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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN">
<!-- Copyright (c) Christian OBRECHT 2001 -->
<html>
<head>
<title>Language description</title>
<meta http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<meta name="description" content="Language description">
<meta name="keywords" content="eukleides geometry tex latex language description">
<meta name="nameAutor" content="Christian OBRECHT">
</head>
<body>
<br>
<br>
<h1>Language description</h1>
<ul>
<li><a href="#Design">The design of the language</a>
<li><a href="#Numbers">Handling numbers</a>
<li><a href="#Vectors">Handling vectors</a>
<li><a href="#Points">Point valued functions</a>
<li><a href="#Lines">Line valued functions</a>
<li><a href="#Segments">Segment valued functions</a>
<li><a href="#Circles">Circle valued functions</a>
<li><a href="#Transformations">Geometrical transformation functions</a>
<li><a href="#Triangles">Defining triangles</a>
<li><a href="#Polygons">Defining polygons</a>
<li><a href="#Intersections">Determining intersection points</a>
<li><a href="#Interactive">Defining interactive variables</a>
<li><a href="#Graphic">General graphical commands</a>
<li><a href="#Drawing">Drawing commands</a>
<li><a href="#Concept%20index">Concept index</a>
<li><a href="#Command%20index">Command index</a>
</ul>
<h1><a name="Design">Design of the language</a></h1>
<p>An Eukleides source file can contain:
<ul>
<li>Comments, i.e. any text beginning with `%' and ending at the end of the line.
<li>Simple assignments, i.e. a variable name followed by `=' and an expression.
<li>Multiple assignments, i.e. a variable name list followed by a multiple assignment command (triangle assignment, polygon assignment
or intersection assignment).
<li>Graphical commands, i.e. parameter setting commands or drawing commands.
</ul>
<p>A variable name is a letter, possibly followed by any letter or digit. Warning: Eukleides is case sensitive.
An expression can have several type of values : number, vector, line, segment, circle.
A line of the source file can contain a unique assignment or command. It can also contain several ones, in this case they must be
separed by semicolons. (No semicolon at the end of the line.)
<p>We'll use the following notations (possibly followed by a digit) to describe the possible types of the parameters in a command:
<ul>
<li><var>x</var>, <var>y</var>, <var>z</var>: number.
<li><var>ang</var> : angle measure.
<li><var>A</var>, <var>B</var>, <var>C</var>, <var>D</var>, <var>E</var>, <var>F</var>, <var>G</var>: point.
<li><var>u</var>, <var>v</var>: vector.
<li><var>l</var>: line.
<li><var>s</var>: segment.
<li><var>cir</var>: circle.
<li><var>str</var>: string.
<li><var>flg</var>: flag.
</ul>
<p>An angle measure is a number expression followed by `:' (degrees) or `<' (radians).
A string is any text contained in one line and enclosed in double quotes.
<p>We'll use square brackets to indicate optional parameters.
<h1><a name="Numbers">Handling numbers and number valued functions</a></h1>
<p>To compute usual arithmetic operations, use the symbols : `(', `)', `+', `-', `*', `/', `^' (for exponentiation).
<p>Here are all the number valued functions:
<ul>
<li><code>sqrt(<var>x</var>)</code>
<li><code>pi</code>
<li><code>sin(<var>x</var>)</code>
<li><code>cos(<var>x</var>)</code>
<li><code>tan(<var>x</var>)</code>
<li><code>asin(<var>x</var>)</code>
<li><code>acos(<var>x</var>)</code>
<li><code>atan(<var>x</var>)</code>
<li><code>deg(<var>x</var>)</code>
<li><code>rad(<var>x</var>)</code>
<li><code>abscissa(<var>A</var>)</code> or <code>abscissa(<var>u</var>)</code>
<li><code>ordinate(<var>A</var>)</code> or <code>ordinate(<var>u</var>)</code>
<li><code>distance(<var>A</var>, <var>B</var>)</code> or <code>distance(<var>A</var>, <var>l</var>)</code>
<li><code>length(<var>u</var>)</code> or <code>length(<var>s</var>)</code>
<li><code>radius(<var>cir</var>)</code>
<li><code>height(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Distance between point <var>B</var> and line (<var>AC</var>).
