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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>
<title>CSS 2D Transforms</title>
<link rel="stylesheet" type="text/css" href="default.css">
<style type="text/css">
.rhs { white-space: pre-wrap; }
code { font-size: inherit; }
#box-shadow-samples td { background: white; color: black; }
</style>
<link rel="stylesheet" type="text/css"
href="http://www.w3.org/StyleSheets/TR/W3C-WD.css">
</head>
<body>
<div class="head">
<!--logo-->
<h1>CSS 2D Transforms</h1>
<h2 class="no-num no-toc">[LONGSTATUS] [DATE]</h2>
<dl>
<dt>This version:
<dd>
<a href="[VERSION]">http://dev.w3.org/csswg/css3-2d-transforms/</a>
<!--http://www.w3.org/TR/[YEAR]/WD-[SHORTNAME]-[CDATE]-->
<dt>Latest version:
<dd><a
href="http://www.w3.org/TR/css3-2d-transforms">[LATEST]</a>
<dt>Previous version:
<dd><a href="http://www.w3.org/TR/2009/WD-css3-2d-transforms-20090320/">
http://www.w3.org/TR/2009/WD-css3-2d-transforms-20090320/</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>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>
<dd>Edward O'Connor (<a href="http://www.apple.com/">Apple Inc</a>) <eoconnor @apple.com>
</dl>
<!--copyright-->
<hr title="Separator for header">
</div>
<h2 class="no-num no-toc" id="abstract">Abstract</h2>
<p>CSS 2D Transforms allows elements rendered by CSS to be transformed
in two-dimensional space.
<h2 class="no-num no-toc" id="status">Status of this document</h2>
<!--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>
The CSS <a href="http://www.w3.org/TR/REC-CSS2/visuren.html">visual
formatting model</a> describes a coordinate system within which each
element is positioned. Positions and sizes in this coordinate space can
be thought of as being expressed in pixels, starting in the upper left
corner of the parent with positive values proceeding to the right and
down.
</p>
<p>
This coordinate space can be modified with the <span
class="prop-name">'transform'</span> property. Using transform, elements
can be translated, rotated and scaled in two dimensional space.
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.
</p>
<p>
Transforms apply to block-level and atomic inline-level
elements, but do not apply to elements which may be split into
multiple inline-level boxes.
</p>
<p>
Specifying a value other than 'none' for the <span
class="prop-name">'transform'</span> property establishes a new
<em>local coordinate system</em> at the element that it is applied to.
Transformations are cumulative. That is, elements establish their local
coordinate system within the coordinate system of their parent. In this
way, a <span class="prop-name">'transform'</span> property effectively
accumulates all the <span class="prop-name">'transform'</span>
properties of its ancestors. The accumulation of these transforms
defines a <em>current transformation matrix (CTM)</em> for the element.
</p>
<p>
The transform property does not affect the flow of the content
surrounding the transformed element. However, the value of the overflow
area takes into account transformed elements. This behavior is similar
to what happens when elements are translated via relative positioning.
Therefore, if the value of the <span class="prop-name">'overflow'</span>
property is <span class="prop-value">'scroll'</span> or <span
class="prop-value">'auto'</span>, scrollbars will appear as needed to
see content that is transformed outside the visible area.
</p>
<p>
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>
<div class="todo">
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.
</div>
<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>
<div class="issue">
This property should also be applicable to SVG elements.
</div>
<div class="issue">
We also need to specify that SVG transforms *do* combine with this
transform, e.g., if a <foreignObject> is inside transformed SVG
and then defines a transform of its own. This means we may potentially
have to examine the current SVG transform and combine with it to set the
correct transform.
</div><!-- ======================================================================================================= -->
<h2 id="transform-property">
The <span class="prop-name">'transform'</span> Property
</h2>
<p>
A two-dimensional transformation is applied to an element through the <span
class="prop-name">'transform'</span> property. This property contains a
list of <a href="#transform-functions">transform functions</a>. The
final transformation value for an element is obtained by performing a
matrix concatenation of each entry in the list. The set of transform
functions is similar to those allowed by SVG.
