csswg-drafts/css3-transforms/Overview.html at a50ba0d2ce2c2a606c2e33266c23109724c938a4 · simonwuelker/csswg-drafts · GitHub

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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">

<html lang=en>
 <head profile="http://www.w3.org/2006/03/hcard"><meta
  content="text/html; charset=utf-8" http-equiv=Content-Type>

  <title>CSS Transforms</title>
  <link href="../default.css" rel=stylesheet type="text/css">
  <link href="http://www.w3.org/StyleSheets/TR/W3C-ED.css" rel=stylesheet
  type="text/css">
  <script defer
  src="http://test.csswg.org/harness/annotate.js#CSS3-TRANSFORMS_DEV"
  type="text/javascript"></script>

  <style type="text/css">
      .term {
        font-style: italic;
      }

     .todo {
         font-weight: bold;
         border-left: 0.5em solid #f44;
         padding-left: 1em;
         margin-top: 0.5em;
         color: #a0a0a0;
     }

     .todo:before {
         content: "TO DO : ";
         color: #f44;
     }
  </style>

 <body>
  <div class=head id=div-head> <!--begin-logo-->
   <p><a href="http://www.w3.org/"><img alt=W3C height=48
    src="http://www.w3.org/Icons/w3c_home" width=72></a> <!--end-logo-->

   <h1>CSS Transforms</h1>

   <h2 class="no-num no-toc" id=longstatus-date>Editor's Draft 8 May 2012</h2>

   <dl>
    <dt>This version:

    <dd> <a
     href="http://www.w3.org/TR/2012/ED-css3-transforms-20120508/">http://dev.w3.org/csswg/css3-transforms/</a>
     <!--http://www.w3.org/TR/2012/WD-css3-transforms-20120508/-->

    <dt>Latest version:

    <dd><a
     href="http://www.w3.org/TR/css3-transforms/">http://www.w3.org/TR/css3-transforms/</a>


    <dt>Editor's draft:

    <dd><a
     href="http://dev.w3.org/csswg/css3-transforms/">http://dev.w3.org/csswg/css3-transforms/</a>


    <dt>Previous versions:

    <dd><a
     href="http://www.w3.org/TR/2012/WD-css3-transforms-20120228/">http://www.w3.org/TR/2012/WD-css3-transforms-20120228/</a>


    <dt id=editors-list>Editors:

    <dd>Simon Fraser (<a href="http://www.apple.com/">Apple Inc</a>)
     &lt;simon.fraser &#64;apple.com&gt;

    <dd>Dean Jackson (<a href="http://www.apple.com/">Apple Inc</a>) &lt;dino
     &#64;apple.com&gt;

    <dd>David Hyatt (<a href="http://www.apple.com/">Apple Inc</a>) &lt;hyatt
     &#64;apple.com&gt;

    <dd>Chris Marrin (<a href="http://www.apple.com/">Apple Inc</a>)
     &lt;cmarrin &#64;apple.com&gt;

    <dd>Edward O'Connor (<a href="http://www.apple.com/">Apple Inc</a>)
     &lt;eoconnor &#64;apple.com&gt;

    <dd>Dirk Schulze (<a href="http://www.adobe.com/">Adobe Systems, Inc</a>)
     &lt;dschulze &#64;adobe.com&gt;

    <dd>Aryeh Gregor (<a href="http://www.mozilla.org/">Mozilla</a>) &lt;ayg
     &#64;aryeh.name&gt;

    <dt>Issues list:

    <dd><a
     href="https://www.w3.org/Bugs/Public/buglist.cgi?query_format=advanced&amp;product=CSS&amp;component=Transforms&amp;resolution=---&amp;cmdtype=doit">in
     Bugzilla</a>

    <dt>Test suite:

    <dd>none yet
   </dl>
   <!--begin-copyright-->
   <p class=copyright><a
    href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright"
    rel=license>Copyright</a> &copy; 2012 <a href="http://www.w3.org/"><abbr
    title="World Wide Web Consortium">W3C</abbr></a><sup>&reg;</sup> (<a
    href="http://www.csail.mit.edu/"><abbr
    title="Massachusetts Institute of Technology">MIT</abbr></a>, <a
    href="http://www.ercim.eu/"><abbr
    title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
    <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C <a
    href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
    <a
    href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>
    and <a
    href="http://www.w3.org/Consortium/Legal/copyright-documents">document
    use</a> rules apply.</p>
   <!--end-copyright-->
   <hr title="Separator for header">
  </div>

  <h2 class="no-num no-toc" id=abstract>Abstract</h2>

  <p>CSS transforms allows elements styled with CSS to be transformed in
   two-dimensional or three-dimensional space. This specification is the
   convergence of the <a href="http://www.w3.org/TR/css3-2d-transforms/">CSS
   2D transforms</a>, <a href="http://www.w3.org/TR/css3-3d-transforms/">CSS
   3D transforms</a> and <a
   href="http://www.w3.org/TR/2009/WD-SVG-Transforms-20090320/">SVG
   transforms</a> specifications.

  <h2 class="no-num no-toc" id=status>Status of this document</h2>
  <!--begin-status-->

  <p>This is a public copy of the editors' draft. It is provided for
   discussion only and may change at any moment. Its publication here does
   not imply endorsement of its contents by W3C. Don't cite this document
   other than as work in progress.

