drafts: css3-transforms/Transforms.src.html@3c173d4d4749 (annotated)

css3-transforms/Transforms.src.html@3c173d4d4749 (annotated)

css3-transforms/Transforms.src.html

Mon, 12 Mar 2012 11:30:19 -0600

author: Aryeh Gregor <ayg@aryeh.name>
date: Mon, 12 Mar 2012 11:30:19 -0600
changeset 4736: 3c173d4d4749
parent 4703: 16db95fda02f
child 4737: 9338e35c5058
permissions: -rw-r--r--

Hyperlink two CSS2.1 definitions

 <!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 http-equiv="Content-Type" content="text/html; charset=utf-8" />
   <title>CSS Transforms</title>
   <link rel="stylesheet" type="text/css" href="../default.css" />
   <link rel="stylesheet" type="text/css" href="http://www.w3.org/StyleSheets/TR/W3C-ED.css" />
   <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>
 </head>
 <body>
     <div id="div-head" class="head">
         <!--logo-->
         <h1>CSS Transforms</h1>
         <h2 class="no-num no-toc">[LONGSTATUS] [DATE]</h2>
         <dl>
           <dt>This version:
             <dd>
             <a href="[VERSION]">http://dev.w3.org/csswg/css3-transforms/</a>
             <!--http://www.w3.org/TR/[YEAR]/WD-[SHORTNAME]-[CDATE]-->
           <dt>Latest version:
             <dd><a
               href="http://www.w3.org/TR/css3-transforms">[LATEST]</a>
           <dt>Editor's draft:
             <dd><a href="http://dev.w3.org/csswg/[SHORTNAME]/">http://dev.w3.org/csswg/[SHORTNAME]/</a>
           <dt>Previous version:
             <dd>None
           <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>
         <!--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.</p>
         <h2 class="no-num no-toc" id="status">Status of this document</h2>
         <p class="note">
           This specification merges the former CSS 2D Transforms and CSS 3D Transforms specifications and
           will also merge CSS Transforms and SVG Transforms. The merge is in progress and the specification
           is not yet ready for review.
         </p>
         <!--status-->
         <p>
           The <a href="ChangeLog">list of changes made to this specification</a> is
           available.
         </p>
         <h2 class="no-num no-toc" id="contents">Table of contents</h2>
         <!--toc-->
         <h2>Introduction</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 '<code
             class="property">transform</code>' 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 '<code class="property">transform-origin</code>' property
               provides a convenient way to control the origin about which transforms on
               an element are applied.
             </li>
             <li>
               The '<code class="property">perspective</code>' property allows the author
               to make child elements with three-dimensional transforms appear as if they live in a common
               three-dimensional space.
               The '<code class="property">perspective-origin</code>' property provides control
               over the origin at which perspective is applied, effectively changing the location of
               the "vanishing point".
             </li>
             <li>
               The '<code class="property">transform-style</code>' 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>
             <li>
                The '<code class="property">backface-visibility</code>' 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 'hidden'
                for this property.
             </li>
           </ul>
           <p>
             Note that while some values of the '<code class="property">transform</code>' 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>
           <div class="issue">
             There are two roles for transformations in layout: (1) transformations
             that adjust the position of the affected content without changing the
             normal layout of that content (much like relative positioning) and (2)
             transformation of the content prior to layout that affects the layout
             of that content. See <a
             href="http://lists.w3.org/Archives/Public/www-style/2007Oct/0209">http://lists.w3.org/Archives/Public/www-style/2007Oct/0209</a>
             for examples of both cases. The "transform" property (as defined in
             this document) is equally useful for both roles. This document is
             focused on satisfying the first role. There is, however, an
             architectural question that arises because there needs to be a way to
             distinguish which role an author of a stylesheet wants. The key
             question is which is the default behavior/role for the "transform"
             property and how is the other behavior/role indicated by a stylesheet
             author. If you have an opinion on this topic, please send feedback.
           </div>
           <div class="issue">
             What do fixed backgrounds do in transforms? They should probably ignore
             the transform completely, since - even transformed - the object should
             be acting as "porthole" through which the fixed background can be viewed
             in its original form.
           </div>
         <!-- ======================================================================================================= -->
         <h2 id="module-interactions">Module Interactions</h2>
           <p>Write me</p>
         <h2 id="css-values">CSS Values</h2>
           <p>Write me</p>
         <h2 id="definitions">Definitions</h2>
           <p> When used in this specification, terms have the meanings assigned in
             this section.
           </p>
           <dl>
             <dt id="TermBoundingBox"><dfn>bounding box</dfn></dt>
             <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.
               </p>
             </dd>
             <dt id="TermTransformableElement"><dfn>transformable element</dfn></dt>
             <dd>
               <p>
 				A transformable 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 an element in the SVG namespace
 				(see [[SVG11]]) which has the attributes '<code
 				class="property">transform</code>',
                 'patternTransform' or 'gradientTransform'.
               </p>
             </dd>
             <dt id="TermPerspectiveMatrix"><dfn>perpsective matrix</dfn></dt>
             <dd>
               <p>
                 A matrix computed from the values of the '<code class="property">perspective</code>' and '<code class="property">perspective-origin</code>' properties as described <a href="#perspective-matrix-computation">below</a>.
               </p>
             </dd>
             <dt id="TermTransformationMatrix"><dfn>transformation matrix</dfn></dt>
             <dd>
               <p>
                 A matrix computed from the values of the '<code class="property">transform</code>' and '<code class="property">transform-origin</code>' properties as described <a href="#transformation-matrix-computation">below</a>.
               </p>
             </dd>
             <dt id="Term3DRenderingContext"><dfn>3D rendering context</dfn></dt>
             <dd>
               <p>
                 A containing block hierarchy of one or more levels, instantiated by elements with a computed value for
                 the '<code class="property">transform-style</code>' property of '<code class="css">preserve-3d</code>',
                 whose elements share a common three-dimensional coordinate system.
               </p>
             </dd>
             <!-- Define "three-dimensional transform" ? -->
           </dl>
           <!-- ======================================================================================================= -->
           <h2 id="transform-rendering">The Transform Rendering Model</h2>
             <!-- This section is normative -->
               <p>
                 Specifying a value other than '<code class="css">none</code>' for the '<code class="property">transform</code>'
                 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 '<code class="property">transform</code>'
                 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>
               <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>
               <p id="transformation-matrix-computation">
                 The <a href="#TermTransformationMatrix"><i>transformation matrix</i></a> is computed
                 from the '<code class="property">transform</code>' and '<code class="property">transform-origin</code>' properties
                 as follows:
                 <ol>
                   <li>Start with the identity matrix.</li>
                   <li>Translate by the computed X, Y and Z values of '<code class="property">transform-origin</code>'</li>
                   <li>Multiply by each of the transform functions in '<code class="property">transform</code>' property in turn</li>
                   <li>Translate by the negated computed X, Y and Z values of '<code class="property">transform-origin</code>'</li>
                 </ol>
               </p>
               <p>
                 Transforms apply to <span class="term">transformable elements</span>.
               </p>
               <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 src="transform1.png" alt="The 100px translation in X and Y">
                 </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 '<code class="css">50% 50%</code>'.</p>
               <div class="figure">
                 <img src="compound_transform.png" alt="The transform specified above">
               </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;
 </pre>
             </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 '<code class="property">overflow</code>'
                 property is '<code class="css">scroll</code>' or '<code class="css">auto</code>',
                 scrollbars will appear as needed to see content that is transformed outside the visible area.
               </p>
               <p>
                 In the HTML namespace, any value other than '<code class="css">none</code>' 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">
                 Is this affect 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>
               <h3 id="transform-3d-rendering">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>
               <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 <span class="term">3D rendering context</span>, as described below.
               </p>
               <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 src="examples/simple-3d-example.png" width="210" height="190" alt="Div with a rotateY transform.">
               </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 '<code class="property">perspective</code>' and '<code class="property">perspective-origin</code>'
                 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.
