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svg2: Add new 'arcs' (extrapoloated) line join.

From: SVG Working Group repository <cam@mcc.id.au>
Date: Thu, 29 Nov 2012 11:07:23 -0800
Message-Id: <hg.34d365211ba7.1354216043.3034738116371802840@ps58493.dreamhostps.com>
To: public-svg-wg@w3.org
details:   https://svgwg.org/hg/svg2/rev/34d365211ba7
branches:  
changeset: 403:34d365211ba7
user:      tbah <tavmjong@free.fr>
date:      Thu Nov 29 20:06:19 2012 +0100
description:
Add new 'arcs' (extrapoloated) line join.

diffstat:

 master/images/painting/linejoin-construction-arcs.png |    0 
 master/images/painting/linejoin-construction-arcs.svg |   55 ++
 master/images/painting/linejoin-four.png              |    0 
 master/images/painting/linejoin-four.svg              |   40 +
 master/painting.html                                  |  363 +++++++++++++++++-
 5 files changed, 454 insertions(+), 4 deletions(-)

diffs (1098 lines):

diff --git a/master/images/painting/linejoin-construction-arcs.png b/master/images/painting/linejoin-construction-arcs.png
new file mode 100644
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diff --git a/master/images/painting/linejoin-four.svg b/master/images/painting/linejoin-four.svg
new file mode 100644
--- /dev/null
+++ b/master/images/painting/linejoin-four.svg
@@ -0,0 +1,40 @@
+<?xml version="1.0" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"
+     width="800" height="180" viewBox="0 0 800 180">
+  <desc>Example linecap - demonstrates four stroke-linecap values</desc>
+  <style type="text/css"><![CDATA[
+    .thick { stroke: black; stroke-width: 35px }
+    .thin { stroke: #ccc; stroke-width: 2px }
+    text { text-anchor: middle; font: 16px sans-serif }
+    circle { fill: #ccc; stroke: none }
+  ]]></style>
+  <defs>
+    <path id="path1" d="m 25,130 c 0,-40 50,-75 100,-75 -35,20 -50,50 -50,75" fill="none" />
+    <circle id="circle1" cx="125" cy="55" r="4"/>
+  </defs>
+  <g transform="translate(0,0)">
+    <use class="thick" xlink:href="#path1" stroke-linejoin="miter"/>
+    <use class="thin" xlink:href="#path1"/>
+    <use xlink:href="#circle1"/>
+    <text x="100" y="160">€˜miter€™ join</text>
+  </g>
+  <g transform="translate(200,0)">
+    <use class="thick" xlink:href="#path1" stroke-linejoin="round"/>
+    <use class="thin" xlink:href="#path1"/>
+    <use xlink:href="#circle1"/>
+    <text x="100" y="160">€˜round€™ join</text>
+  </g>
+  <g transform="translate(400,0)">
+    <use class="thick" xlink:href="#path1" stroke-linejoin="bevel"/>
+    <use class="thin" xlink:href="#path1"/>
+    <use xlink:href="#circle1"/>
+    <text x="100" y="160">€˜bevel€™ join</text>
+  </g>
+  <path id="join" d="m 724,37.5 c 18,0 41,3.6 65,17.7 C 769,55.6 750,60.7 733,70.6 Z"/>
+  <g transform="translate(600,0)">
+    <use class="thick" xlink:href="#path1" stroke-linejoin="bevel"/>
+    <use class="thin" xlink:href="#path1"/>
+    <use xlink:href="#circle1"/>
+    <text x="100" y="160">€˜arcs€™ join</text>
+  </g>
+</svg>
diff --git a/master/painting.html b/master/painting.html
--- a/master/painting.html
+++ b/master/painting.html
@@ -722,17 +722,17 @@ and <span class="property">'stroke-miter
 
 <table class="propdef">
   <tr>
     <th>Name:</th>
     <td><dfn id="StrokeLinejoinProperty">stroke-linejoin</dfn></td>
   </tr>
   <tr>
     <th>Value:</th>
-    <td>miter | round | bevel</td>
+    <td>miter | round | bevel | arcs </td>
   </tr>
   <tr>
     <th>Initial:</th>
     <td>miter</td>
   </tr>
   <tr>
     <th>Applies to:</th>
     <td><a>shapes</a> and <a>text content elements</a></td>
@@ -771,22 +771,43 @@ the <a href="implnote.html#PathElementIm
 
   <dt><span class='prop-value'>round</span></dt>
   <dd>This value indicates that a round corner is to be used to join path segments.
   The corner is a circular sector centered on the join point.</dd>
 
