csswg-drafts/css-transforms/Overview.html at f82089ac0475eb45f390599922d711630037ce15 · w3c/csswg-drafts · GitHub

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<!doctype html>
<html lang="en">
 <head>

  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">


  <title>CSS Transforms Module Level 1</title>


  <link href="../default.css" rel="stylesheet" type="text/css">


  <link href="../csslogo.ico" rel="shortcut icon" type="image/x-icon">


  <link href="https://www.w3.org/StyleSheets/TR/W3C-ED" rel="stylesheet" type="text/css">


  <meta content="Bikeshed 1.0.0" name="generator">


  <script defer="" src="//test.csswg.org/harness/annotate.js#css-transforms-1_dev/css-transforms-1" type="text/javascript"></script>


  <style type="text/css">
.example {
  clear:both
}

th {
  text-align:left
}

.pseudo-code {
  font-family:monospace
}
.pseudo-code > ol {
  list-style-type:decimal
}
.pseudo-code > ol > li > ol {
  list-style-type:lower-latin
}
.pseudo-code > ol > li > ol > li > ol {
  list-style-type:lower-roman
}
.pseudo-code ul {
  list-style-type:disc
}

dd > p:nth-child(1) {
  margin-top:0
}
</style>


 </head>


 <body class="h-entry">

  <div class="head">

   <p data-fill-with="logo"><a class="logo" href="http://www.w3.org/">
    <img alt="W3C" height="48" src="https://www.w3.org/Icons/w3c_home" width="72">
</a>
</p>

   <h1 class="p-name no-ref" id="title">CSS Transforms Module Level 1</h1>

   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Editor’s Draft,
    <time class="dt-updated" datetime="2015-08-19">19 August 2015</time></span></h2>

   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://dev.w3.org/csswg/css-transforms/">http://dev.w3.org/csswg/css-transforms/</a>
     <dt>Latest version:
     <dd><a href="http://www.w3.org/TR/css3-transforms/">http://www.w3.org/TR/css3-transforms/</a>
     <dt>Previous Versions:
     <dd><a href="http://www.w3.org/TR/2012/WD-css3-transforms-20120911/" rel="previous">http://www.w3.org/TR/2012/WD-css3-transforms-20120911/</a>
     <dd><a href="http://www.w3.org/TR/2012/WD-css3-transforms-20120403/" rel="previous">http://www.w3.org/TR/2012/WD-css3-transforms-20120403/</a>
     <dt>Feedback:
     <dd><span><a href="mailto:public-fx@w3.org?subject=%5Bcss-transforms%5D%20YOUR%20TOPIC%20HERE">public-fx@w3.org</a> with subject line “<kbd>[css-transforms] <var>… message topic …</var></kbd>” (<a href="http://lists.w3.org/Archives/Public/public-fx/" rel="discussion">archives</a>)</span>
     <dt>Test Suite:
     <dd><a href="http://test.csswg.org/suites/css-transforms-1_dev/nightly-unstable/">http://test.csswg.org/suites/css-transforms-1_dev/nightly-unstable/</a>
     <dt>Issue Tracking:
     <dd><a href="#issues-index">Inline In Spec</a>
     <dt class="editor">Editors:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:simon.fraser@apple.com">Simon Fraser</a> (<a class="p-org org" href="http://www.apple.com/">Apple Inc</a>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:dino@apple.com">Dean Jackson</a> (<a class="p-org org" href="http://www.apple.com/">Apple Inc</a>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:eoconnor@apple.com">Edward O'Connor</a> (<a class="p-org org" href="http://www.apple.com/">Apple Inc</a>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:dschulze@adobe.com">Dirk Schulze</a> (<a class="p-org org" href="http://www.adobe.com/">Adobe Systems Inc</a>)
     <dt>Former Editors:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:hyatt@apple.com">David Hyatt</a> (<a class="p-org org" href="http://www.apple.com/">Apple Inc</a>)
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:cmarrin@apple.com">Chris Marrin</a> (<a class="p-org org" href="http://www.apple.com/">Apple Inc</a>)
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:ayg@aryeh.name">Aryeh Gregor</a> (<a class="p-org org" href="http://www.mozilla.org/">Mozilla</a>)
     <dt>Issues List:
     <dd><span><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></span>
    </dl>
   </div>

   <div data-fill-with="warning"></div>

   <p class="copyright" data-fill-with="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 2015 <a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</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>, <a href="http://ev.buaa.edu.cn/">Beihang</a>). 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>

   <hr title="Separator for header">
</div>


  <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>

  <div class="p-summary" data-fill-with="abstract">
   <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.</p>

</div>


  <h2 class="no-num no-toc no-ref heading settled" id="status"><span class="content">Status of this document</span></h2>

  <div data-fill-with="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>
   <p>
	The (<a href="http://lists.w3.org/Archives/Public/public-fx/">archived</a>) public mailing list
	<a href="mailto:public-fx@w3.org?Subject=%5Bcss-transforms%5D%20PUT%20SUBJECT%20HERE">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 “css-transforms” in the subject,
	preferably like this:
	“[css-transforms] <em>…summary of comment…</em>”

</p>
   <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/WG/">SVG Working Group</a> (part of the
	<a href="http://www.w3.org/Graphics/">Graphics Activity</a>).

