.32; y = 0.71; }
else if ...

How can I create colors that aren't predefined in standard drawing? It requires using objects that we'll learn about in Chapter 3. In the meantime, you can use this color guide.

Possible Progress Steps:  Sierpinski

These are purely suggestions for how you might make progress. You do not have to follow these steps. Note that your final program should not be very long (no longer than Htree, not including comments and blank lines).

Reviewing Your Program