   <dt><span class='prop-value'>bevel</span></dt>
   <dd>This value indicates that a bevelled corner is to be used to join path segments.
   The bevel shape is a triangle that fills the area between the two stroked segments.</dd>
+
+  <dt><span class='prop-value'>arcs</span></dt>
+  <dd>This value indicates that an arcs corner is to be used to join
+    path segments. The arcs shape is formed by extending the outer
+    edges of the stroke at the join point with arcs that have the same
+    curvature as the outer edges at the join point.</dd>
 </dl>
 
+<p class="issue">Is there a better name than <i>arcs</i> for this property value?
+I (Tav) prefer <i>talon</i> (as in bird claw). The term <i>arc</i> has other uses
+in SVG and in graphics in general. The term <i>talon</i> would be unique as well
+as fit in with the existing property value names for line-join.</p>
+
+<p class="issue">How does the miter limit apply? (It's hard to get really
+long joins.) Do you fall back to miter or bevel? (Probably miter as it is
+more in the style.)</p>
+
+<p class="note">The <span class='prop-value'>arcs</span> value is new in SVG 2.
+It was added to provide a better looking join when the path segments at the
+join are curved.</p>
+
+<p class="annotation">Adding new line join was approved at <a href="http://www.w3.org/2012/09/19-svg-minutes.html#item08">Rigi Kaltbad group meeting</a>.</p>
+
 <div class="figure">
-  <img class="bordered" src="images/painting/linejoin.svg"
-       alt="Image showing three paths, each with a different line join."/>
-  <p class="caption">The three types of line joins.</p>
+  <img class="bordered" src="images/painting/linejoin-four.svg"
+       alt="Image showing four paths, each with a different line join."/>
+  <p class="caption">The four types of line joins.</p>
 </div>
 
 <table class="propdef">
   <tr>
     <th>Name:</th>
     <td><dfn id="StrokeMiterlimitProperty">stroke-miterlimit</dfn></td>
   </tr>
   <tr>
@@ -826,16 +847,18 @@ the <a href="implnote.html#PathElementIm
 <p>When two line segments meet at a sharp angle and <span
 class='prop-value'>miter</span> joins have been specified for
 <a>'stroke-linejoin'</a>, it is possible for the miter to extend
 far beyond the thickness of the line stroking the path. The
 <a>'stroke-miterlimit'</a> imposes a limit on the ratio of the miter
 length to the <a>'stroke-width'</a>. When the limit is exceeded, the
 join is converted from a miter to a bevel.</p>
 
+<p class="issue">How should this apply to arcs line-joins?</p>
+
 <dl>
   <dt><span class='prop-value'>&lt;number&gt;</span></dt>
   <dd>The limit on the ratio of the miter length to the <a>'stroke-width'</a>.
   The value of <span class='prop-value'>&lt;miterlimit&gt;</span> must be a
   <a>&lt;number&gt;</a> greater than or equal to 1. Any other value is an error (see
   <a href="implnote.html#ErrorProcessing">Error processing</a>).</dd>
 </dl>
 
@@ -1270,16 +1293,33 @@ a subpath is determined as follows:</p>
   <var>P</var>, <var>P</var><sub>1</sub> and <var>P</var><sub>2</sub>.</li>
 
   <li>If <a>'stroke-linejoin'</a> is <span class="prop-value">round</span>, then
   return the union of <var>bevel</var> and a circular sector of radius
   <a>'stroke-width'</a>, centered on <var>P</var>, and which has
   <var>P</var><sub>1</sub> and <var>P</var><sub>2</sub> as the two endpoints of
   the arc.</li> 
 
+  <li>If <a>'stroke-linejoin'</a> is <span class="prop-value">arcs</span>,
+    then find the circles that are tangent to the stroke edges at
+    <var>P</var><sub>1</sub> and <var>P</var><sub>2</sub> with the
+    same curvature as the edges at those points (see below). If both
+    curvatures are zero fall through to <span class="prop-value">miter</span>.
+    Extend the stroke edges using these circles (or a line, in the case
+    of zero curvature). If the two circles (or circle and line)
+    intersect, return the area inside the region defined by the lines
+    that connect <var>P</var> with <var>P</var><sub>1</sub>
+    and <var>P</var><sub>2</sub> and the arcs defined by the circles
+    (or arc and line) between the closest intersection point
+    to <var>P</var>, and <var>P</var><sub>1</sub> and
+    <var>P</var><sub>2</sub>. If the two circles (or circle and line)
+    do not intersect, fall through to <span class="prop-value">miter</span>.
+    Note that the curvatures are calculated in user-space before any
+    transforms are applied.</li>
+
   <li>Let <var>θ</var> be the angle between <var>A</var> and <var>B</var>.</li>
 