  <p>The (<a
   href="http://lists.w3.org/Archives/Public/public-fx/">archived</a>) public
   mailing list <a href="mailto:public-fx@w3.org">public-fx@w3.org</a> (see
   <a href="http://www.w3.org/Mail/Request">instructions</a>) is preferred
   for discussion of this specification. When sending e-mail, please put the
   text &#8220;css3-transforms&#8221; in the subject, preferably like this:
   &#8220;[<!---->css3-transforms<!---->] <em>&hellip;summary of
   comment&hellip;</em>&#8221;

  <p>This document was produced by the <a
   href="http://www.w3.org/Style/CSS/members">CSS Working Group</a> (part of
   the <a href="http://www.w3.org/Style/">Style Activity</a>) and the <a
   href="http://www.w3.org/Graphics/SVG/">SVG Working Group</a> (part of the
   <a href="http://www.w3.org/Graphics/">Graphics Activity</a>).

  <p>This document was produced by groups operating under the <a
   href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February
   2004 W3C Patent Policy</a>. W3C maintains a <a
   href="http://www.w3.org/2004/01/pp-impl/32061/status"
   rel=disclosure>public list of any patent disclosures (CSS)</a> and a <a
   href="http://www.w3.org/2004/01/pp-impl/19480/status"
   rel=disclosure>public list of any patent disclosures (SVG)</a> made in
   connection with the deliverables of each group; these pages also include
   instructions for disclosing a patent. An individual who has actual
   knowledge of a patent which the individual believes contains <a
   href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential
   Claim(s)</a> must disclose the information in accordance with <a
   href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section
   6 of the W3C Patent Policy</a>.</p>
  <!--end-status-->

  <p> This specification replaces the former <a
   href="http://www.w3.org/TR/css3-2d-transforms/"
   title="CSS 2D Transforms">CSS 2D Transforms</a> and <a
   href="http://www.w3.org/TR/css3-3d-transforms/"
   title="CSS 3D Transforms Module Level 3">CSS 3D Transforms</a>
   specifications, as well as <a href="http://www.w3.org/TR/SVG-Transforms/"
   title="SVG Transforms 1.0">SVG Transforms</a>.
   <!-- Does it actually this SVG spec? -->

  <p> The <a href=ChangeLog>list of changes made to this specification</a> is
   available.

  <h2 class="no-num no-toc" id=contents>Table of contents</h2>
  <!--begin-toc-->

  <ul class=toc>
   <li><a href="#introduction"><span class=secno>1. </span>Introduction</a>

   <li><a href="#module-interactions"><span class=secno>2. </span>Module
    Interactions</a>

   <li><a href="#css-values"><span class=secno>3. </span>CSS Values</a>

   <li><a href="#definitions"><span class=secno>4. </span>Definitions</a>

   <li><a href="##two-dimensional-subset"><span class=secno>5. </span> Two
    Dimensional Subset </a>

   <li><a href="#transform-rendering"><span class=secno>6. </span>The
    Transform Rendering Model</a>
    <ul class=toc>
     <li><a href="#transform-3d-rendering"><span class=secno>6.1. </span>3D
      Transform Rendering</a>
    </ul>

   <li><a href="#transform-property"><span class=secno>7. </span> The
    &lsquo;<code class=css><code
    class=property>transform</code></code>&rsquo; Property </a>

   <li><a href="#transform-origin-property"><span class=secno>8. </span> The
    &lsquo;<code class=css><code
    class=property>transform-origin</code></code>&rsquo; Property </a>

   <li><a href="#transform-style-property"><span class=secno>9. </span> The
    &lsquo;<code class=css><code
    class=property>transform-style</code></code>&rsquo; Property </a>

   <li><a href="#perspective-property"><span class=secno>10. </span> The
    &lsquo;<code class=css><code
    class=property>perspective</code></code>&rsquo; Property </a>

   <li><a href="#perspective-origin-property"><span class=secno>11. </span>
    The &lsquo;<code class=css><code
    class=property>perspective-origin</code></code>&rsquo; Property </a>

   <li><a href="#backface-visibility-property"><span class=secno>12. </span>
    The &lsquo;<code class=css><code
    class=property>backface-visibility</code></code>&rsquo; Property </a>

   <li><a href="#svg-transform"><span class=secno>13. </span> The SVG
    &lsquo;<code class=css><code
    class=property>transform</code></code>&rsquo; Attribute </a>
    <ul class=toc>
     <li><a href="#transform-attribute-specificity"><span class=secno>13.1.
      </span>SVG &lsquo;<code class=css><code
      class=property>transform</code></code>&rsquo; attribute specificity</a>


     <li><a href="#svg-syntax"><span class=secno>13.2. </span>Syntax of the
      SVG &lsquo;<code class=property>transform</code>&rsquo; attribute</a>
      <ul class=toc>
       <li><a href="#svg-transform-list"><span class=secno>13.2.1.
        </span>Transform List</a>

       <li><a href="#svg-functional-notation"><span class=secno>13.2.2.
        </span>Functional Notation</a>

