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<!DOCTYPE html public '-//W3C//DTD HTML 4.01//EN' 'http://www.w3.org/TR/html4/strict.dtd'>
<html lang="en">
<head profile="http://www.w3.org/2006/03/hcard">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" >
<title>CSS Transforms</title>
<link rel="stylesheet" type="text/css" href="../default.css" >
<script src='http://test.csswg.org/harness/annotate.js#CSS3-TRANSFORMS_DEV' type='text/javascript' defer></script>
<style type="text/css">
.term {
font-style: italic;
}
</style>
<link rel="stylesheet" type="text/css" href="http://www.w3.org/StyleSheets/TR/W3C-ED.css" >
</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><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>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>
<!--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>
<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 'transform' 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 'transform-origin' property provides a convenient way to control the origin about
which transforms on an element are applied.
</li>
<li>
The 'perspective' property allows the author to make child elements with
three-dimensional transforms appear as if they live in a common three-dimensional
space.
The 'perspective-origin' property provides control over the origin at which
perspective is applied, effectively changing the location of the "vanishing point".
</li>
<li>
The 'transform-style' 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 'backface-visibility' 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 'transform' 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">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 [[!CSS21]]. 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>
<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 [[!CSS21]].
</p>
<p>
Transforms affect the rendering of backgounds on elements with a value of ''fixed'' for the
'<code class="property"><a href="http://www.w3.org/TR/css3-background/#the-background-attachment">background-attachment</a></code>' property,
which is specified in [[!CSS3BG]].
</p>
<h2 id="css-values">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 [[!CSS21]]. Value types not defined in this specification are defined in CSS Level 2 Revision 1 [[!CSS21]].</p>
<p>In addition to the property-specific values listed in their definitions, all properties defined in this specification also accept the <a href="http://www.w3.org/TR/CSS21/cascade.html#value-def-inherit">inherit</a> keyword as their property value. For readability it has not been repeated explicitly.
<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. The bounding box of a table is the border box
of its
<a href="http://www.w3.org/TR/CSS21/tables.html#model">table wrapper box</a>,
not its table box.
</p>
</dd>
<dt id="TermTransformableElement"><dfn>transformable element</dfn></dt>
<dd>
<p>
A transformable element is an element in one of these
categories:
</p>
<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 'display' property
computes to ''table-row'',
''table-row-group'',
''table-header-group'',
''table-footer-group'',
''table-cell'', or
''table-caption'' [[!CSS21]]
</li>
<li>
an element in the SVG namespace and not governed by the CSS box model which has
the attributes 'transform', 'patternTransform' or 'gradientTransform' [[!SVG11]]
</li>
</ul>
</dd>
<dt id="TermLocalCoordinateSystem"><dfn>local coordinate system</dfn></dt>
<dd>
<p>
In general, a coordinate system defines locations and distances on the current
canvas. The current local coordinate system (also user coordinate system) is the
coordinate system that is currently active and which is used to define how
coordinates and lengths are located and computed, respectively, on the current
canvas.
</p>
</dd>
<dt id="TermUserCoordinateSystem"><dfn>user coordinate system</dfn></dt>
<dd>
<p>
See definition of <span class="term">local coordinate system</span>.
</p>
</dd>
<dt id="TermPerspectiveMatrix"><dfn>perspective matrix</dfn></dt>
<dd>
<p>
A matrix computed from the values of the 'perspective' and 'perspective-origin' properties as described <a href="#perspective-matrix-computation">below</a>.
</p>
</dd>
<dt id="TermTransformationMatrix"><dfn>transformation matrix</dfn></dt>
<dd>
<p>
A matrix that defines the mathematical mapping from one coordinate system into another. It is computed from the values of the 'transform' and 'transform-origin' properties as described <a href="#transformation-matrix-computation">below</a>.
</p>
</dd>
<dt id="TermCurrentTransformationMatrix"><dfn>current transformation matrix (CTM)</dfn></dt>
<dd>
<p>
A matrix that defines the mapping from the local coordinate system into the viewport coordinate system.