</p>
   <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 includes 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></div>

  <div data-fill-with="at-risk"></div>


  <h2 class="no-num no-toc no-ref heading settled" id="contents"><span class="content">Table of Contents</span></h2>

  <div data-fill-with="table-of-contents" role="navigation">
   <ul class="toc" role="directory">
    <li><a href="#intro"><span class="secno">1</span> <span class="content">Introduction</span></a>
    <li><a href="#module-interactions"><span class="secno">2</span> <span class="content">Module Interactions</span></a>
    <li><a href="#css-values"><span class="secno">3</span> <span class="content">CSS Values</span></a>
    <li><a href="#terminology"><span class="secno">4</span> <span class="content">Terminology</span></a>
    <li><a href="#two-dimensional-subset"><span class="secno">5</span> <span class="content">Two Dimensional Subset</span></a>
    <li><a href="#transform-rendering"><span class="secno">6</span> <span class="content">The Transform Rendering Model</span></a>
     <ul class="toc">
      <li><a href="#3d-transform-rendering"><span class="secno">6.1</span> <span class="content">3D Transform Rendering</span></a>
       <ul class="toc">
        <li><a href="#perspective"><span class="secno">6.1.1</span> <span class="content">Perspective</span></a>
        <li><a href="#3d-rendering-contexts"><span class="secno">6.1.2</span> <span class="content">3D Rendering Contexts</span></a>
        <li><a href="#transformed-element-hierarchies"><span class="secno">6.1.3</span> <span class="content">Transformed element hierarchies</span></a>
        <li><a href="#accumulated-3d-transformation-matrix-computation"><span class="secno">6.1.4</span> <span class="content">Accumulated 3D Transformation Matrix Computation</span></a>
        <li><a href="#backface-visibility"><span class="secno">6.1.5</span> <span class="content">Backface Visibility</span></a>
       </ul>
      <li><a href="#processing-of-perspective-transformed-boxes"><span class="secno">6.2</span> <span class="content">
  Processing of Perspective-Transformed Boxes
</span></a>
     </ul>
    <li><a href="#transform-property"><span class="secno">7</span> <span class="content">The <span class="property">transform</span> Property</span></a>
     <ul class="toc">
      <li><a href="#serialization-of-transform-functions"><span class="secno">7.1</span> <span class="content">Serialization of <span class="production">&lt;transform-function></span>s</span></a>
      <li><a href="#serialization-of-the-computed-value"><span class="secno">7.2</span> <span class="content">Serialization of the <span>computed value</span> of <span class="production">&lt;transform-list></span></span></a>
     </ul>
    <li><a href="#transform-origin-property"><span class="secno">8</span> <span class="content">The <span class="property">transform-origin</span> Property</span></a>
    <li><a href="#transform-box"><span class="secno">9</span> <span class="content">Transform reference box: the <span class="property">transform-box</span> property</span></a>
    <li><a href="#transform-style-property"><span class="secno">10</span> <span class="content">The <span class="property">transform-style</span> Property</span></a>
     <ul class="toc">
      <li><a href="#grouping-property-values"><span class="secno">10.1</span> <span class="content">Grouping property values</span></a>
     </ul>
    <li><a href="#perspective-property"><span class="secno">11</span> <span class="content">The <span class="property">perspective</span> Property</span></a>
    <li><a href="#perspective-origin-property"><span class="secno">12</span> <span class="content">The <span class="property">perspective-origin</span> Property</span></a>
    <li><a href="#backface-visibility-property"><span class="secno">13</span> <span class="content">The <span class="property">backface-visibility</span> Property</span></a>
    <li><a href="#svg-transform"><span class="secno">14</span> <span class="content">The SVG <span class="property">transform</span> Attribute</span></a>
     <ul class="toc">
      <li><a href="#transform-attribute-specificity"><span class="secno">14.1</span> <span class="content">
  SVG <span class="property">transform</span> attribute specificity
</span></a>
      <li><a href="#svg-syntax"><span class="secno">14.2</span> <span class="content">Syntax of the SVG <span class="property">transform</span> attribute</span></a>
       <ul class="toc">
        <li><a href="#svg-transform-list"><span class="secno">14.2.1</span> <span class="content">Transform List</span></a>
        <li><a href="#svg-functional-notation"><span class="secno">14.2.2</span> <span class="content">Functional Notation</span></a>
        <li><a href="#svg-data-types"><span class="secno">14.2.3</span> <span class="content">SVG Data Types</span></a>
         <ul class="toc">
          <li><a href="#svg-transform-value"><span class="secno">14.2.3.1</span> <span class="content">
  The <span class="production">&lt;length></span> type
</span></a>
          <li><a href="#svg-angle"><span class="secno">14.2.3.2</span> <span class="content">The <span class="production">&lt;angle></span> type</span></a>
          <li><a href="#svg-number"><span class="secno">14.2.3.3</span> <span class="content">The <span class="production">&lt;number></span> type</span></a>
         </ul>
       </ul>
      <li><a href="#svg-gradient-transform-pattern-transform"><span class="secno">14.3</span> <span class="content">
  The SVG <span class="attr-name">gradientTransform</span> and <span class="attr-name">patternTransform</span> attributes
</span></a>
      <li><a href="#svg-transform-functions"><span class="secno">14.4</span> <span class="content">
  SVG transform functions
