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Preview

In this lesson, I will explain programs that use a Turtle object to graph the following mathematical functions:

  • A straight line
  • A parabola
  • A cubic
  • A circle (two approaches)
  • A cosine

I will also show you how to graph a circle without using a Turtle object and compare the two approaches.

General background information

You learned about the World class, the Turtle class, and the Picture class in an earlier lesson titled Java3002: Creating and Manipulating Turtles and Pictures in a World Object . You learned the fundamentals of causing the turtle to move and to draw a linewith different colors and different line widths in the process. For review, Figure 1 shows an image that you learned to create in that earlier lesson.

Figure 1. Two turtles in a World object.

Missing image

In comparison, Figure 2 shows the sort of thing that you will learn to do in this lesson.

Figure 2. Graph of a cubic function.

Missing image

The blue line in Figure 2 shows a graph of the following cubic function in a Cartesian coordinate system:

y = x*x*x

The red lines in Figure 2 show the x and y axes.

The graph in Figure 2 was created by computing the x and y coordinate values (points) for a set of x values uniformly spaced along the x axis and causing the Turtle object to move and connect those points with a blue line. The Turtle object was made invisible.

As a practical matter, computing the coordinate values is relatively simple. The more complex problem is to get everything scaled properly to produce avisually pleasing graph in the space provided by the World object.

Discussion and sample code

I will explain six different programs in this lesson. Complete listings of those programs are provided in Listing 15 through Listing 20 in the section titled Complete program listings .

As is my custom, I will break the programs down and explain them in fragments. However, I will explain only those portions of the programsthat are new to this lesson. I will let the comments in the listings speak to those portions of the code that you should already understand.

Much of the code repeats from one program to the next. I will explain new code the first time that it appears in a program and won't explain that code in theexplanation of programs that follow.

A straight line

In this section, I will present and explain a program named Line01 that can be used to draw a straight line using the standard formula for a straight line given below:

y = slope*x + yIntercept

A complete listing of the program is provided in Listing 15 near the end of the lesson.

Program output for Line01

Before getting into the code, Figure 3 shows the program output.

Figure 3. Program output for Line01.

Missing image

As you can see, in addition to the red axes, this program graphs three different lines in different colors with different slopes and differenty-intercept values. I will touch on the slopes and the y-intercept values as I explain the code.

May need multiple points

At this point, I will explain a practical issue before it becomes a concern to you. As we all know, only two points are required to define a line.However the program that I will explain uses multiple points to define and draw a line. This requirement results from the behavior of a Turtle object when moving from one point to another point.

Questions & Answers

how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, Object-oriented programming (oop) with java. OpenStax CNX. Jun 29, 2016 Download for free at https://legacy.cnx.org/content/col11441/1.201
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