       <li><a href="#svg-data-types"><span class=secno>13.2.3. </span>SVG
        Data Types</a>
        <ul class=toc>
         <li><a href="#svg-transform-value"><span class=secno>13.2.3.1.
          </span>The <var>&lt;translation-value&gt;</var> and
          <var>&lt;length&gt;</var> type</a>

         <li><a href="#svg-angle"><span class=secno>13.2.3.2. </span>The
          <var>&lt;angle&gt;</var> type</a>

         <li><a href="#svg-number"><span class=secno>13.2.3.3. </span>The
          <var>&lt;number&gt;</var> type</a>
        </ul>
      </ul>

     <li><a href="#svg-gradient-transform-pattern-transform"><span
      class=secno>13.3. </span>The SVG &lsquo;<code
      class=property>gradientTransform</code>&rsquo; and &lsquo;<code
      class=property>patternTransform</code>&rsquo; attributes</a>

     <li><a href="#svg-transform-functions"><span class=secno>13.4. </span>
      SVG transform functions </a>

     <li><a href="#svg-three-dimensional-functions"><span class=secno>13.5.
      </span>SVG and 3D transform functions</a>

     <li><a href="#svg-object-bounding-box"><span class=secno>13.6.
      </span>Object bounding box units</a>

     <li><a href="#transform-attribute-dom"><span class=secno>13.7.
      </span>SVG DOM interface for the &lsquo;<code class=css><code
      class=property>transform</code></code>&rsquo; attribute</a>

     <li><a href="#svg-animation"><span class=secno>13.8. </span>SVG
      Animation</a>
      <ul class=toc>
       <li><a href="#svg-animate-element"><span class=secno>13.8.1.
        </span>The SVG &lsquo;<code class=property>animate</code>&rsquo; and
        &lsquo;<code class=property>set</code>&rsquo; element</a>

       <li><a href="#svg-attribute-name"><span class=secno>13.8.2. </span>The
        SVG &lsquo;<code class=property>attributeName</code>&rsquo;
        attribute</a>

       <li><a href="#svg-animateTransform-extension"><span
        class=secno>13.8.3. </span>The SVG &lsquo;<code
        class=property>animateTransform</code>&rsquo; element</a>
      </ul>
    </ul>

   <li><a href="#transform-functions"><span class=secno>14. </span> The
    Transform Functions </a>
    <ul class=toc>
     <li><a href="#two-d-transform-functions"><span class=secno>14.1.
      </span>2D Transform Functions</a>

     <li><a href="#three-d-transform-functions"><span class=secno>14.2.
      </span>3D Transform Functions</a>
    </ul>

   <li><a href="#transform-function-lists"><span class=secno>15. </span> The
    Transform Function Lists </a>

   <li><a href="#animation"><span class=secno>16. </span> Interpolation of
    Transforms </a>
    <ul class=toc>
     <li><a href="#transform-primitives"><span class=secno>16.1. </span>
      Transform function primitives and derivatives </a>

     <li><a href="#interpolation-of-transform-functions"><span
      class=secno>16.2. </span> Interpolation of primitives and derived
      transform functions </a>
    </ul>

   <li><a href="#matrix-decomposition"><span class=secno>17. </span> Matrix
    Decomposition for Animation </a>
    <ul class=toc>
     <li><a href="#unmatrix"><span class=secno>17.1. </span>Unmatrix</a>

     <li><a href="#animating-the-components"><span class=secno>17.2.
      </span>Animating the components</a>

     <li><a href="#recomposing-the-matrix"><span class=secno>17.3.
      </span>Recomposing the matrix</a>
    </ul>

   <li><a href="#mathematical-description"><span class=secno>18. </span>
    Mathematical Description of Transform Functions </a>

   <li><a href="#references"><span class=secno>19. </span>References</a>
    <ul class=toc>
     <li class=no-num><a href="#normative-references">Normative
      references</a>

     <li class=no-num><a href="#other-references">Other references</a>
    </ul>

   <li class=no-num><a href="#property-index">Property index</a>

   <li class=no-num><a href="#index">Index</a>
  </ul>
  <!--end-toc-->

  <h2 id=introduction><span class=secno>1. </span>Introduction</h2>

  <p><em>This section is not normative.</em>

  <p> The CSS <a href="http://www.w3.org/TR/REC-CSS2/visuren.html">visual
   formatting model</a> describes a coordinate system within each element is
   positioned. Positions and sizes in this coordinate space can be thought of
   as being expressed in pixels, starting in the origin of point with
   positive values proceeding to the right and down.

  <p> This coordinate space can be modified with the &lsquo;<a
   href="#effects"><code class=css><code
   class=property>transform</code></code></a>&rsquo; property. Using
   transform, elements can be translated, rotated and scaled in two or three
   dimensional space.

  <p> Additional properties make working with transforms easier, and allow
   the author to control how nested three-dimensional transforms interact.

  <ul>
   <li> The &lsquo;<a href="#transform-origin"><code class=css><code
    class=property>transform-origin</code></code></a>&rsquo; property
    provides a convenient way to control the origin about which transforms on
    an element are applied.