<li><code>angle(<var>u</var>)</code> or <code>angle(<var>l</var>)</code> or <code>angle(<var>s</var>)</code><br>
Argument of the object, i.e. measure of the angle between the object and the horizontal direction.
<li><code>angle(<var>u</var>, <var>v</var>)</code><br>
Measure of the angle between vector <var>u</var> and vector <var>v</var>.
<li><code>angle(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Measure of the angle under <var>ABC</var>.
</ul>
<h1><a name="Vectors">Handling vectors</a></h1>
<p>To compute usual vector operations, use the symbols : `(', `)', `+', `-', `*' (multiply by a number), `/' (divide by a number).
To compute the scalar product of two vectors, use the symbol : `*'.
<p>Here are all the vector valued functions:
<ul>
<li><code>vector(<var>x</var>, <var>y</var>)</code><br>
Vector of abscissa <var>x</var> and ordinate <var>y</var>.
<li><code>vector(<var>x</var>, <var>ang</var>)</code><br>
Vector of length <var>x</var> and argument <var>ang</var>.
<li><code>vector(<var>A</var>, <var>B</var>)</code><br>
Vector from point <var>A</var> to point <var>B</var>.
<li><code>vector(<var>l</var>)</code><br>
Unit length vector with same direction than line <var>l</var>.
<li><code>vector(<var>s</var>)</code><br>
Vector from begin of segment <var>s</var> to end of <var>s</var>.
<li><code>rotation(<var>u</var>, <var>ang</var>)</code><br>
</ul>
<h1><a name="Points">Point valued functions</a></h1>
<p>Here are all the point valued functions, except <a href="#Transformations">transformations</a>.
<ul>
<li><code>point(<var>x</var>, <var>y</var>)</code><br>
Point of abscissa <var>x</var> and ordinate <var>y</var>.
<li><code>point(<var>x</var>, <var>ang</var>)</code><br>
Point of radial coordinate <var>x</var> and argument <var>ang</var>.
<li><code>point(<var>l</var>, <var>x</var>)</code><br>
Point of abscissa <var>x</var> on the graduated line <var>l</var>.
<li><code>point(<var>s</var>, <var>x</var>)</code><br>
Point of abscissa <var>x</var> on the graduated line containing <var>s</var> (the origin is set to the begin of <var>s</var>).
<li><code>point(<var>cir</var>, <var>ang</var>)</code><br>
Point of argument <var>ang</var> on circle <var>cir</var>.
<li><code>projection(<var>A</var>, <var>l1</var> [, <var>l2</var>])</code><br>
Projection of point <var>A</var> on line <var>l1</var> in direction of line <var>l2</var> (default: in perpendicular direction of line <var>l1</var>).
<li><code>barycenter(<var>A</var> [, <var>x</var>], <var>B</var> [, <var>y</var>])</code><br>
Barycenter of <var>A</var> and <var>B</var> with coefficient <var>x</var> and <var>y</var> (default: 1 and 1). Similar syntax for 3 or 4 points.
<li><code>intersection(<var>l1</var>, <var>l2</var>)</code><br>
Intersection point of lines <var>l1</var> and <var>l2</var>.
<li><code>abscissa(<var>l</var>, <var>x</var>)</code><br>
Point of abscissa <var>x</var> on line <var>l</var>.
<li><code>ordinate(<var>l</var>, <var>y</var>)</code><br>
Point of ordinate <var>y</var> on line <var>l</var>.
<li><code>midpoint(<var>s</var>)</code>
<li><code>begin(<var>s</var>)</code>
<li><code>end(<var>s</var>)</code>
<li><code>center(<var>cir</var>)</code>
<li><code>orthocenter(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Orthocenter of triangle <var>ABC</var>.
</ul>
<h1><a name="Lines">Line valued functions</a></h1>
<p>Here are all the line valued functions, except <a href="#Transformations">transformations</a>.
<ul>
<li><code>line(<var>A</var>, <var>B</var>)</code>
<li><code>line(<var>A</var>, <var>u</var>)</code>
<li><code>line(<var>s</var>)</code>
<li><code>line(<var>A</var>, <var>ang</var>)</code><br>
Line containing point <var>A</var> with argument <var>ang</var>.
<li><code>line(<var>cir</var>, <var>ang</var>)</code><br>
Tangent line of circle <var>cir</var> containing point of argument <var>ang</var>.