</p>
</dd>
<dt id="TermAccumulated3DTransformationMatrix">
<dfn>accumulated 3D transformation matrix</dfn>
</dt>
<dd>
<p>
A matrix computed for elements in a
<a href="#d-rendering-context">3D rendering context</a>, as
described
<a href="#accumulated-3d-transformation-matrix-computation">below</a>.
</p>
</dd>
<dt id="TermIdentityTransformFunction">
<dfn>identity transform function</dfn>
</dt>
<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 ''translate(0)'', ''translate3d(0, 0, 0)'', ''translateX(0)'',
''translateY(0)'', ''translateZ(0)'', ''scale(1)'', ''scaleX(1)'', ''scaleY(1)'',
''scaleZ(1)'', ''rotate(0)'', ''rotate3d(1, 1, 1, 0)'', ''rotateX(0)'',
''rotateY(0)'', ''rotateZ(0)'', ''skew(0, 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)''. A special
case is perspective: ''perspective(infinity)''. The value of m<sub>34</sub>
becomes infinitesimal small and the transform function is therefore assumed to be
equal to the identity matrix.
</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 'transform-style' property of ''preserve-3d'', whose elements
share a common three-dimensional coordinate system.
</p>
</dd>
</dl>
<!-- ======================================================================================================= -->
<h2 id="two-dimensional-subset">
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 'transform-style', 'perspective', 'perspective-origin' and
'backface-visibility' 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>).
</p>
<div class="figure">
<img src="3x3matrix.png" alt="3x3 matrix" title="\begin{bmatrix} a & c & e \\ b
& d & f \\ 0 & 0 & 1 \end{bmatrix}" width="82" height="79">
<p class="caption">
3x3 matrix for two-dimensional transformations.
</p>
</div>
<div class="example">
<p>
Authors can easily provide a fallback if UAs do not provide support for
three-dimensional transforms. The following example has two property definitions
for 'transform'. The first one consists of two two-dimensional transform
functions. The second one has a two-dimensional and a three-dimensional transform
function.
</p>
<pre>div {
transform: scale(2) rotate(45deg);
transform: scale(2) rotate3d(0, 0, 1, 45deg);
}</pre>
<p>
With 3D support, the second definition will override the first one. Without 3D
support, the second definition is invalid and a UA falls back to the first
definition.
</p>
</div>
<!-- ======================================================================================================= -->
<h2 id="transform-rendering">The Transform Rendering Model</h2>
<p><em>This section is normative.</em></p>
<p>
Specifying a value other than ''none'' for the ''transform'' property establishes a
new <span class="term">local coordinate system</span> 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 <span class="term">transformation
matrix</span>. 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 'transform' properties of its
ancestors as well as any local transform applied to it. The accumulation of these
transforms defines a <span class="term">current transformation matrix (CTM)</span> for
the element.
</p>
<p>
The coordinate space is a
coordinate system with two axes: the X axis increases horizontally to the right; the
Y axis increases vertically downwards. Three-dimensional transform functions extend
this coordinate space into three dimensions, adding a Z axis perpendicular to the
plane of the screen, that increases towards the viewer.
</p>
<div class="figure">
<img src="coordinates.svg" width="270" height="240" alt="Demonstration of the initial coordinate space">
<p class="caption">
Demonstration of the initial coordinate space.
</p>
</div>
<p id="transformation-matrix-computation">
The <span class="term">transformation matrix</span> is computed
from the 'transform' and 'transform-origin' properties as follows:
<ol>
<li>Start with the identity matrix.</li>
<li>Translate by the computed X, Y and Z values of 'transform-origin'</li>
<li>Multiply by each of the transform functions in 'transform' property from left to right</li>
<li>Translate by the negated computed X, Y and Z values of 'transform-origin'</li>
</ol>
<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="examples/translate1.svg" alt="The 100px translation in X and Y"
width="470" height="250">
</div>
</div>
<div class="example">
<pre>div {
height: 100px; width: 100px;
transform-origin: 50px 50px;
transform: rotate(45deg);
}</pre>
<p>
The 'transform-origin' property moves the point of origin by 50 pixels in both
the X and Y directions. The transform rotates the element clockwise by 45° about
the point of origin. After all transform functions were applied, the translation
of the origin gets translated back by -50 pixels in both the X and Y directions.