   <li> The &lsquo;<a href="#perspective"><code class=css><code
    class=property>perspective</code></code></a>&rsquo; property allows the
    author to make child elements with three-dimensional transforms appear as
    if they live in a common three-dimensional space. The &lsquo;<a
    href="#perspective-origin"><code class=css><code
    class=property>perspective-origin</code></code></a>&rsquo; property
    provides control over the origin at which perspective is applied,
    effectively changing the location of the "vanishing point".

   <li> The &lsquo;<a href="#transform-style"><code class=css><code
    class=property>transform-style</code></code></a>&rsquo; property allows
    3D-transformed elements and their 3D-transformed descendants to share a
    common three-dimensional space, allowing the construction of hierarchies
    of three-dimensional objects.

   <li> The &lsquo;<a href="#backface-visibility"><code class=css><code
    class=property>backface-visibility</code></code></a>&rsquo; property
    comes into play when an element is flipped around via three-dimensional
    transforms such that its reverse side is visible to the viewer. In some
    situations it is desirable to hide the element in this situation, which
    is possible using the value of &lsquo;<code
    class=property>hidden</code>&rsquo; for this property.
  </ul>

  <p> Note that while some values of the &lsquo;<a href="#effects"><code
   class=css><code class=property>transform</code></code></a>&rsquo; property
   allow an element to be transformed in a three-dimensional coordinate
   system, the elements themselves are not three-dimensional objects.
   Instead, they exist on a two-dimensional plane (a flat surface) and have
   no depth.</p>
  <!-- ======================================================================================================= -->

  <h2 id=module-interactions><span class=secno>2. </span>Module Interactions</h2>

  <p>This module defines a set of CSS properties that affect the visual
   rendering of elements to which those properties are applied; these effects
   are applied after elements have been sized and positioned according to the
   <a href="http://www.w3.org/TR/CSS2/visuren.html"
   title="Visual formatting model">Visual formatting model</a> from <a
   href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>. Some values of
   these properties result in the creation of a <a
   href="http://www.w3.org/TR/CSS2/visuren.html#containing-block"
   title="Visual formatting model">containing block</a>, and/or the creation
   of a <a href="http://www.w3.org/TR/CSS2/visuren.html#z-index"
   title="Visual formatting model">stacking context</a>.

  <p> Three-dimensional transforms can also affect the visual layering of
   elements, and thus override the back-to-front painting order described in
   <a href="http://www.w3.org/TR/CSS2/zindex.html"
   title="Elaborate description of Stacking Contexts">Appendix E</a> of <a
   href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>.</p>
  <!-- Probably need more here. -->

  <h2 id=css-values><span class=secno>3. </span>CSS Values</h2>

  <p>This specification follows the <a
   href="http://www.w3.org/TR/CSS21/about.html#property-defs">CSS property
   definition conventions</a> from <a href="#CSS21"
   rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>. Value types not defined in
   this specification are defined in CSS Level 2 Revision 1 <a
   href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>.

  <p>In addition to the property-specific values listed in their definitions,
   all properties defined in this specification also accept the <a
   href="http://www.w3.org/TR/CSS21/cascade.html#valu
364A
e-def-inherit">inherit</a>
   keyword as their property value. For readability it has not been repeated
   explicitly.

  <h2 id=definitions><span class=secno>4. </span>Definitions</h2>

  <p> When used in this specification, terms have the meanings assigned in
   this section.

  <dl>
   <dt id=TermBoundingBox><dfn id=bounding-box>bounding box</dfn>

   <dd>
    <p> A bounding box is the object bounding box for all SVG elements
     without an associated CSS layout box and the border box for all other
     elements. The bounding box of a table is the border box of its <a
     href="http://www.w3.org/TR/CSS21/tables.html#model">table wrapper
     box</a>, not its table box.</p>

   <dt id=TermTransformableElement><dfn
    id=transformable-element>transformable element</dfn>

   <dd>
    <p> A transformable element is an element in the HTML namespace which is
     either a <a
     href="http://www.w3.org/TR/CSS2/visuren.html#block-level">block-level</a>
     or <a href="http://www.w3.org/TR/CSS2/visuren.html#x13">atomic
     inline-level element</a>, or whose &lsquo;<code class=css><code
     class=property>display</code></code>&rsquo; property computes to
     &lsquo;<code class=css><code class=css>table-row</code></code>&rsquo;,
     &lsquo;<code class=css><code
     class=css>table-row-group</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>table-header-group</code></code>&rsquo;,
     &lsquo;<code class=css><code
     class=css>table-footer-group</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>table-cell</code></code>&rsquo;, or
     &lsquo;<code class=css><code
     class=css>table-caption</code></code>&rsquo;; or an element in the SVG
     namespace (see <a href="#SVG11"
     rel=biblioentry>[SVG11]<!--{{SVG11}}--></a>) which has the attributes
     &lsquo;<a href="#effects"><code class=css><code
     class=property>transform</code></code></a>&rsquo;, &lsquo;<code
     class=property>patternTransform</code>&rsquo; or &lsquo;<code
     class=property>gradientTransform</code>&rsquo;.</p>

   <dt id=TermPerspectiveMatrix><dfn id=perspective-matrix>perspective
    matrix</dfn>