<li><code>parallel(<var>l</var>, <var>A</var>)</code> or <code>parallel(<var>s</var>, <var>A</var>)</code>
<li><code>perpendicular(<var>l</var>, <var>A</var>)</code> or <code>perpendicular(<var>s</var>, <var>A</var>)</code>
<li><code>bisector(<var>s</var>)</code><br>
Perpendicular bisector of segment <var>s</var>.
<li><code>bisector(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Bissector of angle under <var>ABC</var>.
<li><code>altitude(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Altitude of triangle <var>ABC</var> containing point <var>A</var>.
<li><code>median(<var>s</var>)</code>
</ul>
<h1><a name="Segments">Segment valued functions</a></h1>
<p>Here are all the segment valued functions, except <a href="#Transformations">transformations</a>.
<ul>
<li><code>segment(<var>A</var>, <var>B</var>)</code>
<li><code>segment(<var>A</var>, <var>u</var>)</code>
<li><code>segment(<var>A</var>, <var>x</var>, <var>ang</var>)</code><br>
Segment of length <var>x</var> and argument <var>ang</var>, beginning with <var>A</var>.
<li><code>segment(<var>cir</var>, <var>ang</var>)</code><br>
Segment from center of circle <var>cir</var> to point of argument <var>ang</var>.
</ul>
<h1><a name="Circles">Circle valued functions</a></h1>
<p>Here are all the circle valued functions, except <a href="#Transformations">transformations</a>.
<ul>
<li><code>circle(<var>A</var>, <var>B</var>)</code><br>
Circle of diameter [<var>AB</var>]
<li><code>circle(<var>A</var>, <var>B</var>, <var>C</var>)</code><br>
Circumcircle of triangle <var>ABC</var>.
<li><code>circle(<var>A</var>, <var>x</var>)</code><br>
Circle of center <var>A</var> and radius <var>x</var>.
<li><code>incircle(<var>A</var>, <var>B</var>, <var>C</var>)</code>
</ul>
<h1><a name="Transformations">Geometrical transformation functions</a></h1>
<p>We'll note <var>obj</var> an object which can be a point, a line, a segment or a circle.
<p>Here are all the transformation functions:
<ul>
<li><code>translation(<var>obj</var>, <var>u</var>)</code>
<li><code>reflection(<var>obj</var>, <var>l</var>)</code>
<li><code>rotation(<var>obj</var>, <var>A</var> [, <var>ang</var>])</code><br>
Rotation of center <var>A</var> and angle <var>ang</var> (default: 180 degrees).
<li><code>homothecy(<var>obj</var>, <var>A</var>, <var>x</var>)</code><br>
Homothecy, i.e. expansion or dilation, of center <var>A</var> and ratio <var>x</var>.
</ul>
<h1><a name="Triangles">Defining triangles</a></h1>
<p>A triangle assignment is a list of 3 variable names followed by the word <code>triangle</code>, <code>right</code>, <code>isosceles</code>
or <code>equilateral</code> and some optional parameters. If the first variable is already defined as a point, the triangle will be
constructed from this point. If not, the point will be set to origin.
<p>Here are all the ways to define a triangle:
<ul>
<li><code><var>A</var> <var>B</var> <var>C</var> triangle[(<var>x</var> [ , <var>ang</var>])]</code><br>
Defines a scalenes triangle with <var>AB</var> = <var>x</var> (default: 6). The triangle is an optimal scalenes triangle.
<li><code><var>A</var> <var>B</var> <var>C</var> triangle(<var>x</var>, <var>y</var>, <var>z</var> [ , <var>ang</var>])</code><br>
Defines a scalenes triangle with <var>AB</var> = <var>x</var>, <var>BC</var> = <var>y</var> and <var>CA</var> = <var>z</var>.
<li><code><var>A</var> <var>B</var> <var>C</var> triangle(<var>x</var>, <var>ang1</var>, <var>ang2</var> [ , <var>ang3</var>])]</code><br>
Defines a scalenes triangle with <var>AB</var> = <var>x</var>, measure of the angle under <var>BAC</var> equals <var>ang1</var>, measure of the angle under
<var>CBA</var> equals <var>ang2</var>.
