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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<html lang=en>
<head
profile="http://dublincore.org/documents/2008/08/04/dc-html/ http://www.w3.org/2006/03/hcard">
<meta content="text/html; charset=utf-8" http-equiv=Content-Type>
<title>CSS Transforms</title>
<link href="http://purl.org/dc/terms/" rel=schema.dcterms>
<link href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright"
rel=dcterms.rights>
<meta content="CSS Transforms" name=dcterms.title>
<meta content=text name=dcterms.type>
<meta content=2013-05-20 name=dcterms.date>
<meta content="Simon Fraser" name=dcterms.creator>
<meta content="Dean Jackson" name=dcterms.creator>
<meta content="Edward O'Connor" name=dcterms.creator>
<meta content="Dirk Schulze" name=dcterms.creator>
<meta content="Aryeh Gregor" name=dcterms.creator>
<meta content=W3C name=dcterms.publisher>
<meta content="http://dev.w3.org/csswg/css3-transforms/"
name=dcterms.identifier>
<script defer=defer
src="http://test.csswg.org/harness/annotate.js#CSS3-TRANSFORMS_DEV"
type="text/javascript"></script>
<link href="http://www.w3.org/StyleSheets/TR/W3C-ED.css" rel=stylesheet
type="text/css">
<link href=default.css rel=stylesheet type="text/css">
<body>
<div class=head id=div-head> <!--begin-logo-->
<p><a href="http://www.w3.org/"><img alt=W3C height=48
src="http://www.w3.org/Icons/w3c_home" width=72></a> <!--end-logo-->
<h1>CSS Transforms Level 1</h1>
<h2 class="no-num no-toc" id=longstatus-date>Editor's Draft 20 May 2013</h2>
<dl>
<dt>This version:
<dd> <a
href="http://dev.w3.org/csswg/css3-transforms/">http://dev.w3.org/csswg/css3-transforms/</a>
<!--http://www.w3.org/TR/2013/WD-css3-transforms-20130520/-->
<dt>Latest version:
<dd><a
href="http://www.w3.org/TR/css3-transforms/">http://www.w3.org/TR/css3-transforms/</a>
<dt>Editor's draft:
<dd><a
href="http://dev.w3.org/csswg/css3-transforms/">http://dev.w3.org/csswg/css3-transforms/</a>
<dt>Previous version:
<dd><a
href="http://www.w3.org/TR/2012/WD-css3-transforms-20120911/">http://www.w3.org/TR/2012/WD-css3-transforms-20120911/</a>
<dt id=editors-list>Editors:
<dd>Simon Fraser (<a href="http://www.apple.com/">Apple Inc</a>)
<simon.fraser @apple.com>
<dd>Dean Jackson (<a href="http://www.apple.com/">Apple Inc</a>) <dino
@apple.com>
<dd>Edward O'Connor (<a href="http://www.apple.com/">Apple Inc</a>)
<eoconnor @apple.com>
<dd>Dirk Schulze (<a href="http://www.adobe.com/">Adobe Systems, Inc</a>)
<dschulze @adobe.com>
<dd>Aryeh Gregor (<a href="http://www.mozilla.org/">Mozilla</a>) <ayg
@aryeh.name>
<dt id=former-editors-list>Former Editors:
<dd>David Hyatt (<a href="http://www.apple.com/">Apple Inc</a>) <hyatt
@apple.com>
<dd>Chris Marrin (<a href="http://www.apple.com/">Apple Inc</a>)
<cmarrin @apple.com>
<dt>Issues list:
<dd><a
href="https://www.w3.org/Bugs/Public/buglist.cgi?query_format=advanced&product=CSS&component=Transforms&resolution=---&cmdtype=doit">in
Bugzilla</a>
<dt>Feedback:
<dd><a
href="mailto:www-style@w3.org?subject=%5B[css-transforms]%5D%20feedback">www-style@w3.org</a>
with subject line “<kbd>[css-transforms] <var>… message topic
…</var></kbd>” (<a
href="http://lists.w3.org/Archives/Public/www-style/"
rel=discussion>archives</a>)
<dt>Test suite:
<dd>none yet
</dl>
<!--begin-copyright-->
<p class=copyright><a
href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright"
rel=license>Copyright</a> © 2013 <a href="http://www.w3.org/"><abbr
title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup> (<a
href="http://www.csail.mit.edu/"><abbr
title="Massachusetts Institute of Technology">MIT</abbr></a>, <a
href="http://www.ercim.eu/"><abbr
title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
<a href="http://www.keio.ac.jp/">Keio</a>, <a
href="http://ev.buaa.edu.cn/">Beihang</a>), All Rights Reserved. W3C <a
href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
<a
href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>
and <a
href="http://www.w3.org/Consortium/Legal/copyright-documents">document
use</a> rules apply.</p>
<!--end-copyright-->
<hr title="Separator for header">
</div>
<h2 class="no-num no-toc" id=abstract>Abstract</h2>
<p>CSS transforms allows elements styled with CSS to be transformed in
two-dimensional or three-dimensional space. This specification is the
convergence of the <a href="http://www.w3.org/TR/css3-2d-transforms/">CSS
2D transforms</a>, <a href="http://www.w3.org/TR/css3-3d-transforms/">CSS
3D transforms</a> and <a
href="http://www.w3.org/TR/2009/WD-SVG-Transforms-20090320/">SVG
transforms</a> specifications.