</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 | <transform-function> [ <transform-function> ]*
</td>
</tr>
<tr>
<td>
<em>Initial:</em>
</td>
<td>
none
</td>
</tr>
<tr>
<td>
<em>Applies to:</em>
</td>
<td>
block-level and atomic inline-level elements
</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 border 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><!-- ======================================================================================================= -->
<h2 id="transform-origin-property">
The <span class="prop-name">'transform-origin'</span> Property
</h2>
<p>
The <span class="prop-name">'transform-origin'</span> property
establishes the origin of transformation for an element. This property
is applied by first translating the element by the negated value of the
property, then applying the element's transform, then translating by the
property value. This effectively moves the desired transformation origin
of the element to (0,0) in the local coordinate system, then applies
77EC
the element's transform, then moves the element back to its original
position.
</p>
<p>If only one value is specified, the second value is assumed to be
'center'. If two values are given and at least one value is not a keyword,
then the first value represents the horizontal position (or offset) and
the second represents the vertical position (or
offset). <var><percentage></var> and <var><length></var>
values here represent an offset of the transform origin from the top left corner
of the element's border box.
</p>
<p>If three or four values are given, then
each <var><percentage></var> or<var><length></var>
represents an offset and must be preceded by a keyword,
which specifies from which edge the offset is given. For example,
''transform-origin: bottom 10px right 20px'' represents a
''10px'' vertical offset up from the bottom edge and a
''20px'' horizontal offset leftward from the right edge. If
three values are given, the missing offset is assumed to be zero.
</p>
<p>Positive values represent an offset <em>inward</em> from the edge of
the border box. Negative values represent an offset
<em>outward</em> from the edge of the border box.
</p>
<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>
[ top | bottom ] |<br>
[ <percentage> | <length> | left | center | right ] [ <percentage> | <length> | top | center | bottom ]? |<br>
[ center | [ left | right ] [ <percentage> | <length> ]? ] && [ center | [ top | bottom ] [ <percentage> | <length> ]? ]<br>
</td>
</tr>
<tr>
<td>
<em>Initial:</em>
</td>
<td>
50% 50%
</td>
</tr>
<tr>
<td>
<em>Applies to:</em>
</td>
<td>
block-level and atomic inline-level elements
</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 border box
</td>
</tr>
<tr>
<td>
<em>Media:</em>
</td>
<td>
visual
</td>
</tr>
<tr>
<td>
<em>Computed value:</em>
</td>
<td>
For <length> the absolute value, otherwise a percentage
</td>
</tr>
</tbody>
</table>
<!-- ======================================================================================================= -->
<h2 id="transform-functions">
The Transformation Functions
</h2>
<p>
The value of the <span class="prop-name">transform</span> property is a
list of <transform-functions> 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 <translation-value> is defined as a <length> or
<percentage> value, and the <angle> type is defined by <a
href="http://www.w3.org/TR/css3-values/">CSS Values and Units.</a>
</p>
<dl>
<dt>
<span class="prop-value">matrix(<number>, <number>, <number>, <number>, <number>, <number>)</span>
</dt>
<dd>
specifies a 2D transformation in the form of a <a href="http://www.w3.org/TR/SVG/coords.html#TransformMatrixDefined">transformation matrix</a> of six values. <span class="prop-value">matrix(a,b,c,d,e,f)</span> is equivalent to applying the transformation matrix <strong>[a b c d e f]</strong>.
</dd>
<dt>
<span class="prop-value">translate(<translation-value>[, <translation-value>])</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#TranslationDefined">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><ty></em> is not provided, ty has zero as a value.
</dd>
<dt>
<span class="prop-value">translateX(<translation-value>)</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#TranslationDefined">translation</a> by the given amount in the X direction.
</dd>
<dt>
<span class="prop-value">translateY(<translation-value>)</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#TranslationDefined">translation</a> by the given amount in the Y direction.