<li><code><var>A</var> <var>B</var> <var>C</var> right[(<var>x</var>, <var>y</var> [ , <var>ang</var>])]</code><br>
Defines a right triangle (right angle in <var>A</var>) with <var>AB</var> = <var>x</var> and <var>AC</var> = <var>y</var> (default: 6 and 4.5).
<li><code><var>A</var> <var>B</var> <var>C</var> right(<var>x</var>, <var>ang1</var> [ , <var>ang2</var>])</code><br>
Defines a right triangle (right angle in <var>B</var>) with <var>AB</var> = <var>x</var> and measure of the angle under <var>BAC</var> equals <var>ang1</var>.
<li><code><var>A</var> <var>B</var> <var>C</var> isosceles[(<var>x</var>, <var>ang1</var> [ , <var>ang2</var>])]</code><br>
Defines an isosceles triangle with <var>AB</var> = <var>x</var> and measure of the angle under <var>BAC</var> or <var>CBA</var> equals <var>ang1</var>
(default: 6 and 39 degrees).
<li><code><var>A</var> <var>B</var> <var>C</var> isosceles(<var>x</var>, <var>y</var> [ , <var>ang</var>])</code><br>
Defines an isosceles triangle with <var>AB</var> = <var>x</var> and <var>AC</var> = <var>CB</var> = <var>y</var>.
<li><code><var>A</var> <var>B</var> <var>C</var> equilateral[(<var>x</var> [ , <var>ang</var>])]</code><br>
Defines an equilateral triangle of side length <var>x</var> (default: 6).
</ul>
<p><em>Note</em>: The last optional parameter is the argument of segment [<var>AB</var>] (default: 0 degrees).
<h1><a name="Polygons">Defining polygons</a></h1>
<p>A quadrilateral assignment is a list of 4 variable names followed by the word <code>parallelogram</code>, <code>rectangle</code> or <code>square</code>
and some optional parameters. If the first variable is already defined as a point, the quadrilateral will be constructed from this point.
If not, the point will be set to origin.
<p>Here are all the ways to define a quadrilateral:
<ul>
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> parallelogram[(<var>x</var>, <var>y</var>, <var>ang1</var> [ , <var>ang2</var>])]</code><br>
Defines a parallelogram with <var>AB</var> = <var>x</var>, <var>AD</var> = <var>y</var> and angle under <var>BAD</var> equals <var>ang1</var> (default: 5, 4 and
75 degrees).
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> parallelogram(<var>u</var>, <var>v</var> [ , <var>ang</var>])</code><br>
Defines a parallelogram with vector from <var>A</var> to <var>B</var> equals =<var>u</var> and vector from <var>A</var> to <var>D</var> equals <var>v</var>.
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> rectangle[(<var>x</var>, <var>y</var> [ , <var>ang</var>])]</code><br>
Defines a rectangle with <var>AB</var> = <var>x</var> and <var>AD</var> = <var>y</var> (default: 6 and 6 / `golden ratio').
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> square[(<var>x</var> [ , <var>ang</var>])]</code><br>
Defines a square with <var>AB</var> = <var>x</var> (default: 4).
</ul>
<p><em>Note</em>: The last optional parameter is the argument of segment [<var>AB</var>] (default: 0 degrees).
<p>A pentagon assignment is the following command:
<ul>
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> <var>E</var> pentagon(<var>F</var>, <var>x</var>, <var>ang</var>)</code>
</ul>
<p>It defines a pentagon of center <var>F</var>, radius <var>x</var> and such as argument of segment [<var>OA</var>] equals <var>ang</var>.
<p>An hexagon assignment is the following command:
<ul>
<li><code><var>A</var> <var>B</var> <var>C</var> <var>D</var> <var>E</var> <var>F</var> hexagon(<var>G</var>, <var>x</var>, <var>ang</var>)</code>
</ul>
<p>It defines an hexagon of center <var>G</var>, side length <var>x</var> and such as argument of segment [<var>OA</var>] equals <var>ang</var>.