<h2 class="no-num no-toc" id=status>Status of this document</h2>
<!--begin-status-->
<p>This is a public copy of the editors' draft. It is provided for
discussion only and may change at any moment. Its publication here does
not imply endorsement of its contents by W3C. Don't cite this document
other than as work in progress.
<p>The (<a
href="http://lists.w3.org/Archives/Public/public-fx/">archived</a>) public
mailing list <a href="mailto:public-fx@w3.org">public-fx@w3.org</a> (see
<a href="http://www.w3.org/Mail/Request">instructions</a>) is preferred
for discussion of this specification. When sending e-mail, please put the
text “css3-transforms” in the subject, preferably like this:
“[<!---->css3-transforms<!---->] <em>…summary of comment…</em>”
<p>This document was produced by the <a
href="http://www.w3.org/Style/CSS/members">CSS Working Group</a> (part of
the <a href="http://www.w3.org/Style/">Style Activity</a>) and the <a
href="http://www.w3.org/Graphics/SVG/">SVG Working Group</a> (part of the
<a href="http://www.w3.org/Graphics/">Graphics Activity</a>).
<p>This document was produced by groups operating under the <a
href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February
2004 W3C Patent Policy</a>. W3C maintains a <a
href="http://www.w3.org/2004/01/pp-impl/32061/status"
rel=disclosure>public list of any patent disclosures (CSS)</a> and a <a
href="http://www.w3.org/2004/01/pp-impl/19480/status"
rel=disclosure>public list of any patent disclosures (SVG)</a> made in
connection with the deliverables of each group; these pages also include
instructions for disclosing a patent. An individual who has actual
knowledge of a patent which the individual believes contains <a
href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential
Claim(s)</a> must disclose the information in accordance with <a
href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section
6 of the W3C Patent Policy</a>.</p>
<!--end-status-->
<p> This specification replaces the former <a
href="http://www.w3.org/TR/css3-2d-transforms/"
title="CSS 2D Transforms">CSS 2D Transforms</a> and <a
href="http://www.w3.org/TR/css3-3d-transforms/"
title="CSS 3D Transforms Module Level 3">CSS 3D Transforms</a>
specifications, as well as <a href="http://www.w3.org/TR/SVG-Transforms/"
title="SVG Transforms 1.0">SVG Transforms</a>.
<p> The <a href=ChangeLog>list of changes made to this specification</a> is
available.
<h2 class="no-num no-toc" id=contents>Table of contents</h2>
<!--begin-toc-->
<ul class=toc>
<li><a href="#introduction"><span class=secno>1. </span>Introduction</a>
<li><a href="#module-interactions"><span class=secno>2. </span>Module
Interactions</a>
<li><a href="#css-values"><span class=secno>3. </span>CSS Values</a>
<li><a href="#definitions"><span class=secno>4. </span>Terminology</a>
<li><a href="#two-dimensional-subset"><span class=secno>5. </span> Two
Dimensional Subset </a>
<li><a href="#transform-rendering"><span class=secno>6. </span>The
Transform Rendering Model</a>
<ul class=toc>
<li><a href="#transform-3d-rendering"><span class=secno>6.1. </span>3D
Transform Rendering</a>
<li><a href="#processing-of-perspective-transformed-boxes"><span
class=secno>6.2. </span> Processing of Perspective-Transformed Boxes
</a>
</ul>
<li><a href="#transform-property"><span class=secno>7. </span> The
‘<code class=property>transform</code>’ Property </a>
<li><a href="#transform-origin-property"><span class=secno>8. </span> The
‘<code class=property>transform-origin</code>’ Property </a>
<li><a href="#transform-style-property"><span class=secno>9. </span> The
‘<code class=property>transform-style</code>’ Property </a>
<li><a href="#perspective-property"><span class=secno>10. </span> The
‘<code class=property>perspective</code>’ Property </a>
<li><a href="#perspective-origin-property"><span class=secno>11. </span>
The ‘<code class=property>perspective-origin</code>’ Property </a>
<li><a href="#backface-visibility-property"><span class=secno>12. </span>
The ‘<code class=property>backface-visibility</code>’ Property </a>
<li><a href="#svg-transform"><span class=secno>13. </span> The SVG
‘<code class=property>transform</code>’ Attribute </a>
<ul class=toc>
<li><a href="#transform-attribute-specificity"><span class=secno>13.1.