</p>
<div class="figure">
<img alt="The point of origin gets translated temporary" src="examples/origin1.svg"
width="735" height="250">
</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 ''50% 50%''.
</p>
<div class="figure">
<img src="examples/compound_transform.svg" alt="The transform specified above"
width="270" height="270">
</div>
<p>
Note that an identical rendering can be obtained by nesting elements with the
equivalent transforms:
</p>
<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 'overflow' property is ''scroll'' or ''auto'', scrollbars will appear as
needed to see content that is transformed outside the visible area.
</p>
<p>
For elements whose layout is governed by the CSS box model, any value other than
''none'' 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 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>
<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 ''fixed'' for the
'background-attachment' property is treated as if it had a value of ''scroll''. The
computed value of 'background-attachment' 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 ''scale(0.5)'' were specified on the
root element, the dots would shrink to half their size, but
there will be twice as many, so they still cover the whole
viewport.
</p>
<h3 id="transform-3d-rendering">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>
<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 <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? See
<a href="https://www.w3.org/Bugs/Public/show_bug.cgi?id=19637">Bug 19637</a>.</p>
</div>
<div class="example">
<p>This example shows the effect of three-dimensional transform applied to an element.
</p>
<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 src="examples/simple-3d-example.png" width="210" height="190" alt="Div with a rotateY transform.">
</div>
<p>The transform is a 50° rotation about the vertical, Y axis. Note how this makes the blue box appear
narrower, but not three-dimensional.
</p>
</div>
<p>
The 'perspective' and 'perspective-origin' 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
'perspective', is the distance from the drawing plane to the the assumed position of
the viewer's eye.
</p>
<div class="figure">
<img alt="Diagram of scale vs. Z position" src="perspective_distance.png">
<p class="caption">
Diagrams showing how scaling depends on the 'perspective' property and Z position.
In the top diagram, <var>Z</var> is half of <var>d</var>. In order to make it
appear that the original circle (solid outline) appears at <var>Z</var> (dashed
circle), the circle is scaled up by a factor of two, resulting in the light blue
circle. In the bottom diagram, the circle is scaled down by a factor of one-third
to make it appear behind the original position.
</p>
</div>
<p>
Normally the assumed position of the viewer's eye is
centered on a drawing. This position can be moved if
desired – for example, if a web page contains
multiple drawings that should share a common perspective
– by setting 'perspective-origin'.
</p>
<div class="figure">
<img alt="Diagram of different perspective-origin" src="perspective_origin.png">
<p class="caption">
Diagram showing the effect of moving the perspective origin upward.
</p>
</div>
<p id="perspective-matrix-computation">
The <a href="#TermPerspectiveMatrix"><i>perspective matrix</i></a> is computed as follows:
<ol>
<li>Start with the identity matrix.</li>
<li>Translate by the computed X and Y values of 'perspective-origin'</li>
<li>Multiply by the matrix that would be obtained from the '<a href="#perspective-function"><code class="css">perspective(<length>)</code></a>' transform function, where the length is provided by the value of the 'perspective' property</li>
<li>Translate by the negated computed X and Y values of 'perspective-origin'</li>
</ol>
<div class="example">
<p>This example shows how perspective can be used to cause three-dimensional transforms to appear more realistic.
</p>
<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 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.
