Asymptote: Logical Operators and Loops

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Asymptote (Vector Graphics Language)
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Useful functions - CSE5 Package - How to

Asymptote uses loops and logical operators that are almost identical to those in C++. Loops are absolutely essential if you want to make diagrams that look like this:

[asy] import graph; real r=5;  size(r*cm); picture smiley; filldraw(smiley,Circle((0,0),1),yellow,black); fill(smiley,Circle((-.3,.4),.1),black); fill(smiley,Circle((.3,.4),.1),black); draw(smiley,Arc((0,0),.5,-140,-40)); for (int i=0; i<5; ++i) {  for (int j=0; j<5; ++j)  {   if (floor((i-j)/2)==((i-j)/2))   {   add(scale(r/10*cm)*smiley,(i,j));   }  } } [/asy] This particular example was produced with the following code:

import graph;
real r=5; 
size(r*cm);
picture smiley;
filldraw(smiley,Circle((0,0),1),yellow,black);
fill(smiley,Circle((-.3,.4),.1),black);
fill(smiley,Circle((.3,.4),.1),black);
draw(smiley,Arc((0,0),.5,-140,-40));
for (int i=0; i<5; ++i)
{
 for (int j=0; j<5; ++j)
 {
  if (floor((i-j)/2)==((i-j)/2))
  {
  add(scale(r/10*cm)*smiley,(i,j));
  }
 }
}

Above, we created a picture called smiley and added it to currentpicture many times using a for loop, as the indices $i$ and $j$ each ranged from $0$ to $4$. Basically, the arguments in the parentheses for the first for loop first declare $i$ to be an integer and assign to i the value $0$. Then, if $i<5$, it executes what is inside the {} brackets and when it is finished, it adds $1$ to $i$ (++i). This process repeats until the boolean statement $i<5$ has the value false, i.e. 5 times (hence the 5 columns of smileys). The if statement is self-explanatory; if $\lfloor(i-j)/2\rfloor=(i-j)/2$ (which checks if $i$ and $j$ have the same parity or not), then the smiley is added, and if not it skips the brackets that follow.

For more information on logical operators and loops, see [here].

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