</span> SVG ‘<code class=property>transform</code>’ attribute
specificity </a>
<li><a href="#svg-syntax"><span class=secno>13.2. </span> Syntax of the
SVG ‘<code class=property>transform</code>’ attribute </a>
<ul class=toc>
<li><a href="#svg-transform-list"><span class=secno>13.2.1. </span>
Transform List </a>
<li><a href="#svg-functional-notation"><span class=secno>13.2.2.
</span> Functional Notation </a>
<li><a href="#svg-data-types"><span class=secno>13.2.3. </span> SVG
Data Types </a>
<ul class=toc>
<li><a href="#svg-transform-value"><span class=secno>13.2.3.1.
</span> The <var><translation-value></var> and
<var><length></var> type </a>
<li><a href="#svg-angle"><span class=secno>13.2.3.2. </span> The
<var><angle></var> type </a>
<li><a href="#svg-number"><span class=secno>13.2.3.3. </span> The
<var><number></var> type </a>
</ul>
</ul>
<li><a href="#svg-gradient-transform-pattern-transform"><span
class=secno>13.3. </span> The SVG ‘<code
class=property>gradientTransform</code>’ and ‘<code
class=property>patternTransform</code>’ attributes </a>
<li><a href="#svg-transform-functions"><span class=secno>13.4. </span>
SVG transform functions </a>
<li><a href="#svg-three-dimensional-functions"><span class=secno>13.5.
</span>SVG and 3D transform functions</a>
<li><a href="#svg-user-coordinate-space"><span class=secno>13.6. </span>
User coordinate space </a>
<li><a href="#transform-attribute-dom"><span class=secno>13.7. </span>
SVG DOM interface for the ‘<code class=property>transform</code>’
attribute </a>
</ul>
<li><a href="#svg-animation"><span class=secno>14. </span> SVG Animation
</a>
<ul class=toc>
<li><a href="#svg-animate-element"><span class=secno>14.1. </span> The
<code class=element-name><animate></code> and <code
class=element-name><set></code> element </a>
<li><a href="#neutral-element"><span class=secno>14.2. </span> Neutral
element for addition </a>
<li><a href="#svg-attribute-name"><span class=secno>14.3. </span> The
SVG ‘<code class=property>attributeName</code>’ attribute </a>
</ul>
<li><a href="#transform-functions"><span class=secno>15. </span> The
Transform Functions </a>
<ul class=toc>
<li><a href="#two-d-transform-functions"><span class=secno>15.1.
</span>2D Transform Functions</a>
<li><a href="#three-d-transform-functions"><span class=secno>15.2.
</span>3D Transform Functions</a>
</ul>
<li><a href="#transform-function-lists"><span class=secno>16. </span> The
Transform Function Lists </a>
<li><a href="#animation"><span class=secno>17. </span> Interpolation of
Transforms </a>
<li><a href="#transform-primitives"><span class=secno>18. </span>
Transform function primitives and derivatives </a>
<li><a href="#interpolation-of-transform-functions"><span class=secno>19.
</span> Interpolation of primitives and derived transform functions </a>
<li><a href="#matrix-interpolation"><span class=secno>20. </span>
Interpolation of Matrices </a>
<ul class=toc>
<li><a href="#matrix-decomposing"><span class=secno>20.1.
</span>Decomposing the Matrix</a>
<li><a href="#matrix-values-interpolation"><span class=secno>20.2.
</span> Interpolation of decomposed matrix values </a>
<li><a href="#matrix-recomposing"><span class=secno>20.3. </span>
Recomposing the Matrix </a>
</ul>
<li><a href="#mathematical-description"><span class=secno>21. </span>
Mathematical Description of Transform Functions </a>
<li><a href="#conformance"><span class=secno>22. </span>Conformance</a>
<li><a href="#references"><span class=secno>23. </span>References</a>
<ul class=toc>
<li class=no-num><a href="#normative-references">Normative
references</a>
<li class=no-num><a href="#other-references">Other references</a>
</ul>
<li class=no-num><a href="#property-index">Property index</a>
<li class=no-num><a href="#index">Index</a>
</ul>
<!--end-toc-->
<h2 id=introduction><span class=secno>1. </span>Introduction</h2>
<p><em>This section is not normative.</em>
<p> The CSS <a href="http://www.w3.org/TR/REC-CSS2/visuren.html">visual
formatting model</a> describes a coordinate system within each element is
positioned. Positions and sizes in this coordinate space can be thought of
as being expressed in pixels, starting in the origin of point with
positive values proceeding to the right and down.
<p> This coordinate space can be modified with the ‘<a
href="#effects"><code class=property>transform</code></a>’ property.
Using transform, elements can be translated, rotated and scaled in two or
three dimensional space.
