# 3.4 Java3003: drawing graphs with turtles and pixels  (Page 6/13)

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`y = x*x`
Listing 6 . The method named function for Parabola01. ```double function(double xVal){ double yVal = xVal*xVal;return yVal; }//end function```

A plot of the output of the method named function would look like the curve shown in Figure 7 with no offsets if the x and y scaling values were set to one-half the width and height of the world respectively.

Figure 7. Parabola with zero offsets.

It will be instructive to see how this program uses offsets and scaling values to transform the image shown in Figure 7 into the image shown in Figure 6 .

## Drawing parameters for Parabola01

The code fragment shown in Listing 7 shows the drawing parameters that were used to produce the output shown in Figure 6 .

Listing 7 . Drawing parameters for Parabola01. ```double xOff = 0.25;//offset relative to 1.0 double yOff = -0.25;double xScale = 0.75*world.getWidth()/2; double yScale = 1.25*world.getHeight()/2;```

## Drawing parameters with zero offsets

The parameters that were used to produce the output shown in Figure 7 are shown below:

```double xOff = 0.0;//offset relative to 1.0 double yOff = -0.0;double xScale = 1.0*world.getWidth()/2; double yScale = 1.0*world.getHeight()/2;```

Note in particular that the offsets given by xOff and yOff are set to zero and the scale factors given by xScale and yScale are one-half the width and height of the world respectively.

## Changing the offset values

Increasing the offsets for xOff and yOff to 0.25 and -0.25 respectively as shown in Figure 7 and making no other changes produces the output shown in Figure 8

Figure 8. A parabola with offsets.

In comparison with Figure 7 , changing the value of xOff to 0.25 caused the peak to move to the right (positive direction) one-fourth of the way from the center origin to the right edge of the world. (That change also caused a portion of the curve to fall outside the right boundary of the world.)

Similarly, changing the value of yOff to -0.25 caused the peak to move up (negative direction) one-fourth of the way from the center origin to the top edge of the world.

## Changing the scale factors

Following that, changing the values of xScale and yScale to the values shown in Listing 7 produces the graphic output shown in Figure 6 . The change in xScale decreased the total width of the curve and prevented it from exceeding the rightmost boundary of theworld. The change in yScale increased the overall height of the curve causing it to almost touch the lower boundary of the world.

## Draw the parabolic function in BLUE

The code in Listing 8 draws the blue parabolic function shown in Figure 6 .

Listing 8 . Draw the parabolic function in BLUE. ```double yVal = 0; int row = 0;int col = 0; double xVal = -1;turtle.setPenColor(Color.BLUE); for(int cnt=0; cnt<=100;cnt++,xVal += 0.02){ //Get a y-value for the given x-value.yVal = function(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}//end run method```

#### Questions & Answers

what is Nano technology ?
write examples of Nano molecule?
Bob
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brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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Renato
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?
Kyle
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Kyle
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Joe
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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Bharti
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Daniel
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NANO
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s.
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Tarell
what is the actual application of fullerenes nowadays?
Damian
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Tarell
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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?
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Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
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