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<hr/>
<a href="#delta"><delta></a>
<a href="#control-value-delta"><control-value-delta></a>
<a href="#delta-set"><delta-set></a>
<a href="#set-delta-base"><set-delta-base></a>
<a href="#set-delta-base"><with-delta-base></a>
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<a href="#set-delta-shift"><with-delta-shift></a>
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<h1>Deltas</h1>
<p>
A delta is an instruction that operates only at a specific
resolution. There are two kinds of delta, invoked by two
Xgridfit elements: a <delta> element moves points, and
a <control-value-delta> element edits the Control
Value Table.
</p>
<p>
Use delta instructions when the non-resolution-specific
parts of your programming have failed for some reason.
Here are some situations
in which deltas typically make sense:
</p>
<ul>
<li>Rounding of a distance has produced an unattractive
result. (If the distance was from the Control
Value Table, consider using
<control-value-delta>.)</li>
<li>A feature does not render well at particular sizes, and
you wish to remove or modify it. (But programming
can also be made to operate at a range of sizes
using an <if> construction.)</li>
<li>Components of a composite glyph are poorly positioned
relative to each other.</li>
</ul>
<p>
In addition, you may wish to use a delta to smooth a curve
that has developed a kink, or to turn a pixel on or off.
Before you use a delta, however, you should make sure that
the problem you are correcting is not the result of your own
careless programming: failure to use control values
correctly, for example, or failure to think through the
problems presented by a complex feature. It may well be less
trouble to write a great many deltas than to think
intensively about the intersection of two diagonals. But
once you have written non-size-specific code that addresses
a problem, it can easily be adapted to handle similar
problems in the same or another font. The same can rarely be
said of deltas. So think of the delta as a last resort or a
finishing touch.
</p>
<p>
Another situation that may tempt you to use deltas arises
when the original glyph outline contains small
irregularities that show up only at certain low resolutions.
When an <b>o</b> is not quite symmetrical, for example, it
may appear lopsided at times. In this case you should
consider whether the glyph's lack of symmetry is a feature
you wish to preserve or an error you should correct. The
best time to consider such issues as this is before you
start writing the glyph program.
</p>
<p>
If you have used a graphical hinter like the one in FontLab,
it may have left you in some confusion about where deltas
can and should come in the sequence of a glyph program.
Deltas may come anywhere, but they should generally be
placed so as to correct any problems in the positioning of a
point as early as possible. The letter <b>q</b> in the
left-hand figure below illustrates. (The black lines show the
original shape of the glyph and the green lines the
grid-fitted shape; the brown squares show which pixels are
on. The black vertical line shows the original right
margin, and the green vertical line shows the
grid-fitted one.)
</p>
<table>
<tr>
<td>
<img alt="q without delta" src="q-no-delta.gif"/>
</td>
<td>
<img alt="q with delta" src="q-delta.gif"/>
</td>
</tr>
</table>
<p>
The <b>q</b> on the left is too wide, and it bumps into the
right margin. The problem arises after the left-hand curve
has been hinted; then the overall width of the glyph is
regulated by positioning point <tt>b</tt> relative to point
<tt>a</tt>:
</p>
<pre>
<move distance="bdpq-width">
<reference>
<point num="a"/>
</reference>
<point num="b"/>
</move>
</pre>
<p>
The problem is that the distance "bdpq-width" gets rounded
<i>up</i> at 15 ppem when it would be better visually
for it to be rounded <i>down</i>. If you waited till the end
of the glyph program to address this problem, you would need
deltas to correct the position not only of <tt>b</tt>, but
also of <tt>c</tt>, <tt>d</tt>, and several other points not
shown here--for example, those that control the horizonal
positions of the serif ends. All of these points are
positioned relative to point <tt>b</tt>, so if you correct
the position of <tt>b</tt> immediately after the execution
of the instruction above, thus:
</p>
<pre>
<delta>
<delta-set size="6" distance="-8">
<point num="b"/>
</delta-set>
</delta>
</pre>
<p>
then the position of the others will automatically
incorporate the correction, and the result will be the much
better glyph on the right.
</p>
<p>
We can correct the problem even earlier than this, however.
Notice that the <control-value> that controls the
width of the <b>q</b> is named "bdpq-width": this is because
that single entry controls the width of <b>b</b>, <b>d</b>
and <b>p</b> as well as <b>q</b>. As the following figure
demonstrates, the width of all four characters is wrong at
15 ppem:
</p>
<table>
<tr>
<td>
<img alt="b d p q with incorrect width" src="bdpq-no-delta.png"/>
</td>
</tr>
</table>
<p>
We can correct this problem most efficiently with a
<control-value-delta> instruction in the
<pre-program>. First we round the distance, then
execute the delta instruction:
</p>
<pre>
<round value="bdpq-width"/>
<control-value-delta>
<delta-set cv="bdpq-width" size="6" distance="-8"/>
</control-value-delta>
</pre>
<p>
And now, as the figure below shows, the width of all four
characters has been corrected without resorting to the use
of delta instructions in the glyph programs themselves.