   <dd>
    <p> A matrix computed from the values of the &lsquo;<a
  
D576
   href="#perspective"><code class=css><code
     class=property>perspective</code></code></a>&rsquo; and &lsquo;<a
     href="#perspective-origin"><code class=css><code
     class=property>perspective-origin</code></code></a>&rsquo; properties as
     described <a href="#perspective-matrix-computation">below</a>.</p>

   <dt id=TermTransformationMatrix><dfn
    id=transformation-matrix>transformation matrix</dfn>

   <dd>
    <p> A matrix computed from the values of the &lsquo;<a
     href="#effects"><code class=css><code
     class=property>transform</code></code></a>&rsquo; and &lsquo;<a
     href="#transform-origin"><code class=css><code
     class=property>transform-origin</code></code></a>&rsquo; properties as
     described <a href="#transformation-matrix-computation">below</a>.</p>

   <dt id=TermAccumulated3DTransformationMatrix> <dfn
    id=accumulated-3d-transformation-matrix>accumulated 3D transformation
    matrix</dfn>

   <dd>
    <p> A matrix computed for elements in a <a href="#d-rendering-context">3D
     rendering context</a>, as described <a
     href="#accumulated-3d-transformation-matrix-computation">below</a>.</p>

   <dt id=TermIdentityTransformFunction> <dfn
    id=identity-transform-function>Identity transform function</dfn>

   <dd>
    <p> A <a href="#transform-functions">transform function</a> that is
     equivalent to a identity 4x4 matrix (see <a
     href="#mathematical-description">Mathematical Description of Transform
     Functions</a>). Examples for identity transform functions are
     &lsquo;<code class=css><code
     class=css>translate(0)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>translate3d(0, 0, 0)</code></code>&rsquo;,
     &lsquo;<code class=css><code
     class=css>translateX(0)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>translateY(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code
     class=css>translateZ(0)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>scale(1)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>scaleX(1)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>scaleY(1)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>scaleZ(1)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>rotate(0)</code></code>&rsquo;, &lsquo;<code
     class=css><code class=css>rotate3d(1, 1, 1, 0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>rotateX(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>rotateY(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>rotateZ(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>skewX(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>skewY(0)</code></code>&rsquo;,
     &lsquo;<code class=css><code class=css>matrix(1, 0, 0, 1, 0,
     0)</code></code>&rsquo; and &lsquo;<code class=css><code
     class=css>matrix3d(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,
     1)</code></code>&rsquo;. A special case is perspective: &lsquo;<code
     class=css><code class=css>perspective(infinity)</code></code>&rsquo;.
     The value of m<small>34</small> becomes infinitesimal small and the
     transform function is therefore assumed to be equal to the identity
     matrix.</p>

   <dt id=Term3DRenderingContext><dfn id=d-rendering-context>3D rendering
    context</dfn>

   <dd>
    <p> A containing block hierarchy of one or more levels, instantiated by
     elements with a computed value for the &lsquo;<a
     href="#transform-style"><code class=css><code
     class=property>transform-style</code></code></a>&rsquo; property of
     &lsquo;<code class=css><code class=css>preserve-3d</code></code>&rsquo;,
     whose elements share a common three-dimensional coordinate system.</p>
   </dd>
   <!-- Define "three-dimensional transform" ? -->
  </dl>
  <!-- ======================================================================================================= -->

  <h2 id="#two-dimensional-subset"><span class=secno>5. </span> Two
   Dimensional Subset</h2>

  <p> UAs may not always be able to render three-dimensional transforms and
   then just support a two-dimensional subset of this specification. In this
   case <a href="#three-d-transform-functions">three-dimensional
   transforms</a> and the properties &lsquo;<a href="#transform-style"><code
   class=property>transform-style</code></a>&rsquo;, &lsquo;<a
   href="#perspective"><code class=property>perspective</code></a>&rsquo;,
   &lsquo;<a href="#perspective-origin"><code
   class=property>perspective-origin</code></a>&rsquo; and &lsquo;<a
   href="#backface-visibility"><code
   class=property>backface-visibility</code></a>&rsquo; must not be
   supported.Section <a href="#transform-3d-rendering">3D Transform
   Rendering</a> does not apply. Matrix decomposing uses the technique taken
   from the "unmatrix" method in "Graphics Gems II, edited by Jim Arvo",
   simplified for the 2D case. Section <a
   href="#mathematical-description">Mathematical Description of Transform
   Functions</a> is still effective but can be reduced by using a 3x3
   transformation matrix where <em>a</em> equals <em>m11</em>, <em>b</em>
   equals <em>m12</em>, <em>c</em> equals <em>m21</em>, <em>d</em> equals
   <em>m22</em>, <em>e</em> equals <em>m41</em> and <em>f</em> equals
   <em>m42</em> (see <a href="#MatrixDefined">A 2D 3x2 matrix with six
   parameter</a>).