</span></a>
      <li><a href="#svg-three-dimensional-functions"><span class="secno">14.5</span> <span class="content">SVG and 3D transform functions</span></a>
      <li><a href="#svg-user-coordinate-space"><span class="secno">14.6</span> <span class="content">User coordinate space</span></a>
      <li><a href="#transform-attribute-dom"><span class="secno">14.7</span> <span class="content">
  SVG DOM interface for the <span class="property">transform</span> attribute
</span></a>
     </ul>
    <li><a href="#svg-animation"><span class="secno">15</span> <span class="content">SVG Animation</span></a>
     <ul class="toc">
      <li><a href="#svg-animate-element"><span class="secno">15.1</span> <span class="content">
  The <span><code class="element-name">&lt;animate></code></span> and <span><code class="element-name">&lt;set></code></span> element
</span></a>
      <li><a href="#neutral-element"><span class="secno">15.2</span> <span class="content">Neutral element for addition</span></a>
      <li><a href="#svg-attribute-name"><span class="secno">15.3</span> <span class="content">
  The SVG '<span>attributeName</span>' attribute
</span></a>
     </ul>
    <li><a href="#transform-functions"><span class="secno">16</span> <span class="content">The Transform Functions</span></a>
     <ul class="toc">
      <li><a href="#two-d-transform-functions"><span class="secno">16.1</span> <span class="content">2D Transform Functions</span></a>
      <li><a href="#three-d-transform-functions"><span class="secno">16.2</span> <span class="content">3D Transform Functions</span></a>
     </ul>
    <li><a href="#transform-function-lists"><span class="secno">17</span> <span class="content">The Transform Function Lists</span></a>
    <li><a href="#interpolation-of-transforms"><span class="secno">18</span> <span class="content">Interpolation of Transforms</span></a>
    <li><a href="#transform-primitives"><span class="secno">19</span> <span class="content">
  Transform function primitives and derivatives
</span></a>
    <li><a href="#interpolation-of-transform-functions"><span class="secno">20</span> <span class="content">
  Interpolation of primitives and derived transform functions
</span></a>
    <li><a href="#matrix-interpolation"><span class="secno">21</span> <span class="content">Interpolation of Matrices</span></a>
     <ul class="toc">
      <li><a href="#supporting-functions"><span class="secno">21.1</span> <span class="content">Supporting functions</span></a>
      <li><a href="#interpolation-of-2d-matrices"><span class="secno">21.2</span> <span class="content">Interpolation of 2D matrices</span></a>
       <ul class="toc">
        <li><a href="#decomposing-a-2d-matrix"><span class="secno">21.2.1</span> <span class="content">Decomposing a 2D matrix</span></a>
        <li><a href="#interpolation-of-decomposed-2d-matrix-values"><span class="secno">21.2.2</span> <span class="content">
  Interpolation of decomposed 2D matrix values
</span></a>
        <li><a href="#recomposing-to-a-2d-matrix"><span class="secno">21.2.3</span> <span class="content">Recomposing to a 2D matrix</span></a>
       </ul>
      <li><a href="#interpolation-of-3d-matrices"><span class="secno">21.3</span> <span class="content">Interpolation of 3D matrices</span></a>
       <ul class="toc">
        <li><a href="#decomposing-a-3d-matrix"><span class="secno">21.3.1</span> <span class="content">Decomposing a 3D matrix</span></a>
        <li><a href="#interpolation-of-decomposed-3d-matrix-values"><span class="secno">21.3.2</span> <span class="content">
  Interpolation of decomposed 3D matrix values
</span></a>
        <li><a href="#recomposing-to-a-3d-matrix"><span class="secno">21.3.3</span> <span class="content">Recomposing to a 3D matrix</span></a>
       </ul>
     </ul>
    <li><a href="#mathematical-description"><span class="secno">22</span> <span class="content">
  Mathematical Description of Transform Functions
</span></a>
    <li><a href="#changes"><span class="secno"></span> <span class="content">Changes since last publication</span></a>
    <li><a href="#acknowledgments"><span class="secno"></span> <span class="content">Acknowledgments</span></a>
    <li><a href="#conformance"><span class="secno"></span> <span class="content">
Conformance</span></a>
     <ul class="toc">
      <li><a href="#conventions"><span class="secno"></span> <span class="content">
Document conventions</span></a>
      <li><a href="#conformance-classes"><span class="secno"></span> <span class="content">
Conformance classes</span></a>
      <li><a href="#partial"><span class="secno"></span> <span class="content">
Partial implementations</span></a>
      <li><a href="#experimental"><span class="secno"></span> <span class="content">
Experimental implementations</span></a>
      <li><a href="#testing"><span class="secno"></span> <span class="content">
Non-experimental implementations</span></a>
     </ul>
    <li><a href="#index"><span class="secno"></span> <span class="content">Index</span></a>
     <ul class="toc">
      <li><a href="#index-defined-here"><span class="secno"></span> <span class="content">Terms defined by this specification</span></a>
      <li><a href="#index-defined-elsewhere"><span class="secno"></span> <span class="content">Terms defined by reference</span></a>
     </ul>
    <li><a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ul class="toc">
      <li><a href="#normative"><span class="secno"></span> <span class="content">Normative References</span></a>
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ul>
    <li><a href="#property-index"><span class="secno"></span> <span class="content">Property Index</span></a>
    <li><a href="#issues-index"><span class="secno"></span> <span class="content">Issues Index</span></a>
   </ul></div>