<h1><a name="Interactive">Interactive assignments</a></h1>
<p>An interactive assignment is the following command:
<ul>
<li><code><var>x</var> interactive(<var>y</var>, <var>z</var>, [ <var>x1</var> , <var>x2</var> , ] <var>str</var>, <var>flg</var>)</code>
</ul>
<p>With <code>eukleides</code>, variable <var>x</var> is simply set to number <var>y</var>.<br>
With <code>xeukleides</code>, it allows, while viewing, to modify the value of the numerical variable <var>x</var> using the arrow keys. The initial value
of <var>x</var> is <var>y</var>, the increment is <var>z</var>. The optional parameters <var>x1</var> and <var>x2</var> are the lower and upper bound of <var>x</var>.
The string <var>str</var> has to contain one uppercase letter. To modify <var>x</var>, one has to press first the corresponding key (at the beginning,
the default state is `A'). The permitted values of <var>flg</var> are <code>right</code> (in this case, <var>x</var> will be incremented by pressing the
right arrow key and decremented by pressing the left arrow key) or <code>up</code> (in this case, <var>x</var> will be incremented by pressing the up
arrow key and decremented by pressing the down arrow key).
<h1><a name="Intersections">Intersection points</a></h1>
<p>Intersection assignments are:
<ul>
<li><code><var>A</var> <var>B</var> intersection(<var>l</var>, <var>cir</var>)</code>
<li><code><var>A</var> <var>B</var> intersection(<var>cir1</var>, <var>cir2</var>)</code>
</ul>
<p>If the two object are tangent, the two variables will be set to the same point.
<h1><a name="Graphic">General graphical commands</a></h1>
<p>The purpose of general graphical commands is mainly to set some general parameters.<br>
<p>Here are all of them:
<ul>
<li><code>frame(<var>x1</var>, <var>y1</var>, <var>x2</var>, <var>y2</var> [ , <var>z</var>])</code><br>
Sets the visible frame. The lower-left corner has coordinates (<var>x1</var>, <var>y1</var>) and the upper-right corner (<var>x2</var>, <var>y2</var>).
With <code>eukleides</code>, the optional parameter set the unit length to <var>z</var> cm (default: 1). With <code>xeukleides</code>, this parameter
has no effect, because the figure is always drawn using the largest scale such that it fits into the drawing area. If no frame is specified
it is set to default frame: (-2, -2, 8, 6).
<li><code>color(<var>flg</var>)</code><br>
Sets color to <var>flg</var>. Permitted values of <var>flg</var> are black (default), darkgray, gray, lightgray, white, red, green, blue, cyan, magenta
and yellow.
<li><code>color <var>str</var></code><br>
With <code>eukleides</code>, sets color to <var>str</var> (it has to be a valid pstricks color). With <code>xeukleides</code>, it has no effect.
<li><code>tricks <var>str</var></code><br>
With <code>eukleides</code>, adds an initial `\' to <var>str</var> and puts it verbatim to the output. It has to be valid TeX code. You can use it to define your own
colors, draw a curve, etc. With <code>xeukleides</code>, it has no effect.
<li><code>font <var>str</var></code><br>
With <code>xeukleides</code>, changes current font. String <var>str</var> has to be a valid XLFD. With <code>eukleides</code>, it has no effect.
</ul>
<h1><a name="Drawing">Drawing commands</a></h1>
<p>Here are all the drawing commands.
<ul>
<li><code>draw(<var>A</var> [ , <var>flg</var>])</code><br>
Draws point <var>A</var> with a shape corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>dot</code>, <code>box</code>, <code>cross</code>
and <code>plus</code> (default: dot).
<li><code>draw(<var>u</var>, <var>A</var> [ , <var>flg</var>])</code><br>
Draws vector <var>u</var> from point <var>A</var> with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>,
<code>dashed</code> and <code>dotted</code> (default: full).
<li><code>draw(<var>l</var> [ , <var>flg1</var> [ , <var>flg2</var>]])</code><br>
Draws line <var>l</var> with an aspect corresponding to <var>flg1</var> and <var>flg2</var>. Permitted values of <var>flg1</var> are <code>full</code>,
<code>dashed</code> and <code>dotted</code> (default: full). Permitted values of <var>flg2</var> are <code>entire</code>, <code>halfline</code> and <code>backhalfline</code>
(default: entire).