  <div class=figure> <img alt="3x3 matrix" height=79 src=3x3matrix.png
   title="\begin{bmatrix} a & c & e \\ b             & d & f \\ 0 & 0 & 1 \end{bmatrix}"
   width=82>
   <p class=caption> 3x3 matrix for two-dimensional transformations.</p>
  </div>

  <div class=example>
   <p> Authors can easily provide a fallback if UAs do not provide support
    for three-dimensional transforms. The following example has two property
    definitions for &lsquo;<a href="#effects"><code
    class=property>transform</code></a>&rsquo;. The first one consists of two
    two-dimensional transform functions. The second one has a two-dimensional
    and a three-dimensional transform function.</p>

   <pre>div {
    transform: scale(2) rotate(45deg);
    transform: scale(2) rotate3d(0, 0, 1, 45deg);
}</pre>

   <p> With 3D support, the second definition will override the first one.
    Without 3D support, the second definition is invalid and a UA falls back
    to the first definition.</p>
  </div>
  <!-- ======================================================================================================= -->

  <h2 id=transform-rendering><span class=secno>6. </span>The Transform
   Rendering Model</h2>
  <!-- This section is normative -->

  <p> Specifying a value other than &lsquo;<code class=css><code
   class=css>none</code></code>&rsquo; for the &lsquo;<a
   href="#effects"><code class=css><code
   class=property>transform</code></code></a>&rsquo; property establishes a
   new <em>local coordinate system</em> at the element that it is applied to.
   The mapping from where the element would have rendered into that local
   coordinate system is given by the element's <a
   href="#TermTransformationMatrix"><i>transformation matrix</i></a>.
   Transformations are cumulative. That is, elements establish their local
   coordinate system within the coordinate system of their parent. From the
   perspective of the user, an element effectively accumulates all the
   &lsquo;<a href="#effects"><code class=css><code
   class=property>transform</code></code></a>&rsquo; properties of its
   ancestors as well as any local transform applied to it. The accumulation
   of these transforms defines a <em>current transformation matrix (CTM)</em>
   for the element.

  <p> The coordinate space behaves as described in the <a
   href="http://www.w3.org/TR/SVG/coords.html#EstablishingANewUserSpace">coordinate
   system transformations</a> section of the SVG 1.1 specification. This is a
   coordinate system with two axes: the X axis increases horizontally to the
   right; the Y axis increases vertically downwards. Three-dimensional
   transform functions extent this coordinate space into three dimensions,
   adding a Z axis perpendicular to the plane of the screen, that increases
   towards the viewer.

  <p id=transformation-matrix-computation> The <a
   href="#TermTransformationMatrix"><i>transformation matrix</i></a> is
   computed from the &lsquo;<a href="#effects"><code class=css><code
   class=property>transform</code></code></a>&rsquo; and &lsquo;<a
   href="#transform-origin"><code class=css><code
   class=property>transform-origin</code></code></a>&rsquo; properties as
   follows:

  <ol>
   <li>Start with the identity matrix.

   <li>Translate by the computed X, Y and Z values of &lsquo;<a
    href="#transform-origin"><code class=css><code
    class=property>transform-origin</code></code></a>&rsquo;

   <li>Multiply by each of the transform functions in &lsquo;<a
    href="#effects"><code class=css><code
    class=property>transform</code></code></a>&rsquo; property in turn

   <li>Translate by the negated computed X, Y and Z values of &lsquo;<a
    href="#transform-origin"><code class=css><code
    class=property>transform-origin</code></code></a>&rsquo;
  </ol>

  <p> Transforms apply to <a class=term
   href="#transformable-element">transformable elements</a>.

  <div class=example>
   <pre>
div {
    transform: translate(100px, 100px);
}
</pre>

   <p>This transform moves the element by 100 pixels in both the X and Y
    directions.</p>

   <div class=figure> <img alt="The 100px translation in X and Y" height=250
    src="examples/translate1.svg" width=470></div>
  </div>

  <div class=example>
   <pre>div {
    height: 100px; width: 100px;
    transform-origin: 50px 50px;
    transform: rotate(45deg);
}
</pre>

   <p>The &lsquo;<a href="#transform-origin"><code
    class=property>transform-origin</code></a>&rsquo; property moves the
    point of origin by 50 pixels in both the X and Y directions. The
    transform rotates the element clockwise by 45° about the point of
    origin. After all transform functions were applied, the translation of
    the origin gets translated back by -50 pixels in both the X and Y
    directions.</p>

   <div class=figure><img alt="The point of origin gets translated temporary"
    height=250 src="examples/origin1.svg" width=735></div>
  </div>

  <div class=example>
   <pre>
div {
    height: 100px; width: 100px;
    transform: translate(80px, 80px) scale(1.5, 1.5) rotate(45deg);
}
</pre>

   <p>This transform moves the element by 80 pixels in both the X and Y
    directions, then scales the element by 150%, then rotates it 45&deg;
    clockwise about the Z axis. Note that the scale and rotation operate
    about the center of the element, since the element has the default
    transform-origin of &lsquo;<code class=css><code class=css>50%
    50%</code></code>&rsquo;.</p>

   <div class=figure> <img alt="The transform specified above" height=270
    src="examples/compound_transform.svg" width=270></div>

   <p>Note that an identical rendering can be obtained by nesting elements
    with the equivalent transforms:

   <pre>
&lt;div style="transform: translate(80px, 80px)"&gt;
    &lt;div style="transform: scale(1.5, 1.5)"&gt;
        &lt;div style="transform: rotate(45deg)"&gt;&lt;/div&gt;
    &lt;/div&gt;
&lt;/div&gt;
  </div>
  <!-- This "in the HTML namespace" is awkward. Is there a better way? -->

  <p> In the HTML namespace, the transform property does not affect the flow
   of the content surrounding the transformed element. However, the extent of
   the overflow area takes into account transformed elements. This behavior
   is similar to what happens when elements are offset via relative
   positioning. Therefore, if the value of the &lsquo;<code class=css><code
   class=property>overflow</code></code>&rsquo; property is &lsquo;<code
   class=css><code class=css>scroll</code></code>&rsquo; or &lsquo;<code
   class=css><code class=css>auto</code></code>&rsquo;, scrollbars will
   appear as needed to see content that is transformed outside the visible
   area.

