Asymptote: Macros and Packages

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

Definitions

You can define your own functions in Asymptote as well. As an example, let's say you wanted to make a function called newfunction that takes a pair and a real value as input, and returns the pair . In addition, you want it to simply return the pair if no value of is specified, so you want to default to . The code would be as follows:

 pair newfunction(pair z, real r=0)
 {
  real a,b;
  a=z.x;
  b=z.y;
  return (a+r,b+r);
 }

Put this definition in an asymptote document and then test it using some command like

draw(newfunction((20,30))--newfunction((20,30),30)--(0,0)--cycle);  

See if it works!

Notice that the function must be declared a pair since it returns a pair, and each of the variables must be declared some data type too. The default value of was set to by , and the actual function procedure goes in between {}. This is the general format for a function definition.

Packages

 Asymptote comes with several packages that contain useful functions for various purposes.  For example, the package graph.asy contains the function 
 Circle(pair p, real r, int n=400);

which is a more accurate circle (having 400 nodes by default) than the built-in circle command. To use this function and others in graph.asy, simply put the command

include graph;

at the top of your Asymptote document.

You can create your own package by simply creating a new .asy file (say MyMacros.asy) with your own definitions in it, and saving it in the directory in which Asymptote is installed (C:\Program Files\Asymptote by default). Then include MyMacros; in your document, and you'll be set!

The Olympiad Package

   We have created an Olympiad package for Asymptote which includes macros for all the constructions that come up most often in Olympiad geometry problems!  You can obtain the package olympiad.asy by clicking [here], and saving the page as ``olympiad.asy in your Asymptote directory (\verb1C:\Program Files\Asymptote1 by default).  This package includes the following definitions:
   \begin{table}[H]
   \begin{center}
    \begin{tabular}{|l|l|} \hline

\textbf{Command} & \textbf{Description} \\ \hline \verb1origin1 & The pair \verb1(0,0)1. \\\hline \verb1waypoint(path p, real r)1 & The point of the way along\\ & path p with respect to length, \\ & where . \\\hline \verb1midpoint(path p)1 & The midpoint of path p. \\\hline \verb1foot(pair P, A, B)1 & The foot of the perpendicular\\ & from point to line .\\\hline \verb1bisectorpoint(pair A, B, C)1 & A point on the angle bisector \\ & of that is a unit \\ & distance from . \\\hline \verb1bisectorpoint(pair A, B)1 & A point on the perpendicular \\ & bisector of segment AB that is \\ & a unit distance from line AB. \\\hline

     \end{tabular}
   \caption{Useful points defined in the olympiad.asy package}
   \end{center}
   \end{table}
   
   \begin{table}[H]
   \begin{center}
    \begin{tabular}{|l|l|} \hline

\textbf{Command} & \textbf{Description} \\ \hline \verb1circumcenter(pair A, B, C)1 & The circumcenter of .\\\hline \verb1circumradius(pair A, B, C)1 & The circumradius of .\\\hline \verb1circumcircle(pair A, B, C)1 & The circumcircle of .\\\hline \verb1incenter(pair A, B, C)1 & The incenter of .\\\hline \verb1inradius(pair A, B, C)1 & The inradius of .\\\hline \verb1incircle(pair A, B, C)1 & The incircle of .\\\hline \verb~tangent(pair P, pair O,~ & The nth point of tangency\\ \verb~ real r, int n=1)~ & from a point P to the circle\\ & with center O and radius r\\ & where n can be 1 or 2 -\\ & the points of tangency are\\ & labeled in counterclockwise\\ & order around the circle.\\\hline \verb1cyclic(pair A, B, C, D)1 & A boolean function that\\ & returns true if ABCD is \\ & a cyclic quadrilateral.* \\\hline

     \end{tabular}
   \caption{Circle-related definitions in the olympiad.asy package}
   \end{center}
   \end{table}
   
   \begin{table}[H]
   \begin{center}
    \begin{tabular}{|l|l|} \hline

\textbf{Command} & \textbf{Description} \\ \hline \verb1concurrent(pair A, B, C, D, E, F)1 & A boolean function that\\ & returns true if AB, CD, EF are \\ & concurrent or mutually parallel.* \\\hline \verb1collinear(pair A, B, C)1 & A boolean function that\\ & returns true if A, B, and \\ & C are collinear. \\\hline

     \end{tabular}
   \caption{Collinearity and concurrency from the olympiad.asy package}
   \end{center}
   \end{table}
   
   \begin{table}[H]
   \begin{center}
    \begin{tabular}{|l|l|} \hline

\textbf{Command} & \textbf{Description} \\ \hline \verb1centroid(pair A, B, C)1 & The centroid of .\\\hline \verb1orthocenter(pair A, B, C)1 & The orthocenter of . \\\hline

     \end{tabular}
   \caption{Triangle-related definitions in the olympiad.asy package}
   \end{center}
   \end{table}\\
   \begin{table}[H]
   \begin{center}
    \begin{tabular}{|l|l|} \hline

\textbf{Command} & \textbf{Description} \\ \hline \verb1rightanglemark(pair A, B, C, 1 & Marks right angle ABC with\\ \verb1 real s=8)1 & a right angle mark of length s\\\hline \verb1anglemark(pair A, B, C, 1 & Marks angle ABC with several\\ \verb~ real t=8 ... real[] s)~ & circular arcs of radii specified\\ & in the last argument, an array \\ & of real values. \\\hline \verb~pathticks(path g, int n=1,~ & Marks path g with n ticks spaced\\ \verb~ real r=.5, spacing=6, s=8)~ & spacing apart with length s, at\\ & the point r of the way along g \\ & with respect to arc length. \\\hline

     \end{tabular}
   \caption{Tick marks and angle marks in the olympiad.asy package}
   \end{center}
   \end{table}

Note: A sequence of variables without type declarations indicates that they are the same type as the variable preceding it. For example, the notation concurrent(pair A, B, C, D, E, F) indicates that all of the variables should have type pair.

These boolean functions test for equality within ps points in order to avoid approximation errors.