   <li>If <a>'stroke-linejoin'</a> is <span class="prop-value">miter</span> and
   1 / sin(<var>θ</var> / 2) ‰ <a>'stroke-miterlimit'</a>, then return the union
   of <var>bevel</var> and the triangle formed from the three points
   <var>P</var><sub>1</sub>, <var>P</var><sub>2</sub> and <var>P</var><sub>3</sub>.</li>
 
   <li>Return <var>bevel</var>.</li>
@@ -1288,16 +1328,331 @@ a subpath is determined as follows:</p>
 <div class="figure">
   <img class="bordered" src="images/painting/linejoin-construction.svg"
        alt="Image showing the lines and points computed to construct a round line join."/>
   <p class="caption">Construction of a round line join shape, shown in pink.
   The white line is the original path, which has two segments that come to a
   point, and the gray region is the stroke.</p>
 </div>
 
+<div class="figure">
+  <img class="bordered" src="images/painting/linejoin-construction-arcs.svg"
+       alt="Image showing the lines and points computed to construct an arcs line join."/>
+  <p class="caption">Construction of an arcs line join shape, shown in
+    pink. The white line is the original path, which has two segments
+    that come to a point, and the gray region is the stroke. The
+    dashed lines show circles that are tangent to and have the
+    curvature of the segments at the join.  The olive-green circles
+    (concentric with the dashed circles) define the join shape.</p>
+</div>
+
+<h3 id="CurvatureCalculation">Computing the circles for the <span class="prop-value">arcs</span>
+'stroke-linejoin'</h3>
+
+<p>The <span class="prop-value">arcs</span> <a>'stroke-linejoin'</a>
+  requires finding circles that are both tangent to and have the same
+  curvatures as the outer stroke edges at the ends of path
+  segments. To find one of these circles, first calculate the
+  curvature <var>&#x03BA;</var> of the path segment at its end (see
+  below). Next, find the radius of a circle corresponding to this
+  curvature: <var>r</var> = 1/<var>&#x03BA;</var>. Increase or
+  decrease the radius by one half of the stroke width to account for
+  the stroke: <var>r<sub>c</sub></var> = <var>r</var> &#x00b1; &#xbd;
+  stroke-width. The center of the circle will be on a line normal to
+  the path end a distance of <var>r<sub>c</sub></var> away from the
+  outer stroke edge at the end.</p>
+
+<p>For a line: the curvature is infinite. Extend the outer stroke edge by a line.</p>
+
+<p>For an elliptical arc:</p>
+<p class="issue">Need to do. This isn't as trivial as it first looks since we have to deal
+  with rx != ry and an arbitrary rotation.</p>
+
+<p>For a quadratic Bézier:
+
+  <div role="math" aria-describedby="math-quadratic-start">
+    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+      <mi>&#x03BA;<!-- κ --></mi>
+      <mo stretchy="false">(</mo>
+      <mn>0</mn>
+      <mo stretchy="false">)</mo>
+      <mo>=</mo>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mn>1</mn>
+	  <mn>2</mn>
+	</mfrac>
+      </mrow>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mrow>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>0</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+            <mo>&#x00D7;<!-- — --></mo>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+	  </mrow>
+	  <mrow>
+            <mrow class="MJX-TeXAtom-ORD">
+              <mo stretchy="false">|</mo>
+            </mrow>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>0</mn>
+            </msub>
+            <msup>
+              <mrow class="MJX-TeXAtom-ORD">
+		<mo stretchy="false">|</mo>
+              </mrow>
+              <mn>3</mn>
+            </msup>
+	  </mrow>
+	</mfrac>
+      </mrow>
+    </math>
+    <pre id="math-quadratic-start">$$\kappa(0) = {2\over3}{(P_1-P_0)\times((P_0-P_1)+(P_2-P_1))\over|P_1-P_0|^3}$$</pre>
+  </div>
+
+  <div role="math" aria-describedby="math-quadratic-end">
+    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+      <mi>&#x03BA;<!-- κ --></mi>
+      <mo stretchy="false">(</mo>
+      <mn>1</mn>
+      <mo stretchy="false">)</mo>
+      <mo>=</mo>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mn>1</mn>
+	  <mn>2</mn>
+	</mfrac>
+      </mrow>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mrow>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+            <mo>&#x00D7;<!-- — --></mo>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>0</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+	  </mrow>
