Asymptote: Basics

Asymptote (Vector Graphics Language)

Getting Started - Basics - Drawing - Labeling - Filling - Useful functions - Examples - Macros and Packages Help - Reference - Advanced Asymptote - 3D Graphics - CSE5 Package - How to

Syntax

In Asymptote, every command you give it should be followed by a semicolon (;). This tells Asymptote how to separate one command from the next. For example, the command draw(A--B) draws a line segment from point to given as coordinate pairs. Thus, if you wanted to draw two line segments, say one of them from to (in units of PostScript points - see below for the explanation of units and size) and the other from to , you can create the following document:

draw((0,0)--(50,50));
draw((0,50)--(50,0));

The two commands do not need to be on separate lines; it is the semicolon that separates them. However, putting the commands on separate lines does not change the output, so it is often useful to separate you commands in this way in order to organize your code. Whitespaces before and after commands are also not read by Asymptote, so any line can be indented as far as desired for clarity's sake.

Variables and Data Types

 Asymptote parses your code into substrings which have a certain data type, for example a real (like ) or a pair (like ).  Each new variable that you declare must be declared as a data type that Asymptote recognizes, by the command [datatype] [variable];.  For example, if you wanted to declare the variable  to have type integer, you can use the command
 int n;

After it is declared, you can store a specific value in a variable using the symbol, as in

 n=3;

These two commands can be abbreviated by the single command int n=3;, and several integers can also be declared at once (int m,n,d;).

As another example of variable declaration, consider the picture of the X from the Syntax section above. The same picture can be made as follows:

   pair A,B,C,D;
   A=(0,0);
   B=(50,50);
   C=(0,50);
   D=(50,0);
   draw(A--B);
   draw(C--D);

In this particular example, variable declarations made the code longer, but as you will see, declaring variables will significantly clean up your code in messier diagrams.

The most commonly used data types in Asymptote are given in the following table:

 \begin{tabular}{|c|l|l|}\hline
 \textbf{Type} & \textbf{Description} & \textbf{Examples} \\ \hline
  bool & A statement, either true or false. & \verb1true1, \verb1false1, \verb31>23 (false) \\ \hline
  string & A string of characters,& \verb1"Hi!"1,\\
   & enclosed by quotation marks. & \verb1"This is a string."1 \\\hline
  int & An integer value. & \verb -2 ,\verb -1 ,\verb 0 ,\verb 1 ,\verb 2 ,\verb 3  \\ \hline
  real & A real decimal number. & \verb 1.0 , \verb 5.48 , \verb 12345.6789  \\ \hline
  pair & A pair of real numbers or integers. & \verb (0,2) , \verb (-30,42.5)  \\ \hline
  triple & An ordered triple of numbers. & \verb (1,2,3) , \verb (-2.5,5,4) \\ \hline
  path & A fixed cubic spline. & \verb1(0,0)--(5,0)1 \\
    & & \verb2(0,1)..(1,0)..(1,1)--cycle2 \\ \hline
  guide & A cubic spline, like path, & \verb1(0,0)--(5,0)1 \\ 
   & but free to adjust for smoothness & \verb2(0,1)..(1,0)..(1,1)--cycle2 \\
   &  if joined to another guide. & \verb2(0,1)--(1,0)--(1,1)--cycle2 \\\hline
  picture & A canvas for drawing  & \verb1currentpicture1, \\
  & in user coordinates.& any set of objects\\\hline
  frame & A canvas for drawing & \verb1currentpicture1,\\
  & in PostScript coordinates.& any set of objects\\\hline
  pen & An object consisting of a color, & \verb1currentpen1, \verb1red+dashed1,\\ 
  & thickness, and dash pattern & \verb1linetype("6 4")1\\
  & used for drawing & \\\hline
  transform & A transformation of the plane & \verb1scale(2)1, \verb1xscale(2)1, \\
   & that can be applied using * to & \verb1rotate(30)1, \verb1rotate(30,(2,3))1, \\
   & any object that can be drawn. & \verb1shift((2,4))1 \\\hline
  void & Used for declaration of functions& \\
   & having no arguments. & \\ \hline
  
 \end{tabular}

\subsection{Size and Unitsize}
 Asymptote is a primarily coordinate-based graphics language.  Each point is a pair  where  is the -coordinate and  is the -coordinate.
 \par However, there are many ways to choose a Cartesian coordinate system for the plane; one must pick the placement of origin and the scale on each of the - and -axes.  Asymptote will place your image in the center of your output page after it is drawn, so placement of origin is actually irrelevant.  By default, the unit length in both the  and  directions is the PostScript bigpoint, which has length  inches.  Thus, if you do not change the scaling on the picture, the points  and  are exactly one inch apart when drawn in Asymptote.  However, drawing in bigpoints is inconvenient if you wish to draw a figure that is exactly 3cm wide.
 \par The function \verb1unitsize1 can be used to specify the unit length for your picture.  This function takes up to 3 arguments: the picture you want to scale the axes for (if this isn't specified, it defaults to \verb1currentpicture1, the picture you are drawing on), the unit length in the x direction, and the unit length in the y direction.  If only one real argument is given, both the x and y unit sizes are set to this number.  Thus the command \\
 \verb&    unitsize(72); &\\

will tell Asymptote that from now on, your unit length is inch. Be careful when you are redefining your unit length - now that unitsize is set to , the points and are actually inches apart! \par Asymptote has the built-in constants \verb1pt1 (1/72.27 inches), \verb1inch1, \verb1cm1, and \verb1mm1 for convenience when defining lengths, so the above command can also be stated:\\ \verb& unitsize(1inch);& \par The other useful function is \verb1size1, which specifies the exact width and height that your picture (if unspecified as a first argument, this will again default to \verb1currentpicture1) will be drawn to. If only one number is given, that will be the width of the picture and the height will be left free to scale as necessary to keep the x- and y- unit sizes the same. For example, the command \\ \verb& size(5cm,5cm);& \\ will fit the diagram to a cmcm box regardless of the specified unitsizes. \par As an example, make an Asymptote document containing the following two lines: \begin{verbatim} unitsize(2inch); draw(unitsquare);\end{verbatim} and see what happens as you change the inch size to several other values.