<p> Additional properties make working with transforms easier, and allow
the author to control how nested three-dimensional transforms interact.
<ul>
<li> The ‘<a href="#transform-origin"><code
class=property>transform-origin</code></a>’ property provides a
convenient way to control the origin about which transforms on an element
are applied.
<li> The ‘<a href="#perspective"><code
class=property>perspective</code></a>’ property allows the author to
make child elements with three-dimensional transforms appear as if they
live in a common three-dimensional space. The ‘<a
href="#perspective-origin"><code
class=property>perspective-origin</code></a>’ property provides control
over the origin at which perspective is applied, effectively changing the
location of the "vanishing point".
<li> The ‘<a href="#transform-style"><code
class=property>transform-style</code></a>’ property allows
3D-transformed elements and their 3D-transformed descendants to share a
common three-dimensional space, allowing the construction of hierarchies
of three-dimensional objects.
<li> The ‘<a href="#backface-visibility"><code
class=property>backface-visibility</code></a>’ property comes into play
when an element is flipped around via three-dimensional transforms such
that its reverse side is visible to the viewer. In some situations it is
desirable to hide the element in this situation, which is possible using
the value of ‘<code class=css>hidden</code>’ for this property.
</ul>
<p> Note that while some values of the ‘<a href="#effects"><code
class=property>transform</code></a>’ property allow an element to be
transformed in a three-dimensional coordinate system, the elements
themselves are not three-dimensional objects. Instead, they exist on a
two-dimensional plane (a flat surface) and have no depth.</p>
<!-- ======================================================================================================= -->
<h2 id=module-interactions><span class=secno>2. </span>Module Interactions</h2>
<p>This module defines a set of CSS properties that affect the visual
rendering of elements to which those properties are applied; these effects
are applied after elements have been sized and positioned according to the
<a href="http://www.w3.org/TR/CSS2/visuren.html"
title="Visual formatting model">Visual formatting model</a> from <a
href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>. Some values of
these properties result in the creation of a <a
href="http://www.w3.org/TR/CSS2/visuren.html#containing-block"
title="Visual formatting model">containing block</a>, and/or the creation
of a <a href="http://www.w3.org/TR/CSS2/visuren.html#z-index"
title="Visual formatting model">stacking context</a>.
<p> Three-dimensional transforms can also affect the visual layering of
elements, and thus override the back-to-front painting order described in
<a href="http://www.w3.org/TR/CSS2/zindex.html"
title="Elaborate description of Stacking Contexts">Appendix E</a> of <a
href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>.
<p> Transforms affect the results of the Element Interface extensions <a
href="http://www.w3.org/TR/cssom-view/#dom-element-getclientrects">getClientRects()</a>
and <a
href="http://www.w3.org/TR/cssom-view/#dom-element-getboundingclientrect">getBoundingClientRect()</a>,
which are specified in <a href="#CSSOM-VIEW"
rel=biblioentry>[CSSOM-VIEW]<!--{{CSSOM-VIEW}}--></a>.
<p> Transforms affect the rendering of backgounds on elements with a value
of ‘<code class=css>fixed</code>’ for the ‘<code class=css><code
class=property><a
href="http://www.w3.org/TR/css3-background/#the-background-attachment">background-attachment</a></code></code>’
property, which is specified in <a href="#CSS3BG"
rel=biblioentry>[CSS3BG]<!--{{!CSS3BG}}--></a>.
<h2 id=css-values><span class=secno>3. </span>CSS Values</h2>
<p>This specification follows the <a
href="http://www.w3.org/TR/CSS21/about.html#property-defs">CSS property
definition conventions</a> from <a href="#CSS21"
rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>. Value types not defined in
this specification are defined in CSS Level 2 Revision 1 <a
href="#CSS21" rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>.
<p>In addition to the property-specific values listed in their definitions,
all properties defined in this specification also accept the <a
href="http://www.w3.org/TR/CSS21/cascade.html#value-def-inherit">inherit</a>
keyword as their property value. For readability it has not been repeated
explicitly.
<h2 id=definitions><span class=secno>4. </span>Terminology</h2>
<p> When used in this specification, terms have the meanings assigned in
this section.
<dl>
<dt id=TermBoundingBox><dfn id=bounding-box>bounding box</dfn>
<dd>
<p> A bounding box is the object bounding box for all SVG elements
without an associated CSS layout box and the border box for all other
elements. The bounding box of a table is the border box of its <a
href="http://www.w3.org/TR/CSS21/tables.html#model">table wrapper
box</a>, not its table box.
