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<h1>Functions</h1>

<h3>Arithmetic operators and functions</h3>
<dl>
<dt><code>+</code></dt>
<dt><code>-</code></dt>
<dt><code>*</code></dt>
<dt><code>div</code> (division)</dt>
<dt><code>mod</code></dt>
<dt><code>sqrt</code> (square root)</dt>
<dt><code>log</code></dt>
<dt><code>exp</code></dt>
<dt><code>trunc</code> (convert real to integer)</dt>
<dt><code>float</code> (convert an integer to real)</dt>
<dt><code>rand</code> (random number generator)</dt>
<dd>- <code>int rand(int)</code> or <code>real rand(real)</code>
<br>if the argument is an
integer, say <code>10</code>, <code>rand(10)</code> returns
a random number ranged from <code>0</code> to <code>9</code>
inclusive;
<br> if the argument is a real, say <code>1.0</code>, <code>rand(1.0)</code> returns a random
number ranged from <code>0.0</code> to <code>1.0</code> inclusive.
</dd></dl>

<h3>Trigonometric functions</h3>
<dl>
<dt><code>sin</code></dt>
<dt><code>cos</code></dt>
<dt><code>tan</code></dt>
<dt><code>asin</code></dt>
<dt><code>acos</code></dt>
<dt><code>atan</code></dt>
<dd>- accept only real arguments</dd>
</dl>
<h3>Relational operators</h3>
<dl>
<dt><code>&amp;&amp;</code> (and)</dt>
<dt><code>||</code> (or)</dt>
<dt><code>!</code> (not)</dt>
<dt><code>&lt;</code></dt>
<dt><code>&lt;=</code></dt>
<dt><code>==</code> (equal)</dt>
<dt><code>&gt;</code></dt>
<dt><code>&gt;=</code></dt>
</dl>

<h3>Geometric functions</h3>
<dl><dt><code>point midpoint(line)</code></dt>
<dd>- mid-point of a line</dd>
<dt><code>point intersect(line, line)</code></dt>
<dd>- intersection point of two lines
</dd>
<dt><code>line perpend(point, line)</code></dt>
<dd>- the perpendicular line intersecting the point</dd>
<dt><code>real dist(point, point)</code></dt>
<dd>- distance between two points</dd>
<dt><code>bool intersects(line, line)</code></dt>
<dd>- whether the lines intersect</dd>
<dt><code>bool separates(line, point, point)</code></dt>
<dd>- whether the line separates the two points</dd>
<dt><code>bool includes(circle, point)</code></dt>
<dd>- whether the point is inside the circle</dd>
<dt><code>bool incident(line, point)</code></dt>
<dt><code>bool incident(circle, point)</code></dt>
<dd>- whether the point coincides with the path</dd>
<dt><code>bool pt_betwn_pts(point, point, point)</code></dt>
<dd>- whether the 2nd point is within the box bounding the 1st and the
3rd point</dd>
<dt><code>bool colinear(point, point, point)</code></dt>
<dd>- whether the points are colinear</dd>
<dt><code>bool distlarger(point, point, value)</code></dt>
<dt><code>bool distlarger(line, point, value)</code></dt>
<dt><code>bool distsmaller(point, point, value)</code></dt>
<dt><code>bool distsmaller(line, point, value)</code></dt>
<dd>- whether the distance from the point to the point/line is larger
than or smaller than the specified value</dd></dl>

<h3>Shape transformations</h3>
<dl>
<dt><code>trans(shape, x, y)</code></dt>
<dd>- translate a shape (or openshape)</dd>
<dt><code>scale(shape, ratio)</code></dt>
<dd>- scale a shape (or openshape) wrt the origin of the coordinate
system; would not change the font size or the image size of labels</dd>
<dt><code>rot(shape, point, angle)</code></dt>
<dd>- rotate a shape round a point by a certain angle</dd></dl>
<H3>String functions</H3>
<DL>
<dt><code>//</code></dt><dd>string concatenation</dd>
<dt><code>itos(int)</code></dt><dd>- integer to string conversion</dd>
<dt><code>rtos(real, format-string)</code></dt>
<dd>- real to string conversion. format-string would be as
required by the C function fprintf().</dd>
</DL>

<H3>Image functions</H3>
Example:
<PRE>%donald
real xscale, yscale
xscale, yscale = 0.8, 0.8

image zoom, source
source = I!ImageScale(I!ImageFile("gif", "logo.gif"), xscale, yscale)
zoom = I!ImageScale(I!ImageCut(source, 20, 0, 200 * xscale, 200 * yscale), 
	xscale, yscale)

label imgzoom, imgsrc
imgzoom = label(zoom, {500, 200})
imgsrc = label(source, {500, 700})</PRE>
The images are centred at the specified position (same for string labels).
I!<em>functionName</em> denotes a function returning an image.  This function
is translated to an Eden function named as <em>functionName</em>.  The arguments are
not fully type-checked, so may sometimes cause a problem.  Since this kind
of function does not need to be declared beforehand, DoNaLD can easily
be extended to make use of image filters chosen by the user. (See examples
in $PUBLIC/lib/tkeden/scout.init.e for examples of image filters.)

<h3>Other functions</h3>
<dl>
<dt><code>circle(center, radius)</code></dt>
<dt><code>ellipse(center, extreme_point1, extreme_point2)</code></dt>
<dt><code>rectangle(corner1, corner2)</code></dt>
<dt><code>label(string, position)</code></dt>
<dt><code>if</code> <em>boolean_expression</em> <code>then</code> <em>expr</em> <code>else</code> <em>expr</em></dt>
<dt><code>.1, .2</code></dt>
<dd>- 1st and 2nd points of a line or 1st and 2nd coordinate of a
point, for example:
<pre>
line l
l = [{0,0}, {100,100}]
point p
p = l.2		# i.e. {100,100}
real x
x = p.1		# i.e. 100
</pre></dd>
<dt>.x, .y</dt>
<dd>- the projection of a point onto the x- and y- axies, e.g.: 
<pre>point p, q
p = {100, 200}
q = p.x		# i.e. {100, 0}
</pre>
</dd></dl>

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