  <p> In the HTML namespace, any value other than &lsquo;<code
   class=css><code class=css>none</code></code>&rsquo; for the transform
   results in the creation of both a stacking context and a containing block.
   The object acts as a containing block for fixed positioned descendants.

  <p class=issue> Is this effect on position:fixed necessary? If so, need to
   go into more detail here about why fixed positioned objects should do
   this, i.e., that it's much harder to implement otherwise.

  <p> <a href="http://dev.w3.org/csswg/css3-background/#fixed0">Fixed
   backgrounds</a> are affected by any transform specified for the root
   element, and not by any other transforms.

  <p class=note> Thus an element with a fixed background still acts like a
   "porthole" into an image that's fixed to the viewport, and transforms on
   the element affect the porthole, not the background behind it. On the
   other hand, transforming the root element will still transform everything
   on the page, rather than everything except for fixed backgrounds.

  <p> If the root element is transformed, the transformation applies to the
   entire canvas, including any background specified for the root element.
   Since <a
   href="http://dev.w3.org/csswg/css3-background/#special-backgrounds">the
   background painting area for the root element</a> is the entire canvas,
   which is infinite, the transformation might cause parts of the background
   that were originally off-screen to appear. For example, if the root
   element's background were repeating dots, and a transformation of
   &lsquo;<code class=css><code class=css>scale(0.5)</code></code>&rsquo;
   were specified on the root element, the dots would shrink to half their
   size, but there will be twice as many, so they still cover the whole
   viewport.

  <h3 id=transform-3d-rendering><span class=secno>6.1. </span>3D Transform
   Rendering</h3>
  <!-- Maybe define "tranform container" in the definitions, and use it everywhere
              in place of "containing block"? I'm not sure if "containing block" is exactly right. -->

  <p> Normally, elements render as flat planes, and are rendered into the
   same plane as their containing block. Often this is the plane shared by
   the rest of the page. Two-dimensional transform functions can alter the
   appearance of an element, but that element is still rendered into the same
   plane as its containing block.

  <p> Three-dimensional transforms can result in transformation matrices with
   a non-zero Z component<!-- clarify -->, potentially lifting them off the
   plane of their containing block. Because of this, elements with
   three-dimensional transformations could potentially render in an
   front-to-back order that different from the normal CSS rendering order,
   and intersect with each other. Whether they do so depends on whether the
   element is a member of a <a class=term href="#d-rendering-context">3D
   rendering context</a>, as described below.

  <div class=issue>
   <p class=desc>This description does not exactly match what WebKit
    implements. Perhaps it should be changed to match current
    implementations?</p>
  </div>

  <div class=example>
   <p>This example shows the effect of three-dimensional transform applied to
    an element.</p>

   <pre>
&lt;style&gt;
div {
    height: 150px;
    width: 150px;
}
.container {
    border: 1px solid black;
}
.transformed {
    transform: rotateY(50deg);
}
&lt;/style&gt;

&lt;div class="container"&gt;
    &lt;div class="transformed"&gt;&lt;/div&gt;
&lt;/div&gt;
</pre>

   <div class=figure> <img alt="Div with a rotateY transform." height=190
    src="examples/simple-3d-example.png" width=210></div>

   <p>The transform is a 50&deg; rotation about the vertical, Y axis. Note
    how this makes the blue box appear narrower, but not three-dimensional.</p>
  </div>

  <p> The &lsquo;<a href="#perspective"><code class=css><code
   class=property>perspective</code></code></a>&rsquo; and &lsquo;<a
   href="#perspective-origin"><code class=css><code
   class=property>perspective-origin</code></code></a>&rsquo; properties can
   be used to add a feeling of depth to a scene by making elements higher on
   the Z axis (closer to the viewer) appear larger, and those further away to
   appear smaller. The scaling is proportional to <var>d</var>/(<var>d</var>
   &minus; <var>Z</var>) where <var>d</var>, the value of &lsquo;<a
   href="#perspective"><code class=css><code
   class=property>perspective</code></code></a>&rsquo;, is the distance from
   the drawing plane to the the assumed position of the viewer's eye.