<dt id=TermTransformableElement><dfn
id=transformable-element>transformable element</dfn>
<dd>
<p> A transformable element is an element in one of these categories:
<ul>
<li> an element whose layout is governed by the CSS box model which is
either a <a
href="http://www.w3.org/TR/CSS2/visuren.html#block-level">block-level</a>
or <a href="http://www.w3.org/TR/CSS2/visuren.html#x13">atomic
inline-level element</a>, or whose ‘<code
class=property>display</code>’ property computes to ‘<code
class=css>table-row</code>’, ‘<code
class=css>table-row-group</code>’, ‘<code
class=css>table-header-group</code>’, ‘<code
class=css>table-footer-group</code>’, ‘<code
class=css>table-cell</code>’, or ‘<code
class=css>table-caption</code>’ <a href="#CSS21"
rel=biblioentry>[CSS21]<!--{{!CSS21}}--></a>
<li> an element in the SVG namespace and not governed by the CSS box
model which has the attributes ‘<a href="#effects"><code
class=property>transform</code></a>’, ‘<code
class=property>patternTransform</code>’ or ‘<code
class=property>gradientTransform</code>’ <a href="#SVG11"
rel=biblioentry>[SVG11]<!--{{!SVG11}}--></a>
</ul>
<dt id=TermUserCoordinateSystem><dfn id=user-coordinate-system>user
coordinate system</dfn>
<dt id=TermLocalCoordinateSystem><dfn id=local-coordinate-system>local
coordinate system</dfn>
<dd>
<p> In general, a coordinate system defines locations and distances on
the current canvas. The current local coordinate system (also user
coordinate system) is the coordinate system that is currently active and
which is used to define how coordinates and lengths are located and
computed, respectively, on the current canvas.
<dt id=TermPerspectiveMatrix><dfn id=perspective-matrix>perspective
matrix</dfn>
<dd>
<p> A matrix computed from the values of the ‘<a
href="#perspective"><code class=property>perspective</code></a>’ and
‘<a href="#perspective-origin"><code
class=property>perspective-origin</code></a>’ properties as described
<a href="#perspective-matrix-computation">below</a>.
<dt id=TermTransformationMatrix><dfn
id=transformation-matrix>transformation matrix</dfn>
<dd>
<p> A matrix that defines the mathematical mapping from one coordinate
system into another. It is computed from the values of the ‘<a
href="#effects"><code class=property>transform</code></a>’ and ‘<a
href="#transform-origin"><code
class=property>transform-origin</code></a>’ properties as described <a
href="#transformation-matrix-computation">below</a>.
<dt id=TermCurrentTransformationMatrix><dfn
id=current-transformation-matrix-ctm>current transformation matrix
(CTM)</dfn>
<dd>
<p> A matrix that defines the mapping from the local coordinate system
into the viewport coordinate system.
<dt id=TermAccumulated3DTransformationMatrix> <dfn
id=accumulated-3d-transformation-matrix>accumulated 3D transformation
matrix</dfn>
<dd>
<p> A matrix computed for elements in a <a href="#d-rendering-context">3D
rendering context</a>, as described <a
href="#accumulated-3d-transformation-matrix-computation">below</a>.
<dt id=TermIdentityTransformFunction> <dfn
id=identity-transform-function>identity transform function</dfn>
<dd>
<p> A <a href="#transform-functions">transform function</a> that is
equivalent to a identity 4x4 matrix (see <a
href="#mathematical-description">Mathematical Description of Transform
Functions</a>). Examples for identity transform functions are ‘<code
class=css>translate(0)</code>’, ‘<code class=css>translate3d(0, 0,
0)</code>’, ‘<code class=css>translateX(0)</code>’, ‘<code
class=css>translateY(0)</code>’, ‘<code
class=css>translateZ(0)</code>’, ‘<code
class=css>scale(1)</code>’, ‘<code class=css>scaleX(1)</code>’,
‘<code class=css>scaleY(1)</code>’, ‘<code
class=css>scaleZ(1)</code>’, ‘<code class=css>rotate(0)</code>’,
‘<code class=css>rotate3d(1, 1, 1, 0)</code>’, ‘<code
class=css>rotateX(0)</code>’, ‘<code class=css>rotateY(0)</code>’,
‘<code class=css>rotateZ(0)</code>’, ‘<code class=css>skew(0,
0)</code>’, ‘<code class=css>skewX(0)</code>’, ‘<code
class=css>skewY(0)</code>’, ‘<code class=css>matrix(1, 0, 0, 1, 0,
0)</code>’ and ‘<code class=css>matrix3d(1, 0, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 0, 0, 0, 1)</code>’. A special case is perspective: ‘<code
class=css>perspective(infinity)</code>’. The value of m<sub>34</sub>
becomes infinitesimal small and the transform function is therefore
assumed to be equal to the identity matrix.
<dt id=Term3DRenderingContext><dfn id=d-rendering-context>3D rendering
context</dfn>
<dd>
<p> A containing block hierarchy of one or more levels, instantiated by
elements with a computed value for the ‘<a
href="#transform-style"><code
class=property>transform-style</code></a>’ property of ‘<code
class=css>preserve-3d</code>’, whose elements share a common
three-dimensional coordinate system.