               </p>
               <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>
                   <li>Translate by the computed X and Y values of '<code class="property">perspective-origin</code>'</li>
                   <li>Multiply by the matrix that would be obtained from the '<a href="#perspective-function"><code class="css">perspective(&lt;length&gt;)</code></a>' transform function, where the length is provided by the value of the '<code class="property">perspective</code>' property</li>
                   <li>Translate by the negated computed X and Y values of '<code class="property">perspective-origin</code>'</li>
                 </ol>
               </p>
               <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 src="examples/simple-perspective-example.png" width="210" height="190" alt="Div with a rotateY transform,
                     and perspective on its container">
                 </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
                 <span class="term">3D rendering context</span> 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>
               <p>
                 An element with a three-dimensional transform that is contained in a
                 <span class="term">3D rendering context</span> can visibly interact with other elements
                 in that same 3D rendering context; the set of elements participating in the same
                 <span class="term">3D rendering context</span> 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 <span class="term">3D rendering context</span>
                 through each element that is a containing block for the given element, as described below.
                 <!-- More detail required, probably with matrices -->
               </p>
               <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 '<code class="css">transform-style: preserve-3d</code>'. 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 src="examples/3d-rendering-context-flat.png" width="240" height="200" alt="Nested 3D transforms, with flattening">
                 </div>
               </div>
               <p>Elements establish and participate in 3D rendering contexts as follows:</p>
               <ul>
                 <li>
                   A <span class="term">3D rendering context</span> is established by a
                   a <span class="term">transformable element</span> whose computed value for '<code class="property">transform-style</code>' is
                   '<code class="css">preserve-3d</code>', and which itself is not part of a 3D rendering context.
                   Note that such an element is always a containing block. An element that establishes a 3D rendering context
                   also participates in that context.
                 </li>
                 <li>
                   An element whose computed value for '<code class="property">transform-style</code>' is
                   '<code class="css">preserve-3d</code>', and which itself participates in a
                   <span class="term">3D rendering context</span>, extends that 3D rendering context rather than establishing
                   a new one.
                 </li>
                 <li>
                   An element participates in a <span class="term">3D rendering context</span> if its containing block
                   establishes or extends a <span class="term">3D rendering context</span>.
                 </li>
               </ul>
               <p>
                 The final value of the transform used to render an element in a <span class="term">3D rendering context</span>
                 is computed by accumulating a matrix as follows:
               </p>
               <ol>
                 <li>Start with the identity matrix</li>
                 <li>For each containing block between the root of the <span class="term">3D rendering context</span>
                   and the element in question:
                   <ol>
                     <li>multiply the accumulated matrix with the <a href="#TermPerspectiveMatrix"><i>perspective matrix</i></a>
                       on the element's containing block (if any). That contining block is not necessarily a member
                       of the 3D rendering context.</li>
                     <li>apply to the accumulated matrix a translation equivalent to the horizontal and vertical offset of the element relative to
                       its containing block as specified by the CSS visual formatting model. <!-- (tighten this!) --></li>
                     <li>multiply the accumulated matrix with the <a href="#TermTransformationMatrix"><i>transformation matrix</i></a>.</li>
                   </ol>
                 </li>
               </ol>
               <div class="example">
 <pre>
 &lt;style&gt;
 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&gt;
 </pre>
                 <p>This example is identical to the previous example, with the addition of '<code class="css">transform-style: preserve-3d</code>' on the blue element. The blue element now establishes a 3D rendering context, of which the lime element is a member. 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 src="examples/3d-rendering-context-3d.png" width="240" height="200" alt="Nested 3D transforms, with preserve-3d.">
                 </div>
               </div>
               <p>
                 Elements in the same <span class="term">3D rendering context</span> may intersect with each other. User agents must
                 render intersection by subdividing the planes of intersecting elements as described by
                 <a href="http://en.wikipedia.org/wiki/Newell's_algorithm">Newell's algorithm</a>.
               </p>
               <p>
                 Untransformed elements in a <span class="term">3D rendering context</span> render on the Z=0 plane, yet may still
                 intersect with transformed elements.
               </p>
               <p>
                 Within a <span class="term">3D rendering context</span>, the rendering order of non-intersecting elements is
                 based on their position on the Z axis after the application of the accumulated transform. Elements at the same
                 Z position render in <a href="http://www.w3.org/TR/CSS2/zindex.html#painting-order">stacking context order</a>.
               </p>
               <div class="example">
 <pre>
 &lt;style&gt;
 .container {
     background-color: rgba(0, 0, 0, 0.3);
     transform-style: preserve-3d;
     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, 0.75);
     top: 50px;
     height: 100px;
 }
 &lt;/style&gt;
 &lt;div class="container"&gt;
     &lt;div&gt;&lt;/div&gt;
     &lt;div&gt;&lt;/div&gt;
 &lt;/div&gt;
 </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 eachother, and
                   the orange element also intersects with the container.
                 </p>
                 <div class="figure">
                   <img src="examples/3d-intersection.png" width="200" height="200" alt="Intersecting sibling elements.">
                 </div>
               </div>
               <p>
                 Using three-dimensional transforms, it's possible to transform an element such that its reverse side
                 is towards the viewer. 3D-tranformed 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
                 '<code class="property">backface-visibility</code>' 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
                 '<code class="css">backface-visibility: hidden</code>' 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>
               <!-- ======================================================================================================= -->
               <h2 id="transform-property">
                 The '<code class="property">transform</code>' Property
               </h2>
               <p>
                 A transformation is applied to the coordinate system an element
                 renders in through the '<code class="property">transform</code>' property. This property contains a
                 list of <a href="#transform-functions">transform functions</a>. The
                 final transformation value for a coordinate system is obtained by converting
                 each function in the list to its corresponding matrix like defined in <a href="#mathematical-description">Mathematical
                 Description of Transformation Functions</a>, then multiplying the matrices.
               </p>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="effects">transform</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
                       none | &lt;transform-function&gt; [ &lt;transform-function&gt; ]*
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
                       none
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       refer to the size of the element's bounding box
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       See below.
                     </td>
                   </tr>
                 </tbody>
               </table>
               <div class="issue">
                 <p class="desc">We need to resolve whether the computed value is the same as the specified value, or matrix().</p>
               </div>
               <p>The computed value of the transform property is a matrix() or matrix3d() value that describes the matrix that results from concatenating the individual transform functions. If the resulting matrix can be represented as a two-dimensional matrix with no loss of information, then a matrix() value is returned, otherwise a matrix3d() value. For elements with no transform applied, the computed value is 'none'.</p>
               <p>Any value other than '<code class="css">none</code>' 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>
               <!-- ======================================================================================================= -->
               <h2 id="svg-transform">
                 The SVG '<code class="property">transform</code>' Attribute
               </h2>
               <p>
                 The <a href="http://www.w3.org/TR/2011/REC-SVG11-20110816/">SVG 1.1 specification</a> did not
                 specify the attributes '<code class="property">transform</code>', 'gradientTransform' or 'patternTransform' as
                 <a href="http://www.w3.org/TR/2011/REC-SVG11-20110816/styling.html#UsingPresentationAttributes"><em>presentation attributes</em></a>.
                 In order to improve the integration of SVG and HTML, this specification makes these SVG attributes to
                 'presentation attributes' and makes the '<code class="property">transform</code>' property one that applies to <span class="term">transformable elements</span> in the SVG namespace.
               </p>
               <p>
                 This specification will also introduce the new presentation attributes '<code class="property">transform-origin</code>',
                 '<code class="property">perspective</code>', '<code class="property">perspective-origin</code>',
                 '<code class="property">transform-style</code>' and '<code class="property">backface-visibility</code>'
                 in the SVG namespace. All new introduced presentation attributes are animateable.
               </p>
               <h3 id="transform-attribute-specificity">SVG '<code class="property">transform</code>' attribute specificity</h3>
               <p>Since the previously named SVG attributes become presentation attributes, their participation to the CSS
                   cascade is determined by the specificity of presentation attributes, as
                   <a href="http://www.w3.org/TR/2011/REC-SVG11-20110816/styling.html#UsingPresentationAttributes">explained</a>
                   in the SVG specification.
               </p>
               <div class="example">
                 <p>
                   This example shows the combination of the '<code class="property">transform</code>' style property and the '<code class="property">transform</code>' presentation attribute.