</p>
<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 of ''transform-style: preserve-3d''. 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 'transform-style' is
''preserve-3d'', 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 'transform-style' is
''preserve-3d'', 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 id="accumulated-3d-transformation-matrix-computation">
The final value of the transform used to render an element in a <span class="term">3D rendering context</span>
is computed by accumulating an
<a href="#TermAccumulated3DTransformationMatrix">
accumulated 3D transformation matrix</a> 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 <span class="term">perspective matrix</span>
on the element's containing block (if any). That containing 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.</li>
<li>multiply the accumulated matrix with the <span class="term">transformation matrix</span>.</li>
</ol>
</li>
</ol>
<div class="example">
<pre>
<style>
div {
height: 150px;
width: 150px;
}
.container {
perspective: 500px;
border: 1px solid black;
}
.transformed {
<b>transform-style: preserve-3d</b>;
transform: rotateY(50deg);
background-color: blue;
}
.child {
transform-origin: top left;
transform: rotateX(40deg);
background-color: lime;
}
</style>
</pre>
<p>
This example is identical to the previous example, with the addition of
''transform-style: preserve-3d'' 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>
<style>
.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;
}
</style>
<div class="container">
<div></div>
<div></div>
</div>
</pre>
<p>
This example shows show elements in a 3D rendering context can intersect. The container element establishes
a 3D rendering context for itself and its two children. The children intersect with 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-transformed elements show the same content on both sides, so the reverse side
looks like a mirror-image of the front side (as if the element were projected onto a sheet of glass).
Normally, elements whose reverse side is towards the viewer remain visible. However, the
'backface-visibility' 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
''backface-visibility: hidden'' 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>
<h3 id="processing-of-perspective-transformed-boxes">
Processing of Perspective-Transformed Boxes
</h3>
<div class="issue">
<p class="desc">
This is a first pass at an attempt to precisely specify how
exactly to transform elements using the provided matrices.
It might not be ideal, and implementer feedback is
encouraged. See <a
href="https://www.w3.org/Bugs/Public/show_bug.cgi?id=15605">bug
15605</a>.
</p>
</div>
<p>
The <span class="term">accumulated
3D transformation matrix</span> is a 4×4 matrix, while the
objects to be transformed are two-dimensional boxes. To
transform each corner (<var>a</var>, <var>b</var>) of a box, the
matrix must first be applied to (<var>a</var>, <var>b</var>, 0,
1), which will result in a four-dimensional point (<var>x</var>,
<var>y</var>, <var>z</var>, <var>w</var>). This is transformed
back to a three-dimensional point (<var>x</var>′, <var>y</var>′,
<var>z</var>′) as follows:
</p>
<p>
If <var>w</var> > 0, (<var>x</var>′,
<var>y</var>′, <var>z</var>′) =
(<var>x</var>/<var>w</var>, <var>y</var>/<var>w</var>,
<var>z</var>/<var>w</var>).
</p>
<p>
If <var>w</var> = 0, (<var>x</var>′, <var>y</var>′,
<var>z</var>′) = (<var>x</var> ⋅ <var>n</var>,
<var>y</var> ⋅ <var>n</var>, <var>z</var> ⋅
<var>n</var>). <var>n</var> is an implementation-dependent value
that should be chosen so that <var>x</var>′ or
<var>y</var>′ is much larger than the viewport size, if
possible. For example, (5px, 22px, 0px, 0) might become (5000px,
22000px, 0px), with <var>n</var> = 1000, but this value of
<var>n</var> would be too small for (0.1px, 0.05px, 0px, 0).
This specification does not define the value of <var>n</var>
exactly. Conceptually, (<var>x</var>′,
<var>y</var>′, <var>z</var>′) is <a
href="http://en.wikipedia.org/wiki/Plane_at_infinity">infinitely
far</a> in the direction (<var>x</var>, <var>y</var>,
<var>z</var>).
</p>
<p>
If <var>w</var> < 0 for all four corners of the transformed
box, the box is not rendered.
</p>
<p>
If <var>w</var> < 0 for one to three corners of the
transformed box, the box must be replaced by a polygon that has
any parts with <var>w</var> < 0 cut out. This will in general
be a polygon with three to five vertices, of which exactly two
will have <var>w</var> = 0 and the rest <var>w</var> > 0.
These vertices are then transformed to three-dimensional points
using the rules just stated. Conceptually, a point with
<var>w</var> < 0 is "behind" the viewer, so should not be
visible.