</dl>
<!-- ======================================================================================================= -->
<h2 id=two-dimensional-subset><span class=secno>5. </span> Two Dimensional
Subset</h2>
<p> UAs may not always be able to render three-dimensional transforms and
then just support a two-dimensional subset of this specification. In this
case <a href="#three-d-transform-functions">three-dimensional
transforms</a> and the properties ‘<a href="#transform-style"><code
class=property>transform-style</code></a>’, ‘<a
href="#perspective"><code class=property>perspective</code></a>’, ‘<a
href="#perspective-origin"><code
class=property>perspective-origin</code></a>’ and ‘<a
href="#backface-visibility"><code
class=property>backface-visibility</code></a>’ must not be supported.
Section <a href="#transform-3d-rendering">3D Transform Rendering</a> does
not apply. Matrix decomposing uses the technique taken from the "unmatrix"
method in "Graphics Gems II, edited by Jim Arvo", simplified for the 2D
case. Section <a href="#mathematical-description">Mathematical Description
of Transform Functions</a> is still effective but can be reduced by using
a 3x3 transformation matrix where <em>a</em> equals
<em>m<sub>11</sub></em>, <em>b</em> equals <em>m<sub>12</sub></em>,
<em>c</em> equals <em>m<sub>21</sub></em>, <em>d</em> equals
<em>m<sub>22</sub></em>, <em>e</em> equals <em>m<sub>41</sub></em> and
<em>f</em> equals <em>m<sub>42</sub></em> (see <a href="#MatrixDefined">A
2D 3x2 matrix with six parameter</a>).
<div class=figure> <img alt="3x3 matrix" height=79 src=3x3matrix.png
title="\begin{bmatrix} a & c & e \\ b & d & f \\ 0 & 0 & 1 \end{bmatrix}"
width=82>
<p class=caption> 3x3 matrix for two-dimensional transformations.
</div>
<div class=example>
<p> Authors can easily provide a fallback if UAs do not provide support
for three-dimensional transforms. The following example has two property
definitions for ‘<a href="#effects"><code
class=property>transform</code></a>’. The first one consists of two
two-dimensional transform functions. The second one has a two-dimensional
and a three-dimensional transform function.
<pre>div {
transform: scale(2) rotate(45deg);
transform: scale(2) rotate3d(0, 0, 1, 45deg);
}</pre>
<p> With 3D support, the second definition will override the first one.
Without 3D support, the second definition is invalid and a UA falls back
to the first definition.
</div>
<!-- ======================================================================================================= -->
<h2 id=transform-rendering><span class=secno>6. </span>The Transform
Rendering Model</h2>
<p><em>This section is normative.</em>
<p> Specifying a value other than ‘<code class=css>none</code>’ for the
‘<a href="#effects"><code class=css>transform</code></a>’ property
establishes a new <a href="#local-coordinate-system"><var>local coordinate
system</var></a> 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="#transformation-matrix"><var>transformation matrix</var></a>.
Transformations are cumulative. That is, elements establish their local
coordinate system within the coordinate system of their parent. From the
perspective of the user, an element effectively accumulates all the ‘<a
href="#effects"><code class=property>transform</code></a>’ properties of
its ancestors as well as any local transform applied to it. The
accumulation of these transforms defines a <a
href="#current-transformation-matrix-ctm"><var>current transformation
matrix (CTM)</var></a> for the element.
<p> The coordinate space is a coordinate system with two axes: the X axis
increases horizontally to the right; the Y axis increases vertically
downwards. Three-dimensional transform functions extend this coordinate
space into three dimensions, adding a Z axis perpendicular to the plane of
the screen, that increases towards the viewer.
<div class=figure> <img alt="Demonstration of the initial coordinate space"
height=240 src=coordinates.svg width=270>
<p class=caption> Demonstration of the initial coordinate space.
</div>
<p id=transformation-matrix-computation> The <a
href="#transformation-matrix"><var>transformation matrix</var></a> is
computed from the ‘<a href="#effects"><code
class=property>transform</code></a>’ and ‘<a
href="#transform-origin"><code
class=property>transform-origin</code></a>’ properties as follows:
<ol>
<li>Start with the identity matrix.
<li>Translate by the computed X, Y and Z values of ‘<a
href="#transform-origin"><code
class=property>transform-origin</code></a>’
<li>Multiply by each of the transform functions in ‘<a
href="#effects"><code class=property>transform</code></a>’ property
from left to right
<li>Translate by the negated computed X, Y and Z values of ‘<a
href="#transform-origin"><code
class=property>transform-origin</code></a>’
</ol>
<p> Transforms apply to <a href="#transformable-element"><var>transformable
elements</var></a>.