  <main>


   <h2 class="heading settled" data-level="1" id="intro"><span class="secno">1. </span><span class="content">Introduction</span><a class="self-link" href="#intro"></a></h2>


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


   <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>


   <p>This coordinate space can be modified with the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> property. Using transform, elements can be translated, rotated and scaled in two or three dimensional space.</p>


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


   <ul>

    <li>
    The <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a> property provides a convenient way to control the origin about which transforms on an element are applied.


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


    <li>
    The <a class="property" data-link-type="propdesc" href="#propdef-transform-style">transform-style</a> 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 <a class="property" data-link-type="propdesc" href="#propdef-backface-visibility">backface-visibility</a> 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 <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-backgrounds-3/#hidden">hidden</a> for this property.

</ul>


   <p class="note" role="note">Note: While some values of the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> 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 class="heading settled" data-level="2" id="module-interactions"><span class="secno">2. </span><span class="content">Module Interactions</span><a class="self-link" href="#module-interactions"></a></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">Visual formatting model</a> from <a data-link-type="biblio" href="#biblio-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">containing block</a>, and/or the creation of a <a data-link-type="dfn" href="https://drafts.csswg.org/css2/visuren.html#x44">stacking context</a>.</p>


   <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">Appendix E</a> of <a data-link-type="biblio" href="#biblio-css21">[CSS21]</a>.</p>


   <p>Transforms affect the rendering of backgrounds on elements with a value of <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-backgrounds-3/#fixed">fixed</a> for the <a class="property" data-link-type="propdesc" href="https://drafts.csswg.org/css-backgrounds-3/#background-attachment">background-attachment</a> property, which is specified in <a data-link-type="biblio" href="#biblio-css3bg">[CSS3BG]</a>.</p>


   <p>Transforms affect the client rectangles returned by the Element Interface Extensions <a href="http://www.w3.org/TR/cssom-view/#dom-element-getclientrects">getClientRects()</a> and <a href="http://www.w3.org/TR/cssom-view/#dom-element-getboundingclientrect">getBoundingClientRect()</a>, which are specified in <a data-link-type="biblio" href="#biblio-cssom-view">[CSSOM-VIEW]</a>.</p>


   <h2 class="heading settled" data-level="3" id="css-values"><span class="secno">3. </span><span class="content">CSS Values</span><a class="self-link" href="#css-values"></a></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 data-link-type="biblio" href="#biblio-css21">[CSS21]</a>. Value types not defined in these specifications are defined in CSS Values and Units Module Level 3 <a data-link-type="biblio" href="#biblio-css3val">[CSS3VAL]</a>.</p>


   <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#value-def-inherit">inherit</a> keyword as their property value. For readability it has not been repeated explicitly.</p>


   <h2 class="heading settled" data-level="4" id="terminology"><span class="secno">4. </span><span class="content">Terminology</span><a class="self-link" href="#terminology"></a></h2>


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


   <dl>

    <dt><dfn data-dfn-type="dfn" data-noexport="" id="transformable-element">transformable element<a class="self-link" href="#transformable-element"></a></dfn>

    <dd>
    A transformable element is an element in one of these categories:

     <ul>

      <li>
        an element whose layout is governed by the CSS box model 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 <a class="property" data-link-type="propdesc" href="https://drafts.csswg.org/css2/visuren.html#propdef-display">display</a> property computes to <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-row">table-row</a>, <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-row-group">table-row-group</a>, <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-header-group">table-header-group</a>, <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-footer-group">table-footer-group</a>, <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-cell">table-cell</a>, or <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-display-3/#valdef-display-table-caption">table-caption</a> <a data-link-type="biblio" href="#biblio-css21">[CSS21]</a>


      <li>
        an element in the SVG namespace and not governed by the CSS box model which has the attributes <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a>, <a class="attr-name" href="http://www.w3.org/TR/2011/REC-SVG11-20110816/pservers.html#PatternElementPatternTransformAttribute">‘patternTransform‘</a> or <a class="attr-name" data-link-type="maybe" href="http://www.w3.org/TR/2011/REC-SVG11-20110816/pservers.html#LinearGradientElementGradientTransformAttribute">gradientTransform</a> <a data-link-type="biblio" href="#biblio-svg11">[SVG11]</a>.


     </ul>


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="transformed-element">transformed element<a class="self-link" href="#transformed-element"></a></dfn>

    <dd>
    An element with a computed value other than <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a> for the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> property.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="3d_transformed-element">3D-transformed element<a class="self-link" href="#3d_transformed-element"></a></dfn>

    <dd>
    An element whose computed value for the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> property includes one of the <a href="#three-d-transform-functions">3D transform functions</a>


    <dt><dfn data-dfn-type="dfn" data-export="" id="user-coordinate-system">user coordinate system<a class="self-link" href="#user-coordinate-system"></a></dfn>

    <dt><dfn data-dfn-type="dfn" data-export="" id="local-coordinate-system">local coordinate system<a class="self-link" href="#local-coordinate-system"></a></dfn>

    <dd>

     <p>In general, a coordinate system defines locations and distances on the current canvas. The current local coordinate system (also user coordinate system) is the coordinate system that is currently active and which is used to define how coordinates and lengths are located and computed, respectively, on the current canvas.</p>


     <p>The current user coordinate system has its origin at the top-left of a <a data-link-type="dfn" href="#reference-box">reference box</a> specified by the <a class="property" data-link-type="propdesc" href="#propdef-transform-box">transform-box</a> property. Percentage values are relative to the dimension of this reference box. One unit equals one CSS pixel.</p>


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="perspective-matrix">perspective matrix<a class="self-link" href="#perspective-matrix"></a></dfn>

    <dd>
    A matrix computed from the values of the <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a> and <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a> properties as described <a href="#perspective-matrix-computation">below</a>.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="transformation-matrix">transformation matrix<a class="self-link" href="#transformation-matrix"></a></dfn>

    <dd>
    A matrix that defines the mathematical mapping from one coordinate system into another. It is computed from the values of the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> and <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a> properties as described <a href="#transformation-matrix-computation">below</a>.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="current-transformation-matrix-ctm">current transformation matrix (CTM)<a class="self-link" href="#current-transformation-matrix-ctm"></a></dfn>

    <dd>
    A matrix that defines the mapping from the local coordinate system into the viewport coordinate system.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="accumulated-3d-transformation-matrix">accumulated 3D transformation matrix<a class="self-link" href="#accumulated-3d-transformation-matrix"></a></dfn>

    <dd>
    A matrix computed for an element relative to the root of its <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a>, as described <a href="#accumulated-3d-transformation-matrix-computation">below</a>.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="2d-matrix">2D matrix<a class="self-link" href="#2d-matrix"></a></dfn>

