# 3.4 Java3003: drawing graphs with turtles and pixels  (Page 8/13)

 Page 8 / 13

The value returned from the Math.sqrt method can be considered to be either positive or negative. Only the positivevalue is returned by this method. When the returned value is considered to be positive and the results are plotted, one-half of a circle is displayed as shownby the BLUE line in Figure 10 . Similarly, when the returned value is considered to be negative and the results are plotted, the other half of the circle isdisplayed as shown by the GREEN line in Figure 10 .

Listing 10 . The method named function for Circle01. ```double function(double rVal,double xVal){ double yVal = Math.sqrt(rVal*rVal - xVal*xVal + 0.0000000001);return yVal; }//end function```

If the expression passed to the sqrt method is negative, the value returned by that method will not be valid. Because the computations inthis program are performed as type double , and because all floating point computations are only estimates of the truth, the computed differencebetween the radius squared and the x-value squared can actually be an extremely small negative value when it should be zero. A small positive fudge factor wasadded to prevent that value from going negative due to small floating point computational errors. (This sort of thing is often required when doing a lot of floating point computations. There are various ways to do it and there may bebetter ways than the one used here.)

## Draw half the circle in BLUE

The code in Listing 11 draws the BLUE half of the circle shown in Figure 10 .

Listing 11 . Draw half the circle in BLUE. ```for(int cnt=0; cnt<=100;cnt++,xVal += xInc){ //Get a y-value for the given x-value.yVal = function(rVal,xVal); //Apply the offsets and scale the resultscol = (int)((xOff+xVal)*xScale); row = (int)((yOff+yVal)*yScale);//Move to the first point without drawing a line because the// pen is not down. Translate the origin to the center in the // process.turtle.moveTo(col + world.getWidth()/2, row + world.getHeight()/2);//Lower the pen in order to draw a line from each point to the // next point.turtle.penDown(); }//end for loop```

Having initialized xVal and xInc on the basis of the radius in Listing 9 , the code in Listing 11 is essentially the same as the code in the earlier programs in this lesson.

## Draw the other half of the circle in GREEN

The code that draws the GREEN half of the circle is shown in Listing 18 . It is essentially the same as the code in Listing 10 except that the sign on yVal is flipped from positive to negative as discussed above .

## Different line width

One other difference that I haven't mentioned yet is trivial but interesting. You may have noticed that the line width in Figure 10 is about twice that in Figure 9 . I purposely did that to illustrate that one of the useful features of graphing functions with a turtle is that you can control the width of the line.The importance of that capability will become apparent in the next section.

That concludes the interesting differences between this program and the previous programs.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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