  <div class=figure> <img alt="Diagram of scale vs. Z position"
   src="perspective_distance.png">
   <p class=caption> Diagrams showing how scaling depends on the &lsquo;<a
    href="#perspective"><code class=css><code
    class=property>perspective</code></code></a>&rsquo; property and Z
    position. In the top diagram, <var>Z</var> is half of <var>d</var>. In
    order to make it appear that the original circle (solid outline) appears
    at <var>Z</var> (dashed circle), the circle is scaled up by a factor of
    two, resulting in the light blue circle. In the bottom diagram, the
    circle is scaled down by a factor of one-third to make it appear behind
    the original position.</p>
  </div>

  <p> Normally the assumed position of the viewer's eye is centered on a
   drawing. This position can be moved if desired &ndash; for example, if a
   web page contains multiple drawings that should share a common perspective
   &ndash; by setting &lsquo;<a href="#perspective-origin"><code
   class=css><code
   class=property>perspective-origin</code></code></a>&rsquo;.

  <div class=figure> <img alt="Diagram of different perspective-origin"
   src="perspective_origin.png">
   <p class=caption> Diagram showing the effect of moving the perspective
    origin upward.</p>
  </div>

  <p id=perspective-matrix-computation> The <a
   href="#TermPerspectiveMatrix"><i>perspective matrix</i></a> is computed as
   follows: <!-- Make this more mathy, with matrices? -->

  <ol>
   <li>Start with the identity matrix.

   <li>Translate by the computed X and Y values of &lsquo;<a
    href="#perspective-origin"><code class=css><code
    class=property>perspective-origin</code></code></a>&rsquo;

   <li>Multiply by the matrix that would be obtained from the &lsquo;<code
    class=css><a href="#perspective-function"><code
    class=css>perspective(&lt;length&gt;)</code></a></code>&rsquo; transform
    function, where the length is provided by the value of the &lsquo;<a
    href="#perspective"><code class=css><code
    class=property>perspective</code></code></a>&rsquo; property

   <li>Translate by the negated computed X and Y values of &lsquo;<a
    href="#perspective-origin"><code class=css><code
    class=property>perspective-origin</code></code></a>&rsquo;
  </ol>

  <div class=example>
   <p>This example shows how perspective can be used to cause
    three-dimensional transforms to appear more realistic.</p>

   <pre>
&lt;style&gt;
div {
    height: 150px;
    width: 150px;
}
.container {
    perspective: 500px;
    border: 1px solid black;
}
.transformed {
    transform: rotateY(50deg);
}
&lt;/style&gt;

&lt;div class="container"&gt;
    &lt;div class="transformed"&gt;&lt;/div&gt;
&lt;/div&gt;
</pre>

   <div class=figure> <img
    alt="Div with a rotateY transform,                     and perspective on its container"
    height=190 src="examples/simple-perspective-example.png" width=210></div>

   <p>The inner element has the same transform as in the previous example,
    but its rendering is now influenced by the perspective property on its
    parent element. Perspective causes vertices that have positive Z
    coordinates (closer to the viewer) to be scaled up in X and Y, and those
    further away (negative Z coordinates) to be scaled down, giving an
    appearance of depth.</p>
  </div>

  <p> An element with a three-dimensional transform that is not contained in
   a <a class=term href="#d-rendering-context">3D rendering context</a>
   renders with the appropriate transform applied, but does not intersect
   with any other elements. The three-dimensional transform in this case can
   be considered just as a painting effect, like two-dimensional transforms.
   Similarly, the transform does not affect painting order. For example, a
   transform with a positive Z translation may make an element look larger,
   but does not cause that element to render in front of elements with no
   translation in Z.

  <p> An element with a three-dimensional transform that is contained in a <a
   class=term href="#d-rendering-context">3D rendering context</a> can
   visibly interact with other elements in that same 3D rendering context;
   the set of elements participating in the same <a class=term
   href="#d-rendering-context">3D rendering context</a> may obscure each
   other or intersect, based on their computed transforms. They are rendered
   as if they are all siblings, positioned in a common 3D coordinate space.
   The position of each element in that three-dimensional space is determined
   by accumulating the transformation matrices up from the element that
   establishes the <a class=term href="#d-rendering-context">3D rendering
   context</a> through each element that is a containing block for the given
   element, as described below.
   <!-- More detail required, probably with matrices -->

  <div class=example>
   <pre>
&lt;style&gt;
div {
    height: 150px;
    width: 150px;
}
.container {
    perspective: 500px;
    border: 1px solid black;
}
.transformed {
    transform: rotateY(50deg);
    background-color: blue;
}
.child {
    transform-origin: top left;
    transform: rotateX(40deg);
    background-color: lime;
}
&lt;/style&gt;

&lt;div class="container"&gt;
    &lt;div class="transformed"&gt;
        &lt;div class="child"&gt;&lt;/div&gt;
    &lt;/div&gt;
&lt;/div&gt;
</pre>

   <p>This example shows how nested 3D transforms are rendered in the absence
    of &lsquo;<code class=css><code class=css>transform-style:
    preserve-3d</code></code>&rsquo;. The blue div is transformed as in the
    previous example, with its rendering influenced by the perspective on its
    parent element. The lime element also has a 3D transform, which is a
    rotation about the X axis (anchored at the top, by virtue of the
    transform-origin). However, the lime element is being rendered into the
    plane of its parent because it is not a member of a 3D rendering context;
    the parent is "flattening".</p>

   <div class=figure> <img alt="Nested 3D transforms, with flattening"
    height=200 src="examples/3d-rendering-context-flat.png" width=240></div>
  </div>