                 </p>
                 <pre>&lt;svg&gt;
     &lt;style&gt;
     .container {
         transform: translate(100px, 100px);
     }
     &lt;/style&gt;
     &lt;g class="container" transform="translate  (200 200)"&gt;
         &lt;rect width="100" height="100" fill="blue" /&gt;
     &lt;/g&gt;
 &lt;/svg&gt;</pre>
                 <div class="figure">
                   <img src="examples/svg-translate.png" width="200" height="200" alt="Translated SVG container element.">
                 </div>
                 <p>
                   Because of the participation to the CSS cascade, the '<code class="property">transform</code>' style property overrides the
                   '<code class="property">transform</code>' presentation attribute. Therefore the container gets translated by '<code class="css">100px</code>' in horizontal and vertical direction, instead of '<code class="css">200px</code>'.
                 </p>
               </div>
               <h3 id="svg-syntax">Syntax of the SVG '<code class="property">transform</code>' attribute</h3>
               <p>
                 To provide backward compatibility, the syntax of the '<code class="property">transform</code>' presentation attribute differs from
                 the syntax of the '<code class="property">transform</code>' style property like shown in the example above. However, the syntax
                 used for the '<code class="property">transform</code>' style property can be used for a '<code class="property">transform</code>' presentation attribute value.
                 Authors are advised to follow the rules of <a href="http://www.w3.org/TR/css3-values/#functional-notation">CSS Values and Units Module</a>.
                 Therefore an author should write '<code class="css">transform="translate(200px, 200px)"</code>' instead of
                 '<code class="css">transform="translate  (200 200)"</code>' because the second example with the spaces before the '<code class="css">(</code>',
                 the missing comma between the arguments and the values without the explicit unit notation would be valid for
                 the attribute only.
               </p>
               <h4 id="svg-transform-list">Transform List</h4>
               <p>
                 The value for the '<code class="property">transform</code>' attribute consists of a transform list with zero or more transform functions
                 in the <a href="#svg-functional-notation">functional notation</a>. If the transform list consists of more than one
                 transform function, these functions are separated by either a comma (‘<code class="css">,</code>’) with optional whitespace
                 before and after the comma or one or more whitespaces. The transform list can have
                 optional whitespaces before and after the list.
               </p>
               <h4 id="svg-functional-notation">Functional Notations</h4>
               <p>
                 The syntax starts with the name of the function followed by optional whitespaces followed by a left
                 parenthesis followed by optional whitespace followed by the argument(s) to the notation followed by
                 optional whitespace followed by a right parenthesis. If a function takes more than one argument, the
                 arguments are either separated by a comma (‘<code class="css">,</code>’) with optional whitespace before and after the comma
                 or one or more whitespaces.
               </p>
               <h4 id="svg-data-types">SVG Data Types</h4>
               <p>
                 Arguments of transform functions consists of data types in the sense of
                 <a href="http://www.w3.org/TR/css3-values/#functional-notation">CSS Values and Units Module</a>. The definitions of
                 data types in CSS Values and Units Module gets enhanced as follows:
               </p>
               <h5 id="svg-transform-value">The <var>&lt;translation-value&gt;</var> and <var>&lt;length&gt;</var> type</h5>
               <p>
                 A translation-value or length can be a <var>&lt;number&gt;</var> without an unit identifier. In this case
                 the <a href="#svg-number"><var>number</var></a> gets interpreted as "user unit". A user unit in the the
                 <a href="http://www.w3.org/TR/2003/REC-SVG11-20030114/coords.html#InitialCoordinateSystem">initial
                 coordinate system</a> is equivalenced to the parent environment's notion of a pixel unit.
               </p>
               <h5 id="svg-angle">The <var>&lt;angle&gt;</var> type</h5>
               <p>
                 An angle can be a <var>&lt;number&gt;</var> without an unit identifier. In this case the <a href="#svg-number"><i>number</i></a>
                 gets interpreted as a value in degrees.
               </p>
               <h5 id="svg-number">The <var>&lt;number&gt;</var> type</h5>
               <p>
                 SVG supports scientific notations for numbers. Therefore a <var>number</var> gets parsed like described in SVG
                 <a href="http://www.w3.org/TR/SVG/types.html#DataTypeNumber">Basic data types</a> for SVG attributes.
               </p>
               <h3 id="svg-gradient-transform-pattern-transform">The SVG 'gradientTransform' and 'patternTransform' attributes</h3>
               <p>
                 SVG specifies the attributes 'gradientTransform' and 'patternTransform'. This specification
                 makes both attributes to presentation attributes. Both attributes use the same <a href="#svg-syntax">syntax</a> as
                 the SVG '<code class="property">transform</code>' attribute. This specification won't introduce corresponding CSS style properties. Instead the
                 style can be set by the '<code class="property">transform</code>' style property.
               </p>
               <h3 id="svg-transformation-functions">SVG transformation functions</h3>
               <p>
                 For backward compatibility to existing SVG content, this specification must support all transform functions
                 defined by <a href="http://www.w3.org/TR/SVG/coords.html#TransformAttribute">The '<code class="property">transform</code>' attribute</a> in SVG 1.1.
                 Therefore the two-dimensional transform function '<code class="css">rotate(&lt;angle&gt;)</code>' gets extended as follows:
               </p>
               <dl>
                 <dt>
                   <code class="css">rotate(&lt;angle&gt;[, &lt;translation-value&gt;, &lt;translation-value&gt;])</code>
                 </dt>
                 <dd>
                   specifies a <a href="#RotateDefined">2D rotation</a> by the angle specified in the parameter about the origin of the element, as defined
                   by the '<code class="property">transform-origin</code>' property. If the optional translation values are specified, the transform origin is translated by that amount
                   (using the current transformation matrix) for the duration of the rotate operation.
                   For example '<code class="css">rotate(90deg, 100px, 100px)</code>' would elements cause to appear rotated one-quarter of a turn in the clockwise direction after a translation
                   of 100 pixel in the vertical and horizontal direction.
                 </dd>
               </dl>
               <p>
                 User agents are just required to support the two optional arguments for translation on elements in the SVG namespace.
               </p>
               <h3 id="svg-three-dimensional-functions">SVG and 3D transformation functions</h3>
               <p>
                 This specification explicitly allows to apply three-dimensional transform functions to the
                 <a href="http://www.w3.org/TR/SVG/intro.html#TermContainerElement"><em>container elements</em></a>:
                 'a', 'g', 'svg', all <a href="http://www.w3.org/TR/SVG/intro.html#TermGraphicsElement"><em>graphics elements</em></a>, all
                 <a href="http://www.w3.org/TR/SVG/intro.html#TermGraphicsReferencingElement"><em>graphics referencing elements</em></a>
                 and the SVG <a href="http://www.w3.org/TR/SVG/extend.html#ForeignObjectElement">'foreignObject'</a> element.
               </p>
               <p>
                 Three-dimensional transform functions and the properties '<code class="property">perspective</code>',
                 '<code class="property">perspective-origin</code>', '<code class="property">transform-style</code>'
                 and '<code class="property">backface-visibility</code>' can not be used for the elements: 'clipPath', 'mask', 'linearGradient',
                 'radialGradient' and 'pattern'. If a transform list includes a three-dimensional transform function, the complete
                 transform list must be ignored. The values of every previously named property must be ignored.
                 <span class="term">Transformable elements</span> that are contained by one of these elements can have three-dimensional transform functions.
                 Before a 'clipPath', 'mask' or 'pattern' element can get applied to a target element, user agents must take the drawn results as static
                 images in analogue of "flattening" the elements and taking the rendered content as a two-dimensional canvas.
               </p>
               <h3 id="svg-object-bounding-box">Object bounding box units</h3>
               <p>
                 Percentage or fractional values in SVG are either relative to the elements viewport units or to the elements
                 <a href="http://www.w3.org/TR/SVG/coords.html#ObjectBoundingBoxUnits">object bounding box units</a> like
                 specified in SVG 1.1. To align with HTML, all percentage values for all properties defined in this specification
                 are relative to the object bounding box units.