<li><code>draw(<var>s</var> [ , <var>flg1</var> [ , <var>flg2</var>]])</code><br>
Draws segment <var>s</var> with an aspect corresponding to <var>flg1</var> and <var>flg2</var>. Permitted values of <var>flg1</var> are <code>full</code>,
<code>dashed</code> and <code>dotted</code> (default: full). Permitted values of <var>flg2</var> are <code>noarrow</code>, <code>arrow</code>, <code>backarrow</code> and
<code>doublearrow</code> (default: noarrow).
<li><code>draw(<var>cir</var> [ , <var>flg</var>])</code><br>
Draws circle <var>cir</var> with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>, <code>dashed</code> and
<code>dotted</code> (default: full).
<li><code>draw(<var>cir</var>, <var>ang1</var>, <var>ang2</var>, [ , <var>flg1</var> [ , <var>flg2</var>]])</code><br>
Draws an arc of circle <var>cir</var> from point of argument <var>ang1</var> to point of argument <var>ang2</var>, with an aspect corresponding to
<var>flg1</var> and <var>flg2</var>. Permitted values of <var>flg1</var> are <code>full</code>, <code>dashed</code> and <code>dotted</code> (default: full). Permitted
values of <var>flg2</var> are <code>noarrow</code>, <code>arrow</code>, <code>backarrow</code> and <code>doublearrow</code> (default: noarrow).
<li><code>draw(<var>A</var>, <var>B</var>, <var>C</var>, [ , <var>flg</var>])</code><br>
Draws a triangle with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>, <code>dashed</code> and <code>dotted</code>
(default: full).
<li><code>draw(<var>A</var>, <var>B</var>, <var>C</var>, <var>D</var> [ , <var>flg</var>])</code><br>
Draws a quadrilateral with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>, <code>dashed</code> and
<code>dotted</code> (default: full).
<li><code>draw(<var>A</var>, <var>B</var>, <var>C</var>, <var>D</var>, <var>E</var>, [ , <var>flg</var>])</code><br>
Draws a pentagon with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>, <code>dashed</code> and <code>dotted</code>
(default: full).
<li><code>draw(<var>A</var>, <var>B</var>, <var>C</var>, <var>D</var>, <var>E</var>, <var>F</var> [ , <var>flg</var>])</code><br>
Draws an hexagon with an aspect corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>full</code>, <code>dashed</code> and <code>dotted</code>
(default: full).
<li><code>draw(<var>str</var>, <var>A</var>, [ <var>x</var>, ] <var>ang</var>)</code><br>
Prints the text contained in <var>str</var> at a distance <var>x</var> (default: .3) and with argument <var>ang</var> from point <var>A</var>.
<li><code>draw(<var>str</var>, <var>s</var>, [ <var>x</var>, ] <var>ang</var>)</code><br>
Prints the text contained in <var>str</var> at a distance <var>x</var> (default: .3) and with argument <var>ang</var> from the midpoint of segment <var>s</var>.
<li><code>draw(<var>x</var>, [<var>str</var>, ] <var>A</var>, [ <var>y</var>, ] <var>ang</var>)</code><br>
Prints the value of <var>x</var> optionaly formated with <var>str</var> (using the C-language syntax) at a distance <var>y</var> (default: .3) and with
argument <var>ang</var> from point <var>A</var>.
<li><code>draw(<var>x</var>, [<var>str</var>, ] <var>s</var>, [ <var>y</var>, ] <var>ang</var>)</code><br>
Prints the value of <var>x</var> optionaly formated with <var>str</var> (using the C-language syntax) at a distance <var>y</var> (default: .3) and with
argument <var>ang</var> from the midpoint of segment <var>s</var>.
<li><code>draw(<var>x1</var>, <var>x2</var>, <var>str</var>, <var>A</var>, [ <var>y</var>, ] <var>ang</var>)</code><br>
Prints the values of <var>x1</var> and <var>x2</var> formated with <var>str</var> (using the C-language syntax) at a distance <var>y</var> (default: .3) and with
argument <var>ang</var> from point <var>A</var>.
<li><code>draw(<var>x1</var>, <var>x2</var>, <var>str</var>, <var>s</var>, [ <var>y</var>, ] <var>ang</var>)</code><br>
Prints the values of <var>x1</var> and <var>x2</var> formated with <var>str</var> (using the C-language syntax) at a distance <var>y</var> (default: .3) and with
argument <var>ang</var> from the midpoint of segment <var>s</var>.