</p>
<table>
<tr>
<td>
<img alt="b d p q with correct width" src="bdpq-delta.png"/>
</td>
</tr>
</table>
<h2>Elements Relating to Deltas</h2>
<p>
In addition to the following elements, you should know about
the <tt>delta-base</tt> and <tt>delta-shift</tt> graphics
variables, which you may both read and write to.
</p>
<h3 id="delta"><delta></h3>
<p>
A delta instruction moves points at particular
sizes. The <delta> element may contain any
number of <delta-set> elements. When all of
the <delta-set> elements in a <delta>
move the same point, it may be convenient to make
the first element a <point>. This is the
default <point>, which every
<delta-set> will move unless it contains its
own <point>.
</p>
<p>
The direction of the move is determined by the current
setting of the freedom vector. The available
specifications are fuzzy as to the details. You will
experience no surprises when the vectors are set to x or y;
you may experiment with the vectors set at other angles.
</p>
<h3 id="control-value-delta"><control-value-delta></h3>
<p>
The <control-value-delta> element works like the
<delta> element, but operates on the Control
Value Table rather than on a point. Each <delta-set>
inside a control-value-delta element must have <tt>cv</tt>,
<tt>size</tt> and <tt>distance</tt> attributes, but it
may not contain a point.
</p>
<p>
The setting of the vectors has no effect on the
<control-value-delta>. Rather, the <delta-set>
specifies an amount to add to or subtract from the value
stored there.
</p>
<h3 id="delta-set"><delta-set></h3>
<p>
The <delta-set> element encapsulates the essential
information about a single delta move or adjustment: the
resolution at which to apply the delta, the magnitude of the
adjustment, and the point or control value that will be
affected.
</p>
<p>
The resolution is determined by the <tt>size</tt> attribute,
which can be a number from 0 to 47. It is added to
the value set by the <set-delta-base> or
<with-delta-base> instruction to
obtain the resolution (in pixels per em) at which the move
should take place. The default delta base is 9; if
you don't change it, a <tt>size</tt> of "0" means 9 ppem,
"9" means 18 ppem, and so forth up to "47," which means 56
ppem.
</p>
<p>
The <tt>distance</tt> attribute is the distance to shift the
point along the freedom vector, or the amount to add to or
subtract from the control value. Legal values are from -8
to 8 (excluding 0). When moving points, negative numbers
shift against the
direction of the freedom vector (generally down or
left) and positive numbers shift in the direction of the
freedom vector.
</p>
<p>
The default unit by which pixels are moved and control
values adjusted is 1/8 pixel.
The unit is controlled by means of the
<set-delta-shift> or the <with-delta-shift>
instruction.
</p>
<p>
A <delta-set> that is the child of a <delta>
will normally contain a single <point>. However,
the <point> may be omitted in either of two
circumstances: First, when the <delta> is the child
of a <move> element, the <point>, when not
specified, is implicitly the <point> that is the
child of the parent <move>. Second, when the first
child element of the <delta> is <point>, that
point will be moved by any <delta-set> that lacks a
child <point>. These two deltas are equivalent:
</p>
<pre>
<delta>
<delta-set size="3" distance="4">
<point num="p"/>
</delta-set>
<delta-set size="8" distance="-7">
<point num="p"/>
</delta-set>
</delta>
<delta>
<point num="p"/>
<delta-set size="3" distance="4"/>
<delta-set size="8" distance="-7"/>
</delta>
</pre>
<p>
All attribute values in a <delta-set> and a child
<point> must be capable of being resolved to numerical
values at compile time. Variables and function parameters
are not permitted.
</p>
<h3 id="set-delta-base"><set-delta-base><br/><with-delta-base></h3>
<p>
Sets the number that is added to the "size" attribute of a
<delta-set> element to get the resolutioni at which an
adjustment should take place. The default value is 9, and
that rarely needs to be changed.
</p>
<h3 id="set-delta-shift"><set-delta-shift><br/><with-delta-shift></h3>
<p>
The unit by which a delta instruction shifts a point. If the
unit is "2," the smallest shift is half a pixel; if "4," it
is a quarter of a pixel; if "8" (the default) it is one
eighth, and so on.
</p>
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