</dd>
<dt>
<span class="prop-value">scale(<number>[, <number>])</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#ScalingDefined">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.
</dd>
<dt>
<span class="prop-value">scaleX(<number>)</span>
</dt>
<dd>
specifies a scale operation using the [sx,1] scaling vector, where sx is given as the parameter.
</dd>
<dt>
<span class="prop-value">scaleY(<number>)</span>
</dt>
<dd>
specifies a scale operation using the [1,sy] scaling vector, where sy is given as the parameter.
</dd>
<dt>
<span class="prop-value">rotate(<angle>)</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#RotationDefined">2D rotation</a> by the angle specified in the parameter about the origin of the element, as defined by the <em>transform-origin</em> property.
</dd>
<dt>
<span class="prop-value">skewX(<angle>)</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#SkewXDefined">skew transformation along the X axis</a> by the given angle.
</dd>
<dt>
<span class="prop-value">skewY(<angle>)</span>
</dt>
<dd>
specifies a <a href="http://www.w3.org/TR/SVG/coords.html#SkewYDefined">skew transformation along the Y axis</a> by the given angle.
</dd>
</dl>
<h2 id="transform-values">
Transform Values and Lists
</h2>
<p>
The <translation-value> values are defined as [<percentage> | <length>]. 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>
<div style="transform:translate(-10px,-20px) scale(2) rotate(45deg) translate(5px,10px)"/>
</pre>
<p>
is functionally equivalent to:
</p>
<pre>
<div style="transform:translate(-10px,-20px)">
<div style="transform:scale(2)">
<div style="transform:rotate(45deg)">
<div style="transform:translate(5px,10px)">
</div>
</div>
</div>
</div>
</pre>
<div class="example">
<pre>
div {
transform: translate(100px, 100px);
}
</pre>Move the element by 100 pixels in both the X and Y directions.
<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>Move the element by 80 pixels in both the X and Y directions, then scale the element by 150%, then rotate it 45 degrees clockwise about the Z axis. Note that the scale and rotate operate about the center of the element, since the element has the default transform-origin of 50% 50%.
<div class="figure">
<img src="compound_transform.png" alt="The transform specified above">
</div>
</div>
<!-- ======================================================================================================= -->
<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, translateX, translateY, scale,
scaleX, scaleY, rotate, skew, skewX and skewY functions:
<ul>
<li>
the individual components of the function are
interpolated numerically.
</li>
</ul>
</li>
<li>
For matrix:
<ul>
<li>
the matrix is
decomposed using <a
href="http://tog.acm.org/GraphicsGems/gemsii/unmatrix.c">the
method described by unmatrix</a> into separate translation,
scale, rotation and skew matrices, then each
decomposed matrix is interpolated numerically, and finally
combined in order to produce a resulting 3x2 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),
translateX(0), translateY(0), scale(1), scaleX(1), scaleY(1), rotate(0),
skewX(0), skewY(0) and matrix(1, 0, 0, 1, 0, 0).
</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 matrix 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. A 3x2 2D matrix is
therefore first converted to 4x4 homogeneous form.
</p>
<h3>2D matrix to 4x4 matrix conversion</h3>
<div class="issue">
<p>
The pseudocode here is written with column-major matrices, as would be used in C/C++, but the SVG spec
illustrates matrixes using row-major notation. Change this pseudocode to avoid confusion?
</p>
<p>
It's also unfortunate that we have to include math for 4x4 matrices into the 2D transforms spec. Find
a way to avoid that?