    <dd>
    A 3x2 transformation matrix with 6 i
5800
tems or a 4x4 matrix with 16 items, where the items m<sub>31</sub>, m<sub>32</sub>, m<sub>13</sub>, m<sub>23</sub>, m<sub>43</sub>, m<sub>14</sub>, m<sub>24</sub>, m<sub>34</sub> are equal to <span class="css">0</span> and m<sub>33</sub>, m<sub>44</sub> are equal to <span class="css">1</span>.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="3d-matrix">3D matrix<a class="self-link" href="#3d-matrix"></a></dfn>

    <dd>
    A 4x4 matrix which does not fulfill the requirements of an <a data-link-type="dfn" href="#2d-matrix">2D matrix</a>.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="identity-transform-function">identity transform function<a class="self-link" href="#identity-transform-function"></a></dfn>

    <dd>
    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 <span class="css">translate(0)</span>, <span class="css">translate3d(0, 0, 0)</span>, <span class="css">translateX(0)</span>, <span class="css">translateY(0)</span>, <span class="css">translateZ(0)</span>, <span class="css">scale(1)</span>, <span class="css">scaleX(1)</span>, <span class="css">scaleY(1)</span>, <span class="css">scaleZ(1)</span>, <span class="css">rotate(0)</span>, <span class="css">rotate3d(1, 1, 1, 0)</span>, <span class="css">rotateX(0)</span>, <span class="css">rotateY(0)</span>, <span class="css">rotateZ(0)</span>, <span class="css">skew(0, 0)</span>, <span class="css">skewX(0)</span>, <span class="css">skewY(0)</span>, <span class="css">matrix(1, 0, 0, 1, 0, 0)</span> and <span class="css">matrix3d(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)</span>. A special case is perspective: <span class="css">perspective(infinity)</span>. The value of m<sub>34</sub> becomes infinitesimal small and the transform function is therefore assumed to be equal to the identity matrix.


    <dt><dfn data-dfn-type="dfn" data-noexport="" id="3d-rendering-context">3D rendering context<a class="self-link" href="#3d-rendering-context"></a></dfn>

    <dd>
    A set of elements with a common ancestor which share a common three-dimensional coordinate system, as described <a href="#3d-rendering-contexts">below</a>.

</dl>


   <h2 class="heading settled" data-level="5" id="two-dimensional-subset"><span class="secno">5. </span><span class="content">Two Dimensional Subset</span><a class="self-link" href="#two-dimensional-subset"></a></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 <a class="property" data-link-type="propdesc" href="#propdef-transform-style">transform-style</a>, <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a>, <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a> and <a class="property" data-link-type="propdesc" href="#propdef-backface-visibility">backface-visibility</a> must not be supported. Section <a href="#3d-transform-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 m<sub>11</sub>, <em>b</em> equals m<sub>12</sub>, <em>c</em> equals m<sub>21</sub>, <em>d</em> equals m<sub>22</sub>, <em>e</em> equals m<sub>41</sub> and <em>f</em> equals m<sub>42</sub> (see <a href="#MatrixDefined">A 2D 3x2 matrix with six parameter</a>).</p>


   <div class="figure">
  <img alt="3x3 matrix" height="79" src="images/3x3matrix.png" title="\begin{bmatrix} a &amp; c &amp; e \\ b
  &amp; d &amp; f \\ 0 &amp; 0 &amp; 1 \end{bmatrix}" width="82">

    <p class="caption">
     3x3 matrix for two-dimensional transformations.
  </p>
</div>


   <div class="example" id="example-adfb2474"><a class="self-link" href="#example-adfb2474"></a>


    <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 <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a>. 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 class="heading settled" data-level="6" id="transform-rendering"><span class="secno">6. </span><span class="content">The Transform Rendering Model</span><a class="self-link" href="#transform-rendering"></a></h2>


   <p><em>This section is normative.</em></p>


   <p>Specifying a value other than <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a> for the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> property establishes a new <a data-link-type="dfn" href="#local-coordinate-system">local coordinate system</a> at the element that it is applied to. The mapping from where the element would have rendered into that local coordinate system i
B3C0
s given by the element’s <a data-link-type="dfn" href="#transformation-matrix">transformation matrix</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 <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> properties of its ancestors as well as any local transform applied to it. The accumulation of these transforms defines a <a data-link-type="dfn" href="#current-transformation-matrix-ctm">current transformation matrix (CTM)</a> for the element.</p>


   <p>The coordinate space 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 extend this coordinate space into three dimensions, adding a Z axis perpendicular to the plane of the screen, that increases towards the viewer.</p>


   <div class="figure">
  <img alt="Demonstration of the initial coordinate space" height="240" src="images/coordinates.svg" width="270">

    <p class="caption">
     Demonstration of the initial coordinate space.
  </p>
</div>


   <p id="transformation-matrix-computation">
  The <a data-link-type="dfn" href="#transformation-matrix">transformation matrix</a> is computed from the <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> and <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a> properties as follows:
  </p>
   <ol>

    <li>Start with the identity matrix.

    <li>Translate by the computed X, Y and Z values of <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a>

    <li>Multiply by each of the transform functions in <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> property from left to right

    <li>Translate by the negated computed X, Y and Z values of <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a>
  </ol>

   <p></p>


   <p>Transforms apply to <a data-link-type="dfn" href="#transformable-element">transformable elements</a>.</p>


   <p class="note" role="note">Note: Transformations do affect the visual rendering, but have no affect on the CSS layout other than affecting overflow. Transforms are also taken into account when computing client rectangles exposed via the Element Interface Extensions, namely <a href="http://www.w3.org/TR/cssom-view/#dom-element-getclientrects">getClientRects()</a> and <a href="http://www.w3.org/TR/cssom-view/#dom-element-getboundingclientrect">getBoundingClientRect()</a>, which are specified in <a data-link-type="biblio" href="#biblio-cssom-view">[CSSOM-VIEW]</a>.</p>


