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<h2>10. Describing locations
<a name="10. Describing locations"></a>
</h2>

The
location of points can be described in many different ways.
All these forms are interchangeable as for as the pic
language syntax is concerned; where you can use one, any of
the others that would make semantic sense are
allowed.

The
special label Here always refers to the current
position.

<h3>10.1. Absolute Coordinates
<a name="10.1. Absolute Coordinates"></a>
</h3>

The
simplest is absolute coordinates in inches; pic uses
a Cartesian system with (0,0) at the lower left corner of
the virtual drawing surface for each picture (that is,
X&nbsp;increases to the right and Y&nbsp;increases upwards).
An absolute location may always be written in the
conventional form as two comma-separated numbers surrounded
by parentheses (and this is recommended for clarity). In
contexts where it creates no ambiguity, the pair of X and
Y&nbsp;coordinates suffices without parentheses.

It is a
good idea to avoid absolute coordinates, however. They tend
to make picture descriptions difficult to understand and
modify. Instead, there are quite a number of ways to specify
locations relative to pic objects and previous
locations.

Another
possibility of surprise is the fact that pic crops
the picture to the smallest bounding box before writing it
out. For example, if you have a picture consisting of a
small box with its lower left corner at (2,2) and another
small box with its upper right corner at (5,5), the width
and height of the image are both 3&nbsp;units and
not&nbsp;5. To get the origin at (0,0) included, simply add
an invisible object to the picture, positioning the
object&rsquo;s left corner at (0,0).

<h3>10.2. Locations Relative to Objects
<a name="10.2. Locations Relative to Objects"></a>
</h3>

The symbol
Here always refers to the position of the last object
drawn or the destination of the last move.

Alone and
unqualified, a last circle or any other way of
specifying a closed-object or arc location refers as a
position to the geometric center of the object. Unqualified,
the name of a line or spline object refers to the position
of the object start.

Also,
pic objects have quite a few named locations
associated with them. One of these is the object center,
which can be indicated (redundantly) with the suffix
.center (or just .c). Thus, last circle
.center is equivalent to last circle.

<h4>10.2.1. Locations Relative to Closed Objects
<a name="10.2.1. Locations Relative to Closed Objects"></a>
</h4>

Every
closed object (box, circle, ellipse, or block composite)
also has eight compass points associated with it;

Figure
10-1: Compass points

these are
the locations where eight compass rays from the geometric
center would intersect the figure. So when we say last
circle .s we are referring to the south compass point of
the last circle drawn. The explanation of Figure 8-3&rsquo;s
program is now complete.

(In case
you dislike compass points, the names .top,
.bottom, .left and .right are synonyms
for .n, .s, .e, and .w
respectively; they can even be abbreviated to .t,
.b, .l and .r).

The names
center, top, bottom, left,
right, north, south, east, and
west can also be used (without the leading dot) in a
prefix form marked by of; thus, center of last
circle and top of 2nd last ellipse are both valid
object references. Finally, the names left and
right can be prefixed with upper and
lower which both have the obvious meaning.

Arc
objects also have compass points; they are the compass
points of the implied circle.

Non-closed
objects (line, arrow, or spline) have compass points too,
but the locations of them are completely arbitrary. In
particular, different pic implementations return
different locations.

<h4>10.2.2. Locations Relative to Open Objects
<a name="10.2.2. Locations Relative to Open Objects"></a>
</h4>

Every open
object (line, arrow, arc, or spline) has three named points:
.start, .center (or .c), and
.end. They can also be used without leading dots in
the of prefix form. The center of an arc is the
center of its circle, but the center of a line, path, or
spline is halfway between its endpoints.

Figure
10-2: Special points on open objects

<h3>10.3. Ways of Composing Positions
<a name="10.3. Ways of Composing Positions"></a>
</h3>

Once you
have two positions to work with, there are several ways to
combine them to specify new positions.