<div class=example>
<pre>
div {
transform: translate(100px, 100px);
}
</pre>
<p>This transform moves the element by 100 pixels in both the X and Y
directions.
<div class=figure> <img alt="The 100px translation in X and Y" height=250
src="examples/translate1.svg" width=470></div>
</div>
<div class=example>
<pre>div {
height: 100px; width: 100px;
transform-origin: 50px 50px;
transform: rotate(45deg);
}</pre>
<p> The ‘<a href="#transform-origin"><code
class=property>transform-origin</code></a>’ property moves the point of
origin by 50 pixels in both the X and Y directions. The transform rotates
the element clockwise by 45° about the point of origin. After all
transform functions were applied, the translation of the origin gets
translated back by -50 pixels in both the X and Y directions.
<div class=figure> <img
alt="The point of origin gets translated temporary" height=250
src="examples/origin1.svg" width=735></div>
</div>
<div class=example>
<pre>
div {
height: 100px; width: 100px;
transform: translate(80px, 80px) scale(1.5, 1.5) rotate(45deg);
}
</pre>
<p> This transform moves the element by 80 pixels in both the X and Y
directions, then scales the element by 150%, then rotates it 45°
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>’.
<div class=figure> <img alt="The transform specified above" height=270
src="examples/compound_transform.svg" width=270></div>
<p> Note that an identical rendering can be obtained by nesting elements
with the equivalent transforms:
<pre>
<div style="transform: translate(80px, 80px)">
<div style="transform: scale(1.5, 1.5)">
<div style="transform: rotate(45deg)"></div>
</div>
</div></pre>
</div>
<p> For elements whose layout is governed by the CSS box model, the
transform property does not affect the flow of the content surrounding the
transformed element. However, the extent of the overflow area takes into
account transformed elements. This behavior is similar to what happens
when elements are offset via relative positioning. Therefore, if the value
of the ‘<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> For elements whose layout is governed by the CSS box model, 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 class=issue> Is this effect on position:fixed necessary? If so, need to
go into more detail here about why fixed positioned objects should do
this, i.e., that it's much harder to implement otherwise. See <a
href="https://www.w3.org/Bugs/Public/show_bug.cgi?id=16328">Bug 16328</a>.
<p> <a href="http://www.w3.org/TR/css3-background/#fixed0">Fixed
backgrounds</a> on the root element are affected by any transform
specified for that element. For all other elements that are effected by a
transform (i.e. have a transform applied to them, or to any of their
ancestor elements), a value of ‘<code class=css>fixed</code>’ for the
‘<code class=property>background-attachment</code>’ property is
treated as if it had a value of ‘<code class=css>scroll</code>’. The
computed value of ‘<code class=property>background-attachment</code>’
is not affected.
<p class=note> If the root element is transformed, the transformation
applies to the entire canvas, including any background specified for the
root element. Since <a
href="http://www.w3.org/TR/css3-background/#special-backgrounds"> the
background painting area for the root element</a> is the entire canvas,
which is infinite, the transformation might cause parts of the background
that were originally off-screen to appear. For example, if the root
element's background were repeating dots, and a transformation of ‘<code
class=css>scale(0.5)</code>’ were specified on the root element, the
dots would shrink to half their size, but there will be twice as many, so
they still cover the whole viewport.
<h3 id=transform-3d-rendering><span class=secno>6.1. </span>3D Transform
Rendering</h3>
<p> Normally, elements render as flat planes, and are rendered into the
same plane as their containing block. Often this is the plane shared by
the rest of the page. Two-dimensional transform functions can alter the
appearance of an element, but that element is still rendered into the same
plane as its containing block.
<p> Three-dimensional transforms can result in transformation matrices with
a non-zero Z component (where the Z axis projects out of the plane of the
screen). This can result in an element rendering on a different plane than
that of its containing block. This may affect the front-to-back rendering
order of that element relative to other elements, as well as causing it to
intersect with other elements. This behavior depends on whether the
element is a member of a <a href="#d-rendering-context"><var>3D rendering
context</var></a>, as described below.
<div class=issue>
<p class=desc>This description does not exactly match what WebKit
implements. Perhaps it should be changed to match current
implementations? See <a
href="https://www.w3.org/Bugs/Public/show_bug.cgi?id=19637">Bug
19637</a>.
</div>
<div class=example>
<p>This example shows the effect of three-dimensional transform applied to
an element.
<pre>
<style>
div {
height: 150px;
width: 150px;
}
.container {
border: 1px solid black;
}
.transformed {
transform: rotateY(50deg);
}
</style>
<div class="container">
<div class="transformed"></div>
</div>
</pre>
<div class=figure> <img alt="Div with a rotateY transform." height=190
src="examples/simple-3d-example.png" width=210></div>
<p>The transform is a 50° rotation about the vertical, Y axis. Note how
this makes the blue box appear narrower, but not three-dimensional.