<li><code>mark(<var>s</var> [ , <var>flg</var>])</code><br>
Marks the segment <var>s</var> with a symbol corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>simple</code>, <code>double</code>,
<code>triple</code> and <code>cross</code> (default: simple).
<li><code>mark(<var>A</var>, <var>B</var>, <var>C</var> [ , <var>flg</var>])</code><br>
Marks the angle under <var>ABC</var> with a symbol corresponding to <var>flg</var>. Permitted values of <var>flg</var> are <code>simple</code>, <code>double</code>,
<code>triple</code>, <code>dash</code>, <code>arrow</code>, <code>backarrow</code> and <code>right</code> (default: simple).
</ul>
<h1><a name="Concept%20index">Concept index</a></h1>
<ul compact>
<li>angle measures: <a href="#Design">Design</a>
<li>argument: <a href="#Numbers">Numbers</a>
<li>arithmetic operations: <a href="#Numbers">Numbers</a>
<li>circle valued functions: <a href="#Circles">Circles</a>
<li>colors: <a href="#Graphic">Graphic</a>
<li>comments: <a href="#Design">Design</a>
<li>drawing commands: <a href="#Drawing">Drawing</a>
<li>equilateral: <a href="#Triangles">Triangles</a>
<li>fonts: <a href="#Graphic">Graphic</a>
<li>graduated line: <a href="#Points">Points</a>
<li>graphical commands: <a href="#Graphic">Graphic</a>
<li>graphical commands: <a href="#Design">Design</a>
<li>hexagon: <a href="#Polygons">Polygons</a>
<li>homothecy: <a href="#Transformations">Transformations</a>
<li>interactive: <a href="#Interactive">Interactive</a>
<li>intersection: <a href="#Intersections">Intersections</a>, <a href="#Points">Points</a>
<li>isosceles: <a href="#Triangles">Triangles</a>
<li>line valued functions: <a href="#Lines">Lines</a>
<li>multiple assignments: <a href="#Design">Design</a>
<li>notations: <a href="#Design">Design</a>
<li>number valued functions: <a href="#Numbers">Numbers</a>
<li>parallelogram: <a href="#Polygons">Polygons</a>
<li>pentagon: <a href="#Polygons">Polygons</a>
<li>point valued functions: <a href="#Points">Points</a>
<li>polygons: <a href="#Polygons">Polygons</a>
<li>pstricks: <a href="#Graphic">Graphic</a>
<li>quadrilateral: <a href="#Polygons">Polygons</a>
<li>rectangle: <a href="#Polygons">Polygons</a>
<li>reflection: <a href="#Transformations">Transformations</a>
<li>right: <a href="#Triangles">Triangles</a>
<li>rotation: <a href="#Transformations">Transformations</a>, <a href="#Vectors">Vectors</a>
<li>scalar product: <a href="#Vectors">Vectors</a>
<li>scalenes: <a href="#Triangles">Triangles</a>
<li>segment valued functions: <a href="#Segments">Segments</a>
<li>simple assignments: <a href="#Design">Design</a>
<li>square: <a href="#Polygons">Polygons</a>
<li>string: <a href="#Design">Design</a>
<li>transformation: <a href="#Transformations">Transformations</a>
<li>translation: <a href="#Transformations">Transformations</a>
<li>triangle: <a href="#Triangles">Triangles</a>
<li>values: <a href="#Design">Design</a>
<li>vector operations: <a href="#Vectors">Vectors</a>
<li>vector valued functions: <a href="#Vectors">Vectors</a>
</ul>
<h1><a name="Command%20index">Command index</a></h1>
<ul compact>
<li><code>abscissa</code>: <a href="#Points">Points</a>
<li><code>abscissa</code>: <a href="#Numbers">Numbers</a>
<li><code>acos</code>: <a href="#Numbers">Numbers</a>
<li><code>altitude</code>: <a href="#Lines">Lines</a>
<li><code>angle</code>: <a href="#Numbers">Numbers</a>
<li><code>asin</code>: <a href="#Numbers">Numbers</a>
<li><code>atan</code>: <a href="#Numbers">Numbers</a>
<li><code>barycenter</code>: <a href="#Points">Points</a>
