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

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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.

who was the first nanotechnologist
k
Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
what happen with The nano material on The deep space.?
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
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