Ya' Gotta Love Parametric Equations
Assigned November 4, 1998
Due December 9, 1998
This goal of this project is very simple: You are to use parametric
and polar plots to create a drawing in Maple.
For example, try the following in a Maple worksheet:
[> with(plots):
[> p1 := polarplot(5+sin(3*theta),theta = 0 .. 2*Pi,color = violet,
scaling = constrained):
[> p2 := plot([2*cos(t), -1+2*sin(t), t = 5*Pi/4 .. 7*Pi/4],
color = red):
[> p3 := plot([-2+.8*cos(t), 2+.6*sin(t), t = 0 .. 2*Pi],color = blue):
[> p4 := plot([2+.8*cos(t), 2+.6*sin(t), t = 8*Pi/7 .. 13*Pi/7],
color = blue):
[> display(p1,p2,p3,p4);
A couple of comments:
- The colon at the end of the commands is very important. It
prevents Maple from printing out the plot structure each time. If you
forget it once, you'll see what I mean.
- You should make sure that at least one of your plots contains
the option scaling=constrained. This will keep Maple from
scaling your plots differently in the x and y directions.
- You should use at least 50 different functions in your
final image.
- The more creative you are with this, the better your grade will
be. For example, just lines, circles and ellipses would not earn you
a high grade.
- Section 4.1 from the text has some information on
combining linear and circular motion to get more interesting shapes.
We'll talk about this in a couple of weeks.
- For those of you who have had linear algebra, you know how to
stretch, skew, and rotate via matrix multiplication. This gives you
and easy way to manipulate any parametric plot.
If you haven't had linear, ask me (or someone who has had linear) and
we can explain it to you pretty quickly.
- FIRST DRAFT DUE NOVEMBER 23: You should turn in a
hand-drawn sketch of your final project and also a print out of your
Maple worksheet containing a rough idea of your image (with
at least five functions). This will count for 5% of your project
grade.
- We'll have show-and-tell at the end of the semester where everyone
can see each other's projects.
- Finally, HAVE A LOT OF FUN WITH THIS!!!!