<h4>10.3.1. Vector Sums and Displacements
<a name="10.3.1. Vector Sums and Displacements"></a>
</h4>

Positions
may be added or subtracted to yield a new position (to be
more precise, you can only add a position and an expression
pair; the latter must be on the right side of the addition
or subtraction sign). The result is the conventional vector
sum or difference of coordinates. For example, last box
.ne + (0.1, 0) is a valid position. This example
illustrates a common use, to define a position slightly
offset from a named one (say, for captioning
purposes).

<h4>10.3.2. Interpolation Between Positions
<a name="10.3.2. Interpolation Between Positions"></a>
</h4>

A position
may be interpolated between any two positions. The syntax is
&lsquo;fraction of the way between
position1 and position2&rsquo;. For
example, you can say 1/3 of the way between Here and last
ellipse .ne. The fraction may be in
numerator/denominator form or may be an ordinary number
(values are not restricted to [0,1]). As an
alternative to this verbose syntax, you can say
&lsquo;fraction &lt;position1 ,
position2&gt;&rsquo;; thus, the example could
also be written as 1/3 &lt;Here, last
ellipse&gt;.

Figure
10-3: P: 1/3 of the way between last arrow .start and
last arrow .end

This
facility can be used, for example, to draw double
connections.

Figure
10-4: Doubled arrows

You can
get Figure 10-4 from the following program:

.PS
 
A: box &quot;yin&quot;; move; 
B: box &quot;yang&quot;; 
arrow right at 1/4 &lt;A.e,A.ne&gt;; 
arrow left at 1/4 &lt;B.w,B.sw&gt;; 
.PE

Note the
use of the short form for interpolating points.

<h4>10.3.3. Projections of Points
<a name="10.3.3. Projections of Points"></a>
</h4>

Given two
positions p and q, the position
(p, q) has the
X&nbsp;coordinate of p and the Y coordinate of
q. This can be helpful in placing an object at one of
the corners of the virtual box defined by two other
objects.

Figure
10-5: Using (x, y) composition

<h3>10.4. Using Locations
<a name="10.4. Using Locations"></a>
</h3>

There are
four ways to use locations; at, from,
to, and with. All four are object modifiers;
that is, you use them as suffixes to a drawing
command.

The
at modifier says to draw a closed object or arc with
its center at the following location, or to draw a
line/spline/arrow starting at the following
location.

The
to modifier can be used alone to specify a move
destination. The from modifier can be used alone in
the same way as at.

The
from and to modifiers can be used with a
line or arc command to specify start and end
points of the object. In conjunction with named locations,
this offers a very flexible mechanism for connecting
objects. For example, the following program

.PS
 
box &quot;from&quot; 
move 0.75; 
ellipse &quot;to&quot; 
arc cw from 1/3 of the way \ 
between last box .n and last box .ne to last ellipse .n;
 
.PE

yields:

Figure
10-6: A tricky connection specified with English-like
syntax

The
with modifier allows you to identify a named
attachment point of an object (or a position within the
object) with another point. This is very useful for
connecting objects in a natural way. For an example,
consider these two programs:

Figure
10-7: Using the with modifier for
attachments

<h3>10.5. The &lsquo;chop&rsquo; Modifier
<a name="10.5. The &lsquo;chop&rsquo; Modifier"></a>
</h3>

When
drawing lines between circles that don&rsquo;t intersect
them at a compass point, it is useful to be able to shorten
a line by the radius of the circle at either or both ends.
Consider the following program:

.PS
 
circle &quot;x&quot; 
circle &quot;y&quot; at 1st circle - (0.4, 0.6) 
circle &quot;z&quot; at 1st circle + (0.4, -0.6) 
arrow from 1st circle to 2nd circle chop 
arrow from 2nd circle to 3rd circle chop 
arrow from 3rd circle to 1st circle chop 
.PE

It yields
the following:

Figure
10-8: The chop modifier

Notice
that the chop attribute moves arrowheads rather than
stepping on them. By default, the chop modifier
shortens both ends of the line by circlerad. By
suffixing it with a number you can change the amount of
chopping.

If you say
line ... chop r1 chop r2 with
r1 and r2 both numbers, you can vary the
amount of chopping at both ends. You can use this in
combination with trigonometric functions to write code that
deals with more complex intersections.
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