               </p>
               <p>
                 If an SVG element does not provide an object bounding box (like for the 'pattern', 'mask' or 'clipPath' elements), the bounding box
                 is the same like if the position x, y and the dimensions width and height are zero. Percentage values or keywords won't affect the
                 rendering and are treated as if zero was specified.
               </p>
               <div class="example">
                 <p>
                   The '<code class="property">transform-origin</code>' property on the pattern in the following example specifies a '<code class="css">50%</code>' translation of the origin in the horizontal and vertical dimension.
                   The '<code class="property">transform</code>' property specifies a translation as well, but in absolute lengths.
                 </p>
                 <pre>&lt;svg&gt;
     &lt;style&gt;
     pattern {
         transform: translate(50px, 50px) rotate(45deg);
         transform-origin: 50% 50%;
     }
     &lt;/style&gt;
     &lt;defs&gt;
     &lt;pattern id="pattern-1"&gt;
         &lt;rect id="rect1" width="100" height="100" fill="blue" /&gt;
     &lt;/pattern&gt;
     &lt;/defs&gt;
     &lt;rect width="100" height="100" fill="url(#pattern-1)" /&gt;
 &lt;/svg&gt;</pre>
                 <p>
                   A SVG 'pattern' element doesn't have an object bounding box. Therefore the relative values of the
                   '<code class="property">transform-origin</code>' property don't affect the rendering and are treated
                   as if zero was specified. The translation on the '<code class="property">transform</code>' property is in
                   absolute coordinates and translate the coordinate system by 50 pixel in each direction.
                 </p>
               </div>
               <h3 id="transform-attribute-dom">SVG DOM interface for the '<code class="property">transform</code>' attribute</h3>
               <p>
                 The SVG specification defines the
                 '<a href="http://www.w3.org/TR/2011/REC-SVG11-20110816/coords.html#InterfaceSVGAnimatedTransformList"><code class="property">SVGAnimatedTransformList</code></a>'
                 interface in SVG DOM to access the animated and the base value of the SVG transform attribute. To ensure backwards compatibility,
                 this API must still be supported by user agents.
               </p>
               <p>
                 The '<code class="property">transform</code>' property contributes to the CSS cascade. According to SVG 1.1 user agents conceptually insert a
                 <a href="http://www.w3.org/TR/SVG/styling.html#UsingPresentationAttributes">new author
                 style sheet</a> for presentation attributes, which is the first in the author style sheet collection.
                 '<code class="property">baseVal</code>' gives the author the possibility to access and modify the values of the SVG '<code class="property">transform</code>' attribute.
                 To provide the necessary backward compatibility to SVG DOM, '<code class="property">baseVal</code>' must reflect the values of this author style sheet.
                 All modifications to SVG DOM objects of '<code class="property">baseVal</code>' must affect this author style sheet immediately.
               </p>
               <p>
                 '<code class="property">animVal</code>' represents the computed style of the '<code class="property">transform</code>' property. Therefore it includes all applied
                 <a href="http://www.w3.org/TR/css3-transitions/">CSS3 Transitions</a>, <a href="http://www.w3.org/TR/css3-animations/">CSS3
                 Animations</a> or <a href="#svg-animation">SVG Animations</a> if any of those are underway. The computed style and SVG DOM
                 objects of '<code class="property">animVal</code>' can not be modified.
               </p>
               <p>
                 The attribute '<a href="http://www.w3.org/TR/SVG/coords.html#__svg__SVGTransform__type"><code class="property">type</code></a>' of
                 <a href="http://www.w3.org/TR/SVG/coords.html#InterfaceSVGTransform">'SVGTransform'</a>
                 must return '<a href="http://www.w3.org/TR/SVG/coords.html#__svg__SVGTransform__SVG_TRANSFORM_UNKNOWN">
                 <code class="css">SVG_TRANSFORM_UNKNOWN</code></a>' for <a href="#transformation-functions">Transformation Functions</a> or unit types that
                 are not supported by this interface. It might still be possible to get the
                 '<a href="http://www.w3.org/TR/SVG/coords.html#InterfaceSVGMatrix"><code class="property">SVGMatrix</code></a>' by the attribute
                 '<a href="http://www.w3.org/TR/SVG/coords.html#__svg__SVGTransform__matrix"><code class="property">matrix</code></a>'.
               </p>
               <h3 id="svg-animation">SVG Animation</h3>
               <h4 id="svg-animate-element">The SVG 'animate' and 'set' element</h4>
               <p>
                 The SVG 1.1 specification did not define animations of the '<code class="property">transform</code>' attribute for the SVG
                 <a href="http://www.w3.org/TR/SVG/animate.html#AnimateElement">'animate'</a> element or the SVG
                 <a href="http://www.w3.org/TR/SVG/animate.html#SetElement">'set'</a> element.
                 This specification explicitly allows the animation of the presentation attributes '<code class="property">transform</code>', 'gradientTransform' and 'patternTransform'
                 for the 'animate' and 'set' elements. SVG animation must run the same animation steps as described in section
                 <a href="#animation">Transitions and Animations between Transform Values</a>.
               </p>
               <h4 id="svg-attribute-name">The SVG 'attributeName' attribute</h4>
               <p>
                 <a href="http://www.w3.org/TR/SVG/animate.html">SVG 1.1 Animation</a> defines the <a href="http://www.w3.org/TR/SVG/animate.html#TargetAttributes">'attributeName'</a> attribute to specify the
                 name of the target attribute. For the presentation attributes 'gradientTransform' and 'patternTransform' it will also be possible to use
                 the value '<code class="property">transform</code>'. The same presentation attribute style will get animated.
               </p>
               <div class="example">
                 <p>
                   In this example the gradient transformation of the linear gradient gets animated.
                 </p>
                 <pre>&lt;linearGradient gradientTransform="scale(2)"&gt;
     &lt;animate attributeName="gradientTransform" from="scale(2)" to="scale(4)"
           dur="3s" additive="sum"/&gt;
     &lt;animate attributeName="transform" from="translate(0, 0)" to="translate(100px, 100px)"
           dur="3s" additive="sum"/&gt;
 &lt;/linearGradient&gt;</pre>
                 <p>The 'linearGradient' element specifies the 'gradientTransform' presentation attribute. The two 'animate' elements address the target attribute
                   'gradientTransform' and '<code class="property">transform</code>'. Even so all animations apply to the same gradient transformation by taking the value of the 'gradientTransform'
                   presentation attribute, applying the scaling of the first animation and applying the translation of the second animation one after the other.</p>
               </div>
               <h4 id="svg-attribute-type">The SVG 'attributeType' attribute</h4>
               <p>
                 <a href="http://www.w3.org/TR/SVG/animate.html">SVG 1.1 Animation</a> defines the <a href="http://www.w3.org/TR/SVG/animate.html#TargetAttributes">'attributeType'</a> attribute to specify the
                 namespace in which the target attribute and its associated values are defined. The attribute can have the values '<code class="css">CSS</code>', '<code class="css">XML</code>' or
                 '<code class="css">auto</code>', where '<code class="css">auto</code>' is the default value.
               </p>
               <p>
                 However, in the combination with the '<code class="property">transform</code>', 'patternTransform' and 'gradientTransform' presentation attributes, 'attributeType'
                 can just be used to indicate the syntax rules used for the transform attribute values. A value of '<code class="css">CSS</code>' indicates that the transform values should
                 be parsed according to the CSS syntax. A value of '<code class="css">XML</code>' indicates that the transform values should be parsed according to the
                 SVG '<code class="property">transform</code>' <a href="#svg-syntax">syntax</a>.
               </p>
               <p>
                 User agents are recommended to use the more tolerant SVG '<code class="property">transform</code>' <a href="#svg-syntax">syntax</a> for a value of '<code class="css">auto</code>' to parse transform values.
               </p>
               <h4 id="svg-animateTransform-extension">The SVG 'animateTransform' element</h4>
               <p>
                 This specification introduces new transform functions that are not supported by <a href="http://www.w3.org/TR/SVG/animate.html">SVG 1.1 Animation</a>. The
                 SVG '<a href="http://www.w3.org/TR/SVG/animate.html#AnimateTransformElement"><code class="property">type</code></a>' attribute gets extended by all
                 transform functions listed in <a href="#two-d-transform-functions">2D Transformation Functions</a>,
                 <a href="#three-d-transform-functions">3D Transformation Functions</a> and <a href="#svg-transformation-functions">SVG
                 Transformation Functions</a>.