   <div class="example" id="example-0e1aae1f"><a class="self-link" href="#example-0e1aae1f"></a>

    <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" id="example-2dc0e62d"><a class="self-link" href="#example-2dc0e62d"></a>

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


    <p>The <a class="property" data-link-type="propdesc" href="#propdef-transform-origin">transform-origin</a> 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" id="example-f91bd735"><a class="self-link" href="#example-f91bd735"></a>

    <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° 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 <span class="css">50% 50%</span>.</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:</p>


    <pre>&lt;div style="transform: translate(80px, 80px)">
    &lt;div style="transform: scale(1.5, 1.5)">
        &lt;div style="transform: rotate(45deg)">&lt;/div>
    &lt;/div>
&lt;/div></pre>
</div>


   <p>For elements whose layout is governed by the CSS box model, 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 <a class="property" data-link-type="propdesc" href="https://drafts.csswg.org/css-overflow-3/#propdef-overflow">overflow</a> property is <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-backgrounds-3/#scroll">scroll</a> or <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-align-3/#valdef-justify-content-auto">auto</a>, scrollbars will appear as needed to see content that is transformed outside the visible area.</p>


   <p>For elements whose layout is governed by the CSS box model, any value other than <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a> 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>


   <p class="issue" id="issue-fc114988"><a class="self-link" href="#issue-fc114988"></a> Is this effect on <a class="css" data-link-type="propdesc" href="https://drafts.csswg.org/css-position-3/#propdef-position">position: fixed</a> 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. See <a href="https://www.w3.org/Bugs/Public/show_bug.cgi?id=16328">Bug 16328</a>.</p>


   <p><a href="http://www.w3.org/TR/css3-background/#fixed0">Fixed backgrounds</a> on the root element are affected by any transform specified for that element. For all other elements that are effected by a transform (i.e. have a transform applied to them, or to any of their ancestor elements), a value of <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-backgrounds-3/#fixed">fixed</a> for the <a class="property" data-link-type="propdesc" href="https://drafts.csswg.org/css-backgrounds-3/#background-attachment">background-attachment</a> property is treated as if it had a value of <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-backgrounds-3/#scroll">scroll</a>. The computed value of <a class="property" data-link-type="propdesc" href="https://drafts.csswg.org/css-backgrounds-3/#background-attachment">background-attachment</a> is not affected.</p>


   <p class="note" role="note">Note: 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://www.w3.org/TR/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 <span class="css">scale(0.5)</span> 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.</p>


   <h3 class="heading settled" data-level="6.1" id="3d-transform-rendering"><span class="secno">6.1. </span><span class="content">3D Transform Rendering</span><a class="self-link" href="#3d-transform-rendering"></a></h3>


   <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>


   <p>Three-dimensional transforms can result in transformation matrices with a non-zero Z component (where the Z axis projects out of the plane of the screen). This can result in an element rendering on a different plane than that of its containing block. This may affect the front-to-back rendering order of that element relative to other elements, as well as causing it to intersect with other elements.</p>


   <div class="example" id="example-77871040"><a class="self-link" href="#example-77871040"></a>


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


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

&lt;div class="container">
    &lt;div class="transformed">&lt;/div>
&lt;/div></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° rotation about the vertical, Y axis. Note how this makes the blue box appear narrower, but not three-dimensional.</p>
</
5800
div>


   <h4 class="heading settled" data-level="6.1.1" id="perspective"><span class="secno">6.1.1. </span><span class="content">Perspective</span><a class="self-link" href="#perspective"></a></h4>


   <p>The <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a> and <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a> 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> − <var>Z</var>) where <var>d</var>, the value of <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a>, is the distance from the drawing plane to the the assumed position of the viewer’s eye.</p>


   <div class="figure">
  <img alt="Diagram of scale vs. Z position" src="images/perspective_distance.png">

    <p class="caption">
    Diagrams showing how scaling depends on the <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a> 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 – for example, if a web page contains multiple drawings that should share a common perspective – by setting <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a>.</p>


   <div class="figure">
  <img alt="Diagram of different perspective-origin" src="images/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 data-link-type="dfn" href="#perspective-matrix">perspective matrix</a> is computed as follows:
  </p>
   <ol>

    <li>Start with the identity matrix.

    <li>Translate by the computed X and Y values of <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a>

    <li>Multiply by the matrix that would be obtained from the <a class="css" data-link-type="maybe" href="#funcdef-perspective">perspective()</a> transform function, where the length is provided by the value of the <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a> property

    <li>Translate by the negated computed X and Y values of <a class="property" data-link-type="propdesc" href="#propdef-perspective-origin">perspective-origin</a>
  </ol>

   <p></p>


   <div class="example" id="example-71d19196"><a class="self-link" href="#example-71d19196"></a>


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


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

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


   <h4 class="heading settled" data-level="6.1.2" id="3d-rendering-contexts"><span class="secno">6.1.2. </span><span class="content">3D Rendering Contexts</span><a class="self-link" href="#3d-rendering-contexts"></a></h4>


   <p>This section specifies the rendering model for content that uses 3D-transforms and the <span class="css">transform-style</span> property. In order to describe this model, we introduce the concept of a "3D rendering context".</p>


   <p>A <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a> is a set of elements rooted in a common ancestor that, for the purposes of 3D-transform rendering, are considered to share a common three-dimensional coordinate system. The front-to-back rendering of elements in the a 3D rendering context depends on their z-position in that three-dimensional space, and, if the 3D transforms on those elements cause them to intersect, then they are rendered with intersection.</p>


   <p>A 3D rendering context is established by an element which has a used value for transform-style of "flat". Descendant elements with a used value for transform-style of "auto" or "preserve-3d" share their enclosing 3D rendering context. A descendant with a used value for transform-style of "flat" participates in its containing 3D rendering context, but establishes a new 3D rendering context for its descendants. For the purposes of rendering in its containing 3D rendering context, it behaves like a flat plane.</p>