</div>
<p> The ‘<a href="#perspective"><code
class=property>perspective</code></a>’ and ‘<a
href="#perspective-origin"><code
class=property>perspective-origin</code></a>’ properties can be used to
add a feeling of depth to a scene by making elements higher on the Z axis
(closer to the viewer) appear larger, and those further away to appear
smaller. The scaling is proportional to <var>d</var>/(<var>d</var> −
<var>Z</var>) where <var>d</var>, the value of ‘<a
href="#perspective"><code class=property>perspective</code></a>’, is the
distance from the drawing plane to the the assumed position of the
viewer's eye.
<div class=figure> <img alt="Diagram of scale vs. Z position"
src="perspective_distance.png">
<p class=caption> Diagrams showing how scaling depends on the ‘<a
href="#perspective"><code class=property>perspective</code></a>’
property and Z position. In the top diagram, <var>Z</var> is half of
<var>d</var>. In order to make it appear that the original circle (solid
outline) appears at <var>Z</var> (dashed circle), the circle is scaled up
by a factor of two, resulting in the light blue circle. In the bottom
diagram, the circle is scaled down by a factor of one-third to make it
appear behind the original position.
</div>
<p> Normally the assumed position of the viewer's eye is centered on a
drawing. This position can be moved if desired – for example, if a web
page contains multiple drawings that should share a common perspective –
by setting ‘<a href="#perspective-origin"><code
class=property>perspective-origin</code></a>’.
<div class=figure> <img alt="Diagram of different perspective-origin"
src="perspective_origin.png">
<p class=caption> Diagram showing the effect of moving the perspective
origin upward.
</div>
<p id=perspective-matrix-computation> The <a
href="#TermPerspectiveMatrix"><i>perspective matrix</i></a> is computed as
follows:
<ol>
<li>Start with the identity matrix.
<li>Translate by the computed X and Y values of ‘<a
href="#perspective-origin"><code
class=property>perspective-origin</code></a>’
<li>Multiply by the matrix that would be obtained from the ‘<code
class=css><a href="#perspective-function"><code
class=css>perspective(<length>)</code></a></code>’ transform
function, where the length is provided by the value of the ‘<a
href="#perspective"><code class=property>perspective</code></a>’
property
<li>Translate by the negated computed X and Y values of ‘<a
href="#perspective-origin"><code
class=property>perspective-origin</code></a>’
</ol>
<div class=example>
<p>This example shows how perspective can be used to cause
three-dimensional transforms to appear more realistic.
<pre>
<style>
div {
height: 150px;
width: 150px;
}
.container {
perspective: 500px;
border: 1px solid black;
}
.transformed {
transform: rotateY(50deg);
}
</style>
<div class="container">
<div class="transformed"></div>
</div>
</pre>
<div class=figure> <img
alt="Div with a rotateY transform, and perspective on its container"
height=190 src="examples/simple-perspective-example.png" width=210></div>
<p>The inner element has the same transform as in the previous example,
but its rendering is now influenced by the perspective property on its
parent element. Perspective causes vertices that have positive Z
coordinates (closer to the viewer) to be scaled up in X and Y, and those
further away (negative Z coordinates) to be scaled down, giving an
appearance of depth.
</div>
<p> An element with a three-dimensional transform that is not contained in
a <a href="#d-rendering-context"><var>3D rendering context</var></a>
renders with the appropriate transform applied, but does not intersect
with any other elements. The three-dimensional transform in this case can
be considered just as a painting effect, like two-dimensional transforms.
Similarly, the transform does not affect painting order. For example, a
transform with a positive Z translation may make an element look larger,
but does not cause that element to render in front of elements with no
translation in Z.
<p> An element with a three-dimensional transform that is contained in a <a
href="#d-rendering-context"><var>3D rendering context</var></a> can
visibly interact with other elements in that same 3D rendering context;
the set of elements participating in the same <a
href="#d-rendering-context"><var>3D rendering context</var></a> may
obscure each other or intersect, based on their computed transforms. They
are rendered as if they are all siblings, positioned in a common 3D
coordinate space. The position of each element in that three-dimensional
space is determined by accumulating the transformation matrices up from
the element that establishes the <a href="#d-rendering-context"><var>3D
rendering context</var></a> through each element that is a containing
block for the given element, as described below.
<div class=example>
<pre>
<style>
div {
height: 150px;
width: 150px;
}
.container {
perspective: 500px;
border: 1px solid black;
}
.transformed {
transform: rotateY(50deg);
background-color: blue;
}
.child {
transform-origin: top left;
transform: rotateX(40deg);
background-color: lime;
}
</style>
<div class="container">
<div class="transformed">
<div class="child"></div>
</div>
</div>
</pre>
<p>This example shows how nested 3D transforms are rendered in the absence