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="transform-origin-property">
                 The '<code class="property">transform-origin</code>' Property
               </h2>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="transform-origin">transform-origin</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
             [ &lt;percentage> | &lt;length> | left | center | right | top | bottom]<br>
             |<br>
             [<br>
             &nbsp;&nbsp;[ &lt;percentage> | &lt;length&gt; | left | center | right ]<br>
             &nbsp;&nbsp;&amp;&amp;<br>
             &nbsp;&nbsp;[ &lt;percentage> | &lt;length&gt; | top | center | bottom ]<br>
             ] &lt;length&gt;?<br>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
 0 for SVG elements without associated CSS layout box, 50% 50% for all other elements
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       refer to the size of the element's bounding box
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       For &lt;length&gt; the absolute value, otherwise a percentage
                     </td>
                   </tr>
                 </tbody>
               </table>
               <p>
                 The values of the '<code class="property">transform</code>' and
                 '<code class="property">transform-origin</code>' properties are used to compute the
                 <a href="#TermTransformationMatrix"><i>transformation matrix</i></a>, as described above.
               </p>
               <p>If only one value is specified, the second value is assumed to be
               'center'. If one or two values are specified, the third value is
               assumed to be '0px'.
               </p>
               <p>If at least one of the first two values is not a keyword, then
               the first value represents the horizontal position (or offset)
               and the second represents the vertical position (or offset).  The
               third value always represents the Z position (or offset).
               </p>
               <p><var>&lt;percentage&gt;</var> and <var>&lt;length&gt;</var>
               for the first two values represent an offset of the transform
               origin from the top left corner of the element's bounding box.
               </p>
               <p>For SVG elements without an associated CSS layout box the <var>&lt;length&gt;</var>
               values represent an offset from the point of origin of the element's local coordinate space.
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="transform-style-property">
                 The '<code class="property">transform-style</code>' Property
               </h2>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="transform-style">transform-style</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
                       flat | preserve-3d
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
                       flat
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       N/A
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       Same as specified value.
                     </td>
                   </tr>
                 </tbody>
               </table>
               <p>
                 A value of '<code class="css">preserve-3d</code>' for '<code class="property">transform-style</code>'
                 establishes a stacking context.
               </p>
               <p>
                 The following CSS property values require the user agent to create a flattened representation of
                 the descendant elements before they can be applied, and therefore override the behavior of
                 '<code class="property">transform-style</code>': '<code class="css">preserve-3d</code>':
                 <ul>
                   <li>'<code class="property">overflow</code>': any value other than '<code class="property">visible</code>'.</li>
                   <li>'<code class="property">opacity</code>': any value other than 1.</li>
                   <li>'<code class="property">filter</code>': any value other than '<code class="property">none</code>'.</li>
                   <!-- Others? -->
                 </ul>
               </p>
               <div class="issue">
                 <p class="desc">Should this affect the computed value of transform-style?</p>
               </div>
               <p>
                 The values of the '<code class="property">transform</code>' and
                 '<code class="property">transform-origin</code>' properties are used to compute the
                 <a href="#TermTransformationMatrix"><i>transformation matrix</i></a>, as described above.
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="perspective-property">
                 The '<code class="property">perspective</code>' Property
               </h2>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="perspective">perspective</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
                       none | &lt;length&gt;
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
                       none
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       N/A
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       Same as specified value.
                     </td>
                   </tr>
                 </tbody>
               </table>
               <p>
                 If the value is '<code class="css">none</code>', less than or equal to 0 no
                 perspective transform is applied.
               </p>
               <p>
                 The use of this property with any value other than '<code class="css">none</code>' establishes a
                 stacking context. It also establishes a containing block (somewhat
                 similar to '<code class="css">position: relative</code>'), just like the '<code class="property">transform</code>' property does.
               </p>
               <p>
                 The values of the '<code class="property">perspective</code>' and '<code class="property">perspective-origin</code>'
                 properties are used to compute the <a href="#TermPerspectiveMatrix"><i>perspective matrix</i></a>, as described above.
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="perspective-origin-property">
                 The '<code class="property">perspective-origin</code>' Property
               </h2>
               <p>
                 The '<code class="property">perspective-origin</code>' property
                 establishes the origin for the <em>perspective</em> property. It
                 effectively sets the X and Y position at which the viewer appears to be
                 looking at the children of the element.
               </p>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="perspective-origin">perspective-origin</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
                       [ [ &lt;percentage&gt; | &lt;length&gt; | left | center | right ] [
                       &lt;percentage&gt; | &lt;length&gt; | top | center | bottom ]? ] | [ [ left |
                       center | right ] || [ top | center | bottom ] ]
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
 % 50%
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       refer to the size of the element's bounding box
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       Same as specified value.
                     </td>
                   </tr>
                 </tbody>
               </table>
               <p>
                 The values of the '<code class="property">perspective</code>' and '<code class="property">perspective-origin</code>'
                 properties are used to compute the <a href="#TermPerspectiveMatrix"><i>perspective matrix</i></a>, as described above.
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="backface-visibility-property">
                 The '<code class="property">backface-visibility</code>' Property
               </h2>
               <p>
                 The '<code class="property">backface-visibility</code>' property
                 determines whether or not the "back" side of a transformed element is
                 visible when facing the viewer. With an identity transform, the front
                 side of an element faces the viewer. Applying a rotation about Y of 180
                 degrees (for instance) would cause the back side of the element to face
                 the viewer.
               </p>
               <!-- This should not be in a normative section. -->
               <p>
                 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 the inside faces of the box. This is useful when
                 creating the backdrop for a 3 dimensional stage.
               </p>
               <table class="propdef">
                 <tbody>
                   <tr>
                     <td>
                       <em>Name:</em>
                     </td>
                     <td>
                       <dfn id="backface-visibility">backface-visibility</dfn>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Value:</em>
                     </td>
                     <td>
                       visible | hidden
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Initial:</em>
                     </td>
                     <td>
                       visible
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Applies&nbsp;to:</em>
                     </td>
                     <td>
                       <a href="#TermTransformableElement">transformable elements</a>
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Inherited:</em>
                     </td>
                     <td>
                       no
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Percentages:</em>
                     </td>
                     <td>
                       N/A
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Media:</em>
                     </td>
                     <td>
                       visual
                     </td>
                   </tr>
                   <tr>
                     <td>
                       <em>Computed value:</em>
                     </td>
                     <td>
                       Same as specified value.
                     </td>
                   </tr>
                 </tbody>
               </table>
               <p>
                 The visibility of an element with '<code class="css">backface-visibility: hidden</code>' is determined
                 as follows:
                 <ol>
                   <li>Compute a matrix representing the accumulated transform from the viewport, taking the translations
                     due to the CSS visual formatting mode, the perpsective and transformation matrices into account,
                     in a similar manner to the computation of the accumulated transform for an element in a
 D rendering context.
                   </li>
                   <li>
                     If the component of the matrix in row 3, column 3 is negative, then the element should be hidden,
                     otherwise it is visible.
                   </li>
                 </ol>
                 <div class="issue">
                   Is the relevant matrix here really relative to the viewport, or to the root of the 3D rendering context?
                 </div>
               </p>
               <!-- ======================================================================================================= -->
               <h2 id="transform-functions">
                 The Transformation Functions
               </h2>
               <p>
                 The value of the <code class="property">transform</code> property is a
                 list of <var>&lt;transform-functions&gt;</var> applied in the order provided. The
                 individual transform functions are separated by whitespace. The
                 set of allowed transform functions is given below. In this list the
                 type <var>&lt;translation-value&gt;</var> is defined as a <var>&lt;length&gt;</var> or
                 <var>&lt;percentage&gt;</var> value, and the <var>&lt;angle&gt;</var> type is defined by <a
                 href="http://www.w3.org/TR/css3-values/">CSS Values and Units Module.</a>
                 Wherever <var>&lt;angle&gt;</var> is used in this specification, a <var>&lt;number&gt;</var> that is equal to
                 zero is also allowed, which is treated the same as an angle of zero degrees.