   <p class="note" role="note">Note: This is conceptually similar to CSS stacking contexts. A positioned element with explicit z-index establishes a stacking context, while participating in the stacking context of an ancestor.  Similarly, an element can establish a 3D rendering context for its descendants, while participating in the 3D rendering context of an ancestor. Just as elements within a stacking context render in z-index order, elements in a 3D-rendering context render in z-depth order and can intersect.</p>


   <p>Some CSS properties have values that are considered to force "grouping": they require that their element and its descendants are rendered as a group before being composited with other elements; these include opacity, filters and properties that affect clipping. The relevant property values are listed under <a href="#grouping-property-values">grouping property values</a>. These grouping property values force the used value for transform-style to be "flat", and such elements are referred to as <dfn data-dfn-type="dfn" data-noexport="" id="flattening-elements">flattening elements<a class="self-link" href="#flattening-elements"></a></dfn>. Consequently, they always establish a new 3D rendering context. The root element always has a used value of "flat" for transform-style.</p>


   <p>The rendering of elements in a 3D rendering context is as follows (numbers refer to items in <a href="http://www.w3.org/TR/CSS2/zindex.html#painting-order">CSS 2.1, Appendix E, Section E.2 Painting Order</a>):</p>


   <ol style="list-style-type: upper-alpha;">

    <li>The background, borders and other box decorations of the establishing element are rendered (steps 1 and 2)

    <li>The content and descendant elements without 3D transforms, ordered according to steps 3—7, are rendered into a plane at z=0 relative to to the establishing element.

    <li>3D-transformed elements are each rendered into their own plane, transformed by the <a href="#accumulated-3d-transformation-matrix-computation">accumulated 3D transformation matrix</a>.

    <li>Intersection is performed between the set of planes generated by steps B and C, according to <a href="http://en.wikipedia.org/wiki/Newell%27s_algorithm">Newell’s algorithm</a>.

    <li>The resulting set of planes is rendered on top of the backgrounds and box decorations rendered in this step A. Coplanar 3D transformed elements are rendered in painting order.
</ol>


   <p class="issue" id="issue-d667e5bf"><a class="self-link" href="#issue-d667e5bf"></a> is it OK to not pop 2D-transformed elements into their own planes?</p>


   <p class="issue" id="issue-d1f8f85e"><a class="self-link" href="#issue-d1f8f85e"></a> requiring intersection with non-transformed content and descendants requires UAs to allocate additional textures (possibly doubling memory use). Would be more efficient to simply render content and untransformed descendants along with background and borders.</p>


   <p>Note that elements with transforms which have a negative z-component will render behind the content and untransformed descendants of the establishing element, and that 3D transformed elements may interpenetrate with content and untransformed elements.</p>


   <p class="note" role="note">Note: Because the 3D-transformed elements in a 3D rendering context can all depth-sort and intersect with each other, they are effectively rendered as if they were siblings. The effect of transform-style: preserve-3d can then be thought of as causing all the 3D transformed elements in a 3D rendering context to be hoisted up into the establishing element, but still rendered with their <a href="#accumulated-3d-transformation-matrix-computation">accumulated 3D transformation matrix</a>.</p>


   <div class="example" id="example-c766935d"><a class="self-link" href="#example-c766935d"></a>

    <pre>&lt;style>
.container {
    background-color: rgba(0, 0, 0, 0.3);
    perspective: 500px;
}
.container > div {
    position: absolute;
    left: 0;
}
.container > :first-child {
    transform: rotateY(45deg);
    background-color: orange;
    top: 10px;
    height: 135px;
}
.container > :last-child {
    transform: translateZ(40px);
    background-color: rgba(0, 0, 255, 0.6);
    top: 50px;
    height: 100px;
}
&lt;/style>

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


    <p>This example shows show elements in a 3D rendering context can intersect. The container element establishes a 3D rendering context for itself and its two children. The children intersect with each other, and the orange element also intersects with the container.</p>


    <div class="figure">
    <img alt="Intersecting sibling elements." height="198" src="examples/3d-intersection.png" width="210">
  </div>
</div>


   <p>The <span class="css">perspective</span> property can be used to ensure that 3D transformed elements in the resulting 3D rendering context appear to live in a common three-dimensional space with depth, by suppling a common perspective matrix to descendant transformed members of its 3D rendering context, which is taken into account in the <a href="#accumulated-3d-transformation-matrix-computation">accumulated 3D matrix computation</a>.</p>


   <p>By default, elements with value for <span class="css">perspective</span> other than <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a> are flattening, and thus establish a 3D rendering context. However, setting <span class="css">transform-style</span> to <span class="css">preserve-3d</span> allows the perspective element to extend its containing 3D rendering context (provided no other <a href="#grouping-property-values">grouping property values</a> are in effect).</p>


   <div class="example" id="example-c4ff9b27"><a class="self-link" href="#example-c4ff9b27"></a>

    <pre>&lt;style>
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>

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


    <p>This example shows how nested 3D transforms are rendered. 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 the same 3D rendering context; the parent is "flattening". Thus the lime element only appears shorter; it does not "pop out" of the blue element.</p>


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


   <h4 class="heading settled" data-level="6.1.3" id="transformed-element-hierarchies"><span class="secno">6.1.3. </span><span class="content">Transformed element hierarchies</span><a class="self-link" href="#transformed-element-hierarchies"></a></h4>