</p>
<div class="example">
<pre><style>
.transformed {
height: 100px;
width: 100px;
background: lime;
transform: perspective(50px) translateZ(100px);
}
</style></pre>
<p>
All of the box's corners have <var>z</var>-coordinates greater
than the perspective. This means that the box is behind the
viewer and will not display. Mathematically, the point
(<var>x</var>, <var>y</var>) first becomes (<var>x</var>,
<var>y</var>, 0, 1), then is translated to (<var>x</var>,
<var>y</var>, 100, 1), and then applying the perspective
results in (<var>x</var>, <var>y</var>, 100, −1). The
<var>w</var>-coordinate is negative, so it does not display.
An implementation that doesn't handle the <var>w</var> < 0
case separately might incorrectly display this point as
(−<var>x</var>, −<var>y</var>, −100),
dividing by −1 and mirroring the box.
</p>
</div>
<div class="example">
<pre><style>
.transformed {
height: 100px;
width: 100px;
background: radial-gradient(yellow, blue);
transform: perspective(50px) translateZ(50px);
}
</style></pre>
<p>
Here, the box is translated upward so that it sits at the same
place the viewer is looking from. This is like bringing the
box closer and closer to one's eye until it fills the entire
field of vision. Since the default transform-origin is at the
center of the box, which is yellow, the screen will be filled
with yellow.
</p>
<p>
Mathematically, the point (<var>x</var>, <var>y</var>) first
becomes (<var>x</var>, <var>y</var>, 0, 1), then is translated
to (<var>x</var>, <var>y</var>, 50, 1), then becomes
(<var>x</var>, <var>y</var>, 50, 0) after applying perspective.
Relative to the transform-origin at the center, the upper-left
corner was (−50, −50), so it becomes (−50,
−50, 50, 0). This is transformed to something
very far to the upper left, such as (−5000, −5000,
5000). Likewise the other corners are sent very far away. The
radial gradient is stretched over the whole box, now enormous,
so the part that's visible without scrolling should be the
color of the middle pixel: yellow. However, since the box is
not actually infinite, the user can still scroll to the edges
to see the blue parts.
</p>
</div>
<div class="example">
<pre><style>
.transformed {
height: 50px;
width: 50px;
background: lime;
border: 25px solid blue;
transform-origin: left;
transform: perspective(50px) rotateY(-45deg);
}
</style></pre>
<p>
The box will be rotated toward the viewer, with the left edge
staying fixed while the right edge swings closer. The right
edge will be at about <var>z</var> = 70.7px, which is closer
than the perspective of 50px. Therefore, the rightmost edge
will vanish ("behind" the viewer), and the visible part will
stretch out infinitely far to the right.
</p>
<p>
Mathematically, the top right vertex of the box was originally
(100, −50), relative to the transform-origin. It is first
expanded to (100, −50, 0, 1). After applying the
transform specified, this will get mapped to about (70.71,
−50, 70.71, −0.4142). This has <var>w</var> =
−0.4142 < 0, so we need to slice away the part of the
box with <var>w</var> < 0. This results in the new
top-right vertex being (50, −50, 50, 0). This is then
mapped to some faraway point in the same direction, such as
(5000, −5000, 5000), which is up and to the right from
the transform-origin. Something similar is done to the lower
right corner, which gets mapped far down and to the right. The
resulting box stretches far past the edge of the screen.
</p>
<p>
Again, the rendered box is still finite, so the user can scroll
to see the whole thing if he or she chooses. However, the
right part has been chopped off. No matter how far the user
scrolls, the rightmost 30px or so of the original box will not
be visible. The blue border was only 25px wide, so it will be
visible on the left, top, and bottom, but not the right.
</p>
<p>
The same basic procedure would apply if one or three vertices
had <var>w</var> < 0. However, in that case the result of
truncating the <var>w</var> < 0 part would be a triangle or
pentagon instead of a quadrilateral.
</p>
</div>