               </p>
               <h3 id="two-d-transform-functions">2D Transformation Functions</h3>
               <dl>
                 <dt>
                   <code class="css">matrix(&lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a 2D transformation in the form of a <a href="#MatrixDefined">transformation matrix</a> of the six values a-f.
                 </dd>
                 <dt>
                   <code class="css">translate(&lt;translation-value&gt;[, &lt;translation-value&gt;])</code>
                 </dt>
                 <dd>
                   specifies a <a href="#TranslateDefined">2D translation</a> by the vector [tx, ty], where tx is the first translation-value parameter and ty is the optional second translation-value parameter. If <em>&lt;ty&gt;</em> is not provided, ty has zero as a value.
                 </dd>
                 <dt>
                   <code class="css">translateX(&lt;translation-value&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#TranslateDefined">translation</a> by the given amount in the X direction.
                 </dd>
                 <dt>
                   <code class="css">translateY(&lt;translation-value&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#TranslateDefined">translation</a> by the given amount in the Y direction.
                 </dd>
                 <dt>
                   <code class="css">scale(&lt;number&gt;[, &lt;number&gt;])</code>
                 </dt>
                 <dd>
                   specifies a <a href="#ScaleDefined">2D scale</a> operation by the [sx,sy] scaling vector described by the 2 parameters. If the second parameter is not provided, it is takes a value equal to the first. For example, scale(1, 1) would leave an element unchanged, while scale(2, 2) would cause it to appear twice as long in both the X
                   and Y axes, or four times its typical geometric size.
                 </dd>
                 <dt>
                   <code class="css">scaleX(&lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#ScaleDefined">2D scale</a> operation using the [sx,1] scaling vector, where sx is given as the parameter.
                 </dd>
                 <dt>
                   <code class="css">scaleY(&lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#ScaleDefined">2D scale</a> operation using the [1,sy] scaling vector, where sy is given as the parameter.
                 </dd>
                 <dt>
                   <code class="css">rotate(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#RotateDefined">2D rotation</a> by the angle specified in the parameter about the origin of the element, as
                   defined by the '<code class="property">transform-origin</code>' property. For example, '<code class="css">rotate(90deg)</code>'
                   would cause elements to appear rotated one-quarter of a turn in the clockwise direction.
                 </dd>
                 <dt>
                   <code class="css">skew(&lt;angle&gt;[, &lt;angle&gt;])</code>
                 </dt>
                 <dd>
                   specifies a <a href="#SkewDefined">2D skew</a> by [ax,ay] for X and Y. If the second parameter is not provided, it is has a zero value.
                 </dd>
                 <dt>
                   <code class="css">skewX(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#SkewDefined">2D skew transformation along the X axis</a> by the given angle. The skew vector is [ax,0].
                 </dd>
                 <dt>
                   <code class="css">skewY(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#SkewDefined">2D skew transformation along the Y axis</a> by the given angle. The skew vector is [0,ay].
                 </dd>
               </dl>
               <h3 id="three-d-transform-functions">3D Transformation Functions</h3>
               <dl>
                 <dt>
                   <code class="css">matrix3d(&lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a 3D transformation as a 4x4 homogeneous matrix of 16 values in column-major order.
                 </dd>
                 <dt>
                   <code class="css">translate3d(&lt;translation-value&gt;, &lt;translation-value&gt;, &lt;length&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#Translate3dDefined">3D translation</a> by the vector [tx,ty,tz], with tx, ty and tz being the first, second and third translation-value parameters respectively.
                 </dd>
                 <dt>
                   <code class="css">translateZ(&lt;length&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#Translate3dDefined">3D translation</a> by the vector [0,0,tz] with the given amount in the Z direction.
                 </dd>
                 <dt>
                   <code class="css">scale3d(&lt;number&gt;, &lt;number&gt;, &lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#Scale3dDefined">3D scale</a> operation by the [sx,sy,sz] scaling vector described by the 3 parameters.
                 </dd>
                 <dt>
                   <code class="css">scaleZ(&lt;number&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#Scale3dDefined">3D scale</a> operation using the [1,1,sz] scaling vector, where sz is given as the parameter.
                 </dd>
                 <dt>
                   <code class="css">rotate3d(&lt;number&gt;, &lt;number&gt;, &lt;number&gt;, &lt;angle&gt;)</code>
                 </dt>
                 <div class="todo">Clarify "clockwise". Describe in terms of right-hand rule?</div>
                 <dd>
                   specifies a clockwise <a href="#Rotate3dDefined">3D rotation</a> by the angle specified in last
                   parameter about the [x,y,z] direction vector described by the first 3
                   parameters. If the direction vector is not of unit length, it will be
                   normalized. A direction vector that cannot be normalized, such as [0,0,0], will cause the rotation to not be applied.
                 </dd>
                 <dt>
                   <code class="css">rotateX(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a clockwise <a href="#RotateXDefined">3D rotation</a> by the given angle about the X axis.
                 </dd>
                 <dt>
                   <code class="css">rotateY(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a clockwise <a href="#RotateYDefined">3D rotation</a> by the given angle about the Y axis.
                 </dd>
                 <dt>
                   <code class="css">rotateZ(&lt;angle&gt;)</code>
                 </dt>
                 <dd>
                   specifies a clockwise <a href="#RotateZDefined">3D rotation</a> by the given angle about the Z axis. This is a synonym for <code class="css">rotate(&lt;angle&gt;)</code>.
                 </dd>
                 <dt id="perspective-function">
                   <code class="css">perspective(&lt;length&gt;)</code>
                 </dt>
                 <dd>
                   specifies a <a href="#PerspectiveDefined">perspective projection matrix</a>. This matrix scales points in
                   X and Y based on their Z value, scaling points with positive Z values away from the origin, and those with
                   negative Z values towards the origin. Points on the z=0 plane are unchanged. The parameter represents the
                   distance of the z=0 plane from the viewer. Lower values give a more flattened pyramid and therefore a more
                   pronounced perspective effect. For example, a value of 1000px gives a moderate amount of foreshortening
                   and a value of 200px gives an extreme amount. The value for depth must be greater than zero, otherwise the
                   function is invalid.
                 </dd>
               </dl>
               <!-- ======================================================================================================= -->
               <h2 id="transform-values">
                 Transform Values and Lists
               </h2>
               <p>
                 The &lt;translation-value&gt; values are defined as [&lt;percentage&gt; | &lt;length&gt;]. All other value types are described <a href="http://www.w3.org/TR/REC-CSS2/syndata.html#values">as CSS types</a>. If a list of transforms is provided, then the net effect is as if each transform had been specified separately in the order provided. For example,
               </p>
 <pre>
 &lt;div style="transform:translate(-10px,-20px) scale(2) rotate(45deg) translate(5px,10px)"/&gt;
 </pre>
               <p>
                 is functionally equivalent to:
               </p>
 <pre>
 &lt;div style="transform:translate(-10px,-20px)"&gt;
   &lt;div style="transform:scale(2)"&gt;
     &lt;div style="transform:rotate(45deg)"&gt;
       &lt;div style="transform:translate(5px,10px)"&gt;
       &lt;/div&gt;
     &lt;/div&gt;
   &lt;/div&gt;
 &lt;/div&gt;
 </pre>
           <p>
             That is, in the absence of other styling that affects position and dimensions, a nested set of transforms is equivalent to a single list of transform functions, applied from the outside in. The resulting transform is the matrix multiplication of the list of transforms.
           </p>
           <!-- ======================================================================================================= -->
               <h2 id="animation">
                 Transitions and Animations between Transform Values
               </h2>
               <p>
                 When animating or transitioning the value of a transform property
                 the rules described below are applied. The 'from' transform is
                 the transform at the start of the transition or current keyframe. The
                 'end' transform is the transform at the end of the transition or
                 current keyframe.
               </p>
               <ul>
                 <li>
                   If the 'from' and 'to' transforms are both single functions
                   of the same type:
                   <ul>
                     <li>
                       For translate, translate3d, translateX, translateY, translateZ, scale,
                       scale3d, scaleX, scaleY, scaleZ, rotate, rotateX, rotateY, rotateZ, skew, skewX
                       and skewY functions:
                         <ul>
                           <li>
                             the individual components of the function are
                             interpolated numerically.