   <p>By default, <a data-link-type="dfn" href="#transformed-element">transformed elements</a> are flattening, and thus establish a <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a>. However, since it is useful to construct hierarchies of transformed objects that share a common 3-dimensional space, this flattening behavior may be overridden by specifying a value of <span class="css">preserve-3d</span> for the <span class="css">transform-style</span> property, provided no other <a href="#grouping-property-values">grouping property values</a> are in effect. This allows descendants of the transformed element to share the same 3D rendering context. Non-3D-transformed descendants of such elements are rendered into the plane of the element in step C above, but 3D-transformed elements in the same 3D rendering context will "pop out" into their own planes.</p>


   <div class="example" id="example-6a6e3b98"><a class="self-link" href="#example-6a6e3b98"></a>

    <pre>&lt;style>
div {
    height: 150px;
    width: 150px;
}
.container {
    perspective: 500px;
    border: 1px solid black;
}
.transformed {
    <b>transform-style: preserve-3d</b>;
    transform: rotateY(50deg);
    background-color: blue;
}
.child {
    transform-origin: top left;
    transform: rotateX(40deg);
    background-color: lime;
}
&lt;/style></pre>


    <p>This example is identical to the previous example, with the addition of <a class="css" data-link-type="propdesc" href="#propdef-transform-style">transform-style: preserve-3d</a> on the blue element. The blue element now extends the 3D rendering context of its container. Now both blue and lime elements share a common three-dimensional space, so the lime element renders as tilting out from its parent, influenced by the perspective on the container.</p>


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


   <h4 class="heading settled" data-level="6.1.4" id="accumulated-3d-transformation-matrix-computation"><span class="secno">6.1.4. </span><span class="content">Accumulated 3D Transformation Matrix Computation</span><a class="self-link" href="#accumulated-3d-transformation-matrix-computation"></a></h4>


   <p>The final value of the transform used to render an element in a <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a> is computed by accumulating an <a data-link-type="dfn" href="#accumulated-3d-transformation-matrix">accumulated 3D transformation matrix</a> as follows:</p>


   <ol>
    <li data-md="">
     <p>Let <var>transform</var> be the identity matrix.</p>


    <li data-md="">
     <p>Let <var>current element</var> be the transformed element.</p>


    <li data-md="">
     <p>Let <var>ancestor block</var> be the element that establishes the transformed element’s containing block.</p>


    <li data-md="">
     <p>While <var>current element</var> is not the element that establishes the transformed element’s <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a>:</p>


     <ol>
      <li data-md="">
       <p>If <var>current element</var> has a value for <a class="property" data-link-type="propdesc" href="#propdef-transform">transform</a> which is not <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a>, pre-multiply <var>current element</var>’s <a data-link-type="dfn" href="#transformation-matrix">transformation matrix</a> with the <var>transform</var>.</p>


      <li data-md="">
       <p>Compute a translation matrix which represents the offset of <var>current element</var> from its <var>ancestor block</var>, and pre-multiply that matrix into the <var>transform</var>.</p>


      <li data-md="">
       <p>If <var>ancestor block</var> has a value for <a class="property" data-link-type="propdesc" href="#propdef-perspective">perspective</a> which is not <a class="css" data-link-type="maybe" href="https://drafts.csswg.org/css-animations-1/#valdef-animation-name-none">none</a>, pre-multiply the <var>ancestor block</var>’s <a data-link-type="dfn" href="#perspective-matrix">perspective matrix</a> into the <var>transform</var>.</p>


      <li data-md="">
       <p>Let <var>ancestor block</var> be the element that establishes the <var>current element</var>’s containing block.</p>


      <li data-md="">
       <p>Let <var>current element</var> be the <var>ancestor block</var>.</p>

</ol></ol>

   <p class="note" role="note">Note: as described here, the <a data-link-type="dfn" href="#accumulated-3d-transformation-matrix">accumulated 3D transformation matrix</a> takes into account offsets generated by the <a href="http://www.w3.org/TR/REC-CSS2/visuren.html">visual formatting model</a> on the transformed element, and elements in the ancestor chain between the transformed element and the element that establishes the its <a data-link-type="dfn" href="#3d-rendering-context">3D rendering context</a>.</p>


   <h4 class="heading settled" data-level="6.1.5" id="backface-visibility"><span class="secno">6.1.5. </span><span class="content">Backface Visibility</span><a class="self-link" href="#backface-visibility"></a></h4>


   <p>Using three-dimensional transforms, it’s possible to transform an element such that its reverse side is visible. 3D-transformed elements show the same content on both sides, so the reverse side looks like a mirror-image of the front side (as if the element were projected onto a sheet of glass). Normally, elements whose reverse side is towards the viewer remain visible. However, the <a class="property" data-link-type="propdesc" href="#propdef-backface-visibility">backface-visibility</a> property allows the author to make an element invisible when its reverse side is towards the viewer. This behavior is "live"; if an element with <a class="css" data-link-type="propdesc" href="#propdef-backface-visibility">backface-visibility: hidden</a> were animating, such that its front and reverse sides were alternately visible, then it would only be visible when the front side were towards the viewer.</p>


   <p>Visibility of the reverse side of an element is considered using the <a data-link-type="dfn" href="#accumulated-3d-transformation-matrix">accumulated 3D transformation matrix</a>, and is thus relative to the enclosing flattening element.</p>


   <p class="note" role="note">Note: This property is useful when you place two elements back-to-back, as you would to create a playing card. Without this property, the front and back elements could switch places at times during an animation to flip the card. Another example is creating a box out of 6 elements, but where you want to see only the inside faces of the box.</p>


   <div class="example" id="example-15d790d7"><a class="self-link" href="#example-15d790d7"></a>


    <p>This example shows how to make a "card" element that flips over when clicked. Note the "transform-style: preserve-3d" on #card which is necessary to avoid flattening when flipped.</p>


    <pre>&lt;style>.body { perspective: 500px; }