<li><code>begin</code>: <a href="#Points">Points</a>
<li><code>bisector</code>: <a href="#Lines">Lines</a>
<li><code>center</code>: <a href="#Points">Points</a>
<li><code>circle</code>: <a href="#Circles">Circles</a>
<li><code>`-'</code>: <a href="#Vectors">Vectors</a>
<li><code>`-'</code>: <a href="#Numbers">Numbers</a>
<li><code>`/'</code>: <a href="#Vectors">Vectors</a>
<li><code>`/'</code>: <a href="#Numbers">Numbers</a>
<li><code>`^'</code>: <a href="#Numbers">Numbers</a>
<li><code>`*'</code>: <a href="#Vectors">Vectors</a>
<li><code>`*'</code>: <a href="#Numbers">Numbers</a>
<li><code>`+'</code>: <a href="#Vectors">Vectors</a>
<li><code>`+'</code>: <a href="#Numbers">Numbers</a>
<li><code>color</code>: <a href="#Graphic">Graphic</a>
<li><code>cos</code>: <a href="#Numbers">Numbers</a>
<li><code>deg</code>: <a href="#Numbers">Numbers</a>
<li><code>distance</code>: <a href="#Numbers">Numbers</a>
<li><code>draw</code>: <a href="#Drawing">Drawing</a>
<li><code>end</code>: <a href="#Points">Points</a>
<li><code>equilateral</code>: <a href="#Triangles">Triangles</a>
<li><code>font</code>: <a href="#Graphic">Graphic</a>
<li><code>frame</code>: <a href="#Graphic">Graphic</a>
<li><code>height</code>: <a href="#Numbers">Numbers</a>
<li><code>hexagon</code>: <a href="#Polygons">Polygons</a>
<li><code>homothecy</code>: <a href="#Transformations">Transformations</a>
<li><code>interactive</code>: <a href="#Interactive">Interactive</a>
<li><code>intersection</code>: <a href="#Intersections">Intersections</a>
<li><code>intersection</code>: <a href="#Points">Points</a>
<li><code>isosceles</code>: <a href="#Triangles">Triangles</a>
<li><code>length</code>: <a href="#Numbers">Numbers</a>
<li><code>line</code>: <a href="#Lines">Lines</a>
<li><code>mark</code>: <a href="#Drawing">Drawing</a>
<li><code>median</code>: <a href="#Lines">Lines</a>
<li><code>midpoint</code>: <a href="#Points">Points</a>
<li><code>ordinate</code>: <a href="#Points">Points</a>
<li><code>ordinate</code>: <a href="#Numbers">Numbers</a>
<li><code>orthocenter</code>: <a href="#Points">Points</a>
<li><code>parallel</code>: <a href="#Lines">Lines</a>
<li><code>parallelogram</code>: <a href="#Polygons">Polygons</a>
<li><code>pentagon</code>: <a href="#Polygons">Polygons</a>
<li><code>perpendicular</code>: <a href="#Lines">Lines</a>
<li><code>pi</code>: <a href="#Numbers">Numbers</a>
<li><code>point</code>: <a href="#Points">Points</a>
<li><code>projection</code>: <a href="#Points">Points</a>
<li><code>rad</code>: <a href="#Numbers">Numbers</a>
<li><code>radius</code>: <a href="#Numbers">Numbers</a>
<li><code>rectangle</code>: <a href="#Polygons">Polygons</a>
<li><code>reflection</code>: <a href="#Transformations">Transformations</a>
<li><code>right</code>: <a href="#Triangles">Triangles</a>
<li><code>rotation</code>: <a href="#Transformations">Transformations</a>
<li><code>rotation</code>: <a href="#Vectors">Vectors</a>
<li><code>segment</code>: <a href="#Segments">Segments</a>
<li><code>sin</code>: <a href="#Numbers">Numbers</a>
<li><code>sqrt</code>: <a href="#Numbers">Numbers</a>
<li><code>square</code>: <a href="#Polygons">Polygons</a>
<li><code>tan</code>: <a href="#Numbers">Numbers</a>
<li><code>translation</code>: <a href="#Transformations">Transformations</a>
<li><code>triangle</code>: <a href="#Triangles">Triangles</a>
<li><code>tricks</code>: <a href="#Graphic">Graphic</a>
<li><code>vector</code>: <a href="#Vectors">Vectors</a>
</ul>
<br>
</body></html>
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