                           </li>
                         </ul>
                     </li>
                     <li>
                       For perspective, matrix, matrix3d and rotate3d:
                         <ul>
                           <li>
                             the values are first converted to a 4x4 matrix, then
                             decomposed using <a
                             href="#unmatrix">the
                             method described by unmatrix</a> into separate translation,
                             scale, rotation, skew and perspective matrices, then each
                             decomposed matrix is interpolated numerically, and finally
                             combined in order to produce a resulting 4x4 matrix.
                           </li>
                         </ul>
                     </li>
                   </ul>
                 </li>
                 <li>
                   If both the 'from' and 'to' transforms are "none":
                   <ul>
                     <li>
                       There is no interpolation necessary
                     </li>
                   </ul>
                 </li>
                 <li>
                   If one of the 'from' or 'to' transforms is "none":
                   <ul>
                     <li>
                       The 'none' is replaced by an equivalent identity function list for
                       the corresponding transform function list.
                       <p>
                         For example, if the 'from' transform is "scale(2)" and the 'to'
                         transform is "none" then the value "scale(1)" will be used as the
                         'to' value, and animation will proceed using the rule above.
                         Similarly, if the 'from' transform is "none" and the 'to' transform
                         is "scale(2) rotate(50deg)" then the animation will execute as
                         if the 'from' value is "scale(1) rotate(0)".
                       </p>
                       <p>
                         The identity functions are translate(0), translate3d(0, 0, 0),
                         translateX(0), translateY(0), translateZ(0), scale(1), scale3d(1, 1, 1),
                         scaleX(1), scaleY(1), scaleZ(1), rotate(0), rotate3d(1, 1, 1, 0),
                         rotateX(0), rotateY(0), rotateZ(0), skew(0), skewX(0), skewY(0),
                         matrix(1, 0, 0, 1, 0, 0) and
                         matrix3d(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1).
                       </p>
                     </li>
                   </ul>
                 </li>
                 <li>
                   If both the 'from' and 'to' transforms have the same number of
                   transform functions and corresponding functions in each transform
                   list are of the same type:
                   <ul>
                     <li>
                       Each transform function is animated with its corresponding
                       destination function in isolation using the rules described above.
                       The individual values are then applied as a list to produce
                       resulting transform value.
                     </li>
                   </ul>
                 </li>
                 <li>
                   Otherwise:
                   <ul>
                     <li>
                       The transform function lists are each converted into the
                       equivalent matrix3d value and animation proceeds using the rule
                       for a single function above.
                     </li>
                   </ul>
                 </li>
               </ul>
               <p>
                 In some cases, an animation might cause a transformation matrix to
                 be singular or non-invertible. For example, an animation in which
                 scale moves from 1 to -1. At the time when the matrix is in such
                 a state, the transformed element is not rendered.
               </p>
               <h2 id="matrix-decomposition">
                 Matrix Decomposition for Animation
               </h2>
               <p>
                 When interpolating between 2 matrices, each is decomposed into the
                 corresponding translation, rotation, scale, skew and perspective
                 values. Not all matrices can be accurately described by these values.
                 Those that can't are decomposed into the most accurate representation
                 possible, using the technique below. This technique is taken from the
                 "unmatrix" method in "Graphics Gems II, edited by Jim Arvo".
                 The pseudocode below works on a 4x4 homogeneous matrix.
               </p>
               <h3 id="unmatrix">Unmatrix</h3>
               <pre>
           Input:  matrix      ; a 4x4 matrix
           Output: translation ; a 3 component vector
                   rotation    ; Euler angles, represented as a 3 component vector
                   scale       ; a 3 component vector
                   skew        ; skew factors XY,XZ,YZ represented as a 3 component vector
                   perspective ; a 4 component vector
           Returns false if the matrix cannot be decomposed, true if it can
           Supporting functions (point is a 3 component vector, matrix is a 4x4 matrix):
             double  determinant(matrix)         returns the 4x4 determinant of the matrix
             matrix inverse(matrix)              returns the inverse of the passed matrix
             matrix transpose(matrix)            returns the transpose of the passed matrix
             point  multVecMatrix(point, matrix) multiplies the passed point by the passed matrix
                                                 and returns the transformed point
             double  length(point)               returns the length of the passed vector
             point  normalize(point)             normalizes the length of the passed point to 1
             double  dot(point, point)           returns the dot product of the passed points
             double  cos(double)                 returns the cosine of the passed angle in radians
             double  asin(double)                returns the arcsine in radians of the passed value
             double  atan2(double y, double x)   returns the principal value of the arc tangent of
                                                 y/x, using the signs of both arguments to determine
                                                 the quadrant of the return value
           Decomposition also makes use of the following function:
             point combine(point a, point b, double ascl, double bscl)
                 result[0] = (ascl * a[0]) + (bscl * b[0])
                 result[1] = (ascl * a[1]) + (bscl * b[1])
                 result[2] = (ascl * a[2]) + (bscl * b[2])
                 return result
           // Normalize the matrix.
           if (matrix[3][3] == 0)
               return false
           for (i = 0; i < 4; i++)
               for (j = 0; j < 4; j++)
                   matrix[i][j] /= matrix[3][3]
           // perspectiveMatrix is used to solve for perspective, but it also provides
           // an easy way to test for singularity of the upper 3x3 component.
           perspectiveMatrix = matrix
           for (i = 0; i < 3; i++)
               perspectiveMatrix[i][3] = 0
           perspectiveMatrix[3][3] = 1
           if (determinant(perspectiveMatrix) == 0)
               return false
           // First, isolate perspective.
           if (matrix[0][3] != 0 || matrix[1][3] != 0 || matrix[2][3] != 0)
               // rightHandSide is the right hand side of the equation.
               rightHandSide[0] = matrix[0][3];
               rightHandSide[1] = matrix[1][3];
               rightHandSide[2] = matrix[2][3];
               rightHandSide[3] = matrix[3][3];
               // Solve the equation by inverting perspectiveMatrix and multiplying
               // rightHandSide by the inverse.
               inversePerspectiveMatrix = inverse(perspectiveMatrix)
               transposedInversePerspectiveMatrix = transposeMatrix4(inversePerspectiveMatrix)
               perspective = multVecMatrix(rightHandSide, transposedInversePerspectiveMatrix)
                // Clear the perspective partition
               matrix[0][3] = matrix[1][3] = matrix[2][3] = 0
               matrix[3][3] = 1
           else
               // No perspective.
               perspective[0] = perspective[1] = perspective[2] = 0
               perspective[3] = 1
           // Next take care of translation
           translate[0] = matrix[3][0]
           matrix[3][0] = 0
           translate[1] = matrix[3][1]
           matrix[3][1] = 0
           translate[2] = matrix[3][2]
           matrix[3][2] = 0
           // Now get scale and shear. 'row' is a 3 element array of 3 component vectors
           for (i = 0; i < 3; i++)
               row[i][0] = matrix[i][0]
               row[i][1] = matrix[i][1]
               row[i][2] = matrix[i][2]
           // Compute X scale factor and normalize first row.
           scale[0] = length(row[0])
           row[0] = normalize(row[0])
           // Compute XY shear factor and make 2nd row orthogonal to 1st.
           skew[0] = dot(row[0], row[1])
           row[1] = combine(row[1], row[0], 1.0, -skew[0])
           // Now, compute Y scale and normalize 2nd row.
           scale[1] = length(row[1])
           row[1] = normalize(row[1])
           skew[0] /= scale[1];
           // Compute XZ and YZ shears, orthogonalize 3rd row
           skew[1] = dot(row[0], row[2])
           row[2] = combine(row[2], row[0], 1.0, -skew[1])
           skew[2] = dot(row[1], row[2])
           row[2] = combine(row[2], row[1], 1.0, -skew[2])
           // Next, get Z scale and normalize 3rd row.
           scale[2] = length(row[2])
           row[2] = normalize(row[2])
           skew[1] /= scale[2]
           skew[2] /= scale[2]
           // At this point, the matrix (in rows) is orthonormal.