+	  <mrow>
+            <mrow class="MJX-TeXAtom-ORD">
+              <mo stretchy="false">|</mo>
+            </mrow>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <msup>
+              <mrow class="MJX-TeXAtom-ORD">
+		<mo stretchy="false">|</mo>
+              </mrow>
+              <mn>3</mn>
+            </msup>
+	  </mrow>
+	</mfrac>
+      </mrow>
+    </math>
+    <pre id="math-quadratic-start">$$\kappa(0) = {2\over3}{(P_1-P_0)\times((P_0-P_1)+(P_2-P_1))\over|P_1-P_0|^3}$$</pre>
+  </div>
+
+  Where <var>&#x03BA;(0)</var> and <var>&#x03BA;(1)</var> are the
+  signed curvatures at the start and end of the path segment
+  respectively, and the <var>P</var>'s are the three points that
+  define the quadratic Bézier.</p>
+
+<p>For a cubic Bézier:
+
+  <div role="math" aria-describedby="math-cubic-start">
+    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+      <mi>&#x03BA;<!-- κ --></mi>
+      <mo stretchy="false">(</mo>
+      <mn>0</mn>
+      <mo stretchy="false">)</mo>
+      <mo>=</mo>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mn>2</mn>
+	  <mn>3</mn>
+	</mfrac>
+      </mrow>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mrow>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>0</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+            <mo>&#x00D7;<!-- — --></mo>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+	  </mrow>
+	  <mrow>
+            <mrow class="MJX-TeXAtom-ORD">
+              <mo stretchy="false">|</mo>
+            </mrow>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>0</mn>
+            </msub>
+            <msup>
+              <mrow class="MJX-TeXAtom-ORD">
+		<mo stretchy="false">|</mo>
+              </mrow>
+              <mn>3</mn>
+            </msup>
+	  </mrow>
+	</mfrac>
+      </mrow>
+    </math>
+    <pre id="math-cubic-start">$$\kappa(0) = {2\over3}{(P_1-P_0)\times((P_0-P_1)+(P_2-P_1))\over|P_1-P_0|^3}$$</pre>
+  </div>
+
+  <div role="math" aria-describedby="math-cubic-end">
+    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+      <mi>&#x03BA;<!-- κ --></mi>
+      <mo stretchy="false">(</mo>
+      <mn>1</mn>
+      <mo stretchy="false">)</mo>
+      <mo>=</mo>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mn>2</mn>
+	  <mn>3</mn>
+	</mfrac>
+      </mrow>
+      <mrow class="MJX-TeXAtom-ORD">
+	<mfrac>
+	  <mrow>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>3</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+            <mo>&#x00D7;<!-- — --></mo>
+            <mo stretchy="false">(</mo>
+            <msub>
+              <mi>P</mi>
+              <mn>1</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <mo stretchy="false">)</mo>
+	  </mrow>
+	  <mrow>
+            <mrow class="MJX-TeXAtom-ORD">
+              <mo stretchy="false">|</mo>
+            </mrow>
+            <msub>
+              <mi>P</mi>
+              <mn>3</mn>
+            </msub>
+            <mo>&#x2212;<!-- ˆ’ --></mo>
+            <msub>
+              <mi>P</mi>
+              <mn>2</mn>
+            </msub>
+            <msup>
+              <mrow class="MJX-TeXAtom-ORD">
+		<mo stretchy="false">|</mo>
+              </mrow>
+              <mn>3</mn>
+            </msup>
+	  </mrow>
+	</mfrac>
+      </mrow>
+    </math>
+    <pre id="math-cubic-end">$$\kappa(1) = {2\over3}{(P_3-P_2)\times((P_1-P_2)+(P_3-P_2))\over|P_3-P_2|^3}$$</pre>
+  </div>
+
+  Where <var>&#x03BA;(0)</var> and <var>&#x03BA;(1)</var> are the
+  signed curvatures at the start and end of the path segment
+  respectively, and the <var>P</var>'s are the four points that define
+  the cubic Bézier. Note, if
+  <var>P<sub>0</sub></var> and <var>P<sub>1</sub></var>, or
+  <var>P<sub>2</sub></var> and <var>P<sub>3</sub></var> are degenerate, the
+  curvature will be infinite and a line should be used in constructing the join.</p>
+
+
 <h2 id="VisibilityControl">Controlling visibility: the effect of the <span
 class="property">'display'</span> and <span class="property">'visibility'</span>
 properties</h2>
 
 <p class="note">See the CSS 2.1 specification for the definitions
 of <a>'display'</a> and <a>'visibility'</a>.
 [<a href="refs.html#ref-CSS21">CSS21</a>]</p>
 
Received on Thursday, 29 November 2012 19:08:42 UTC

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