# 3.4 Java3003: drawing graphs with turtles and pixels  (Page 2/13)

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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.

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.

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.

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.

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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