           // Check for a coordinate system flip.  If the determinant
           // is -1, then negate the matrix and the scaling factors.
           pdum3 = cross(row[1], row[2])
           if (dot(row[0], pdum3) < 0)
               for (i = 0; i < 3; i++) {
                   scale[0] *= -1;
                   row[i][0] *= -1
                   row[i][1] *= -1
                   row[i][2] *= -1
           // Now, get the rotations ou
           rotate[1] = asin(-row[0][2]);
           if (cos(rotate[1]) != 0)
              rotate[0] = atan2(row[1][2], row[2][2]);
              rotate[2] = atan2(row[0][1], row[0][0]);
           else
              rotate[0] = atan2(-row[2][0], row[1][1]);
              rotate[2] = 0;
           return true;</pre>
               <h3>Animating the components</h3>
               <p>
                   Once decomposed, each component of each returned value of the source matrix is linearly interpolated
                   with the corresponding component of the destination matrix. For instance, the translate[0] and
                   translate[1] values are interpolated numerically, and the result is used to set the
                   translation of the animating element.
               </p>
               <h3>Recomposing the matrix</h3>
               <p><em>This section is not normative.</em></p>
               <p>
                   After interpolation the resulting values are used to position the element. One way to use these values
                   is to recompose them into a 4x4 matrix. This can be done using the transform functions of the
                   'transform' property. This can be done by the following pseudo code. The
                   values passed in are the output of the Unmatrix function above:
               </p>
               <pre>
           matrix3d(1,0,0,0, 0,1,0,0, 0,0,1,0, perspective[0], perspective[1], perspective[2], perspective[3])
           translate3d(translation[0], translation[1], translation[2])
           rotateX(rotation[0]) rotateY(rotation[1]) rotateZ(rotation[2])
           matrix3d(1,0,0,0, 0,1,0,0, 0,skew[2],1,0, 0,0,0,1)
           matrix3d(1,0,0,0, 0,1,0,0, skew[1],0,1,0, 0,0,0,1)
           matrix3d(1,0,0,0, skew[0],1,0,0, 0,0,1,0, 0,0,0,1)
           scale3d(scale[0], scale[1], scale[2])</pre>
               <h2 id="mathematical-description">
                 Mathematical Description of Transformation Functions
               </h2>
               <p>
                 Mathematically, all transform functions can be represented as 4x4 transformation matrices of the following form:
               </p>
               <img src="4x4matrix.png" alt="\begin{bmatrix} m11 & m21 & m31 & m41 \\ m12 & m22 & m32 & m42 \\ m13 & m23 & m33 & m43 \\ m14 & m24 & m34 & m44 \end{bmatrix}" width="222" height="106">
               <ul>
                 <li id="MatrixDefined">
                   <p>
                     A 2D 3x2 matrix with six parameters <em>a</em>, <em>b</em>, <em>c</em>, <em>d</em>, <em>e</em> and <em>f</em> is equivalent to to the matrix:
                   </p>
                   <img src="matrix.png" alt="\begin{bmatrix} a & c & 0 & e \\ b & d & 0 & f \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="108" height="106">
                 </li>
                 <li id="TranslateDefined">
                   <p>
                     A 2D translation with the parameters <em>tx</em> and <em>ty</em> is equivalent to a <a href="#Translate3dDefined">3D translation</a> where <em>tz</em> has zero as a value.
                   </p>
                 </li>
                 <li id="ScaleDefined">
                   <p>
                     A 2D scaling with the parameters <em>sx</em> and <em>sy</em> is equivalent to a <a href="#Scale3dDefined">3D scale</a> where <em>sz</em> has one as a value.
                   </p>
                 </li>
                 <li id="RotateDefined">
                   <p>
                     A 2D rotation with the parameter <em>alpha</em> is equivalent to a <a href="#RotateZDefined">rotation around the Z axis</a>.
                   </p>
                 </li>
                 <li id="SkewDefined">
                   <p>
                     A 2D skew transformation with the parameters <em>alpha</em> and <em>beta</em> is equivalent to the matrix:
                   </p>
                   <img src="skew.png" alt="\begin{bmatrix} 1 & \tan(\alpha) & 0 & 0 \\ \tan(\beta) & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="205" height="106">
                 </li>
                 <li id="Translate3dDefined">
                   <p>
                     A 3D translation with the parameters <em>tx</em>, <em>ty</em> and <em>tz</em> is equivalent to the matrix:
                   </p>
                   <img src="translate3d.png" alt="\begin{bmatrix} 1 & 0 & 0 & tx \\ 0 & 1 & 0 & ty \\ 0 & 0 & 1 & tz \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="114" height="106">
                 </li>
                 <li id="Scale3dDefined">
                   <p>
                     A 3D scaling with the parameters <em>sx</em>, <em>sy</em> and <em>sz</em> is equivalent to the matrix:
                   </p>
                   <img src="scale3d.png" alt="\begin{bmatrix} sx & 0 & 0 & 0 \\ 0 & sy & 0 & 0 \\ 0 & 0 & sz & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="137" height="106">
                 </li>
                 <li id="Rotate3dDefined">
                   <p>
                     A 3D rotation with the vector [x,y,z] and the parameter <em>alpha</em> is equivalent to the matrix:
                   </p>
                   <img src="rotate3dmatrix.png" alt="\begin{bmatrix} 1 - 2 \cdot (y^2 + z^2) \cdot sq & 2 \cdot (x \cdot y \cdot sq - z \cdot sc) & 2 \cdot (x \cdot z \cdot sq + y \cdot sc) & 0 \\ 2 \cdot (x \cdot y \cdot sq + z \cdot sc) & 1 - 2 \cdot (x^2 + z^2) \cdot sq & 2 \cdot (y \cdot z \cdot sq - x \cdot sc) & 0 \\ 2 \cdot (x \cdot z \cdot sq - y \cdot sc) & 2 \cdot (y \cdot z \cdot sq + x \cdot sc) & 1 - 2 \cdot (x^2 + y^2) \cdot sq & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="647" height="106">
                   <p>
                     where:
                   </p>
                   <img src="rotate3dvariables.png" alt="\newline sc = \sin (\alpha/2) \cdot \cos (\alpha/2) \newline sq = \sin^2 (\alpha/2)" width="221" height="50">
                 </li>
                 <li id="RotateXDefined">
                   <p>
                     A 3D rotation about the X axis with the parameter <em>alpha</em> is equivalent to the matrix:
                   </p>
                   <img src="rotateX.png" alt="\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\alpha) & -\sin(\alpha) & 0 \\ 0 & \sin(\alpha) & \cos(\alpha) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="220" height="106">
                 </li>
                 <li id="RotateYDefined">
                   <p>
                     A 3D rotation about the Y axis with the parameter <em>alpha</em> is equivalent to the matrix:
                   </p>
                   <img src="rotateY.png" alt="\begin{bmatrix} \cos(\alpha) & 0 & \sin(\alpha) & 0 \\ 0 & 1 & 0 & 0 \\ -\sin(\alpha) & 0 & \cos(\alpha) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="220" height="106">
                 </li>
                 <li id="RotateZDefined">
                   <p>
                     A 3D rotation about the Z axis with the parameter <em>alpha</em> is equivalent to the matrix:
                   </p>
                   <img src="rotateZ.png" alt="\begin{bmatrix} \cos(\alpha) & -\sin(\alpha) & 0 & 0 \\ \sin(\alpha) & \cos(\alpha) & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}" width="220" height="106">
                 </li>
                 <li id="PerspectiveDefined">
                   <p>
                     A perspective projection matrix with the parameter <em>d</em> is equivalent to the matrix:
                   </p>
                   <img src="perspective.png" alt="\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -1/d & 1 \end{bmatrix}" width="143" height="106">
                 </li>
               </ul>
         <h2>References</h2>
         <h3 class="no-num">Normative references</h3>
         <!--normative-->
         <h3 class="no-num">Other references</h3>
         <!--informative-->
         <h2 class="no-num">Property index</h2>
         <!-- properties -->
         <h2 class="no-num" id="index">Index</h2>
         <!--index-->
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