</p>
</div>
<pre>
Input: matrix2d ; a 3x2 transformation matrix
; rotation matrix in m11,m12,m21,m22
; x,y translation in m31,m32
Output: matrix ; a 4x4 homgeneous matrix
matrix[0][0] = matrix2d[0][0]
matrix[0][1] = matrix2d[0][1]
matrix[0][2] = 0
matrix[0][3] = 0
matrix[1][0] = matrix2d[1][0]
matrix[1][1] = matrix2d[1][1]
matrix[1][2] = 0
matrix[1][3] = 0
matrix[2][0] = 0
matrix[2][1] = 0
matrix[2][2] = 1
matrix[2][3] = 0
matrix[3][0] = matrix2d[2][0]
matrix[3][1] = matrix2d[2][1]
matrix[3][2] = 0
matrix[3][3] = 1
return matrix
</pre>
<h3 id="unmatrix">Unmatrix</h3>
<pre>
Input: matrix ; a 4x4 matrix
Output: translate ; a 3 component vector
rotate ; 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):
float 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
float length(point) returns the length of the passed vector
point normalize(point) normalizes the length of the passed point to 1
float dot(point, point) returns the dot product of the passed points
float cos(float) returns the cosine of the passed angle in radians
float asin(float) returns the arcsine in radians of the passed value
float atan2(float y, float 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, float ascl, float 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, make 3rd row orthogonal
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 out
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],
translate[1] and translate[2] 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 Transformation Functions of the
<em>transform</em> property. The following JavaScript example produces a string for this purpose. The
values passed in are the output of the Unmatrix function above:
</p>
<pre>
function compose(translate, rotate, scale, skew, perspective, elementID)
{
var s = "matrix3d(1,0,0,0, 0,1,0,0, 0,0,1,0, " +
perspective[0] + ", " + perspective[1] + ", " +
perspective[2] + ", " + perspective[3] + ")";
s += " translate3d(" + translate[0] + ", " + translate[1] + ", " + translate[2] + ")";
s += " rotateX(" + rotate[0] + ")";
s += " rotateY(" + rotate[0] + ")";
s += " rotateZ(" + rotate[0] + ")";
s += " matrix3d(1,0,0,0, 0,1,0,0, 0," + skew[2] + ",1,0, 0,0,0,1)";
s += " matrix3d(1,0,0,0, 0,1,0,0, " + skew[1] + ",0,1,0, 0,0,0,1)";
s += " matrix3d(1,0,0,0, " + skew[0] + ",1,0,0, 0,0,1,0, 0,0,0,1)";
s += " scale3d(" + scale[0] + ", " + scale[1] + ", " + scale[2] + ")";
document.getElementById(elementID).style.transform = s;
}</pre>
<h2 id="dom-interfaces">
DOM Interfaces
</h2>
<p>
This section describes the interfaces and functionality added to the DOM
to support runtime access to the functionality described above.
</p>
<h3 id="cssmatrix-interface">
CSSMatrix
</h3>
<dl>
<dt>
<b>Interface <i><a id="DOM-CSSMatrix" name='DOM-CSSMatrix'>CSSMatrix</a></i></b>
</dt>
<dd>
<p>
The <code>CSSMatrix</code> interface represents a 4x4 homogeneous matrix.
</p>
<div class="issue">
We actually describe a 3x2 matrix here, similar to <a href="http://www.w3.org/TR/SVG/coords.html#InterfaceSVGMatrix">SVGMatrix</a>.
</div>
<dl>
<dt>
<b>IDL Definition</b>
</dt>
<dd>
<div class='idl-code'>
<pre>
interface CSSMatrix {
attribute float a;
attribute float b;
attribute float c;
attribute float d;
attribute float e;
attribute float f;
void setMatrixValue(in DOMString string) raises(DOMException);
CSSMatrix multiply(in CSSMatrix secondMatrix);
CSSMatrix inverse() raises(DOMException);
CSSMatrix translate(in float x, in float y);
CSSMatrix scale(in float scaleX, in float scaleY);
CSSMatrix skewX(in float angle);
CSSMatrix skewY(in float angle);
CSSMatrix rotate(in float angle);
};</pre>
</div><br>
</dd> <!-- IDL -->
<dt>
<b>Attributes</b>
</dt>
<dd>
<dl>
<dt>
<code class='attribute-name'><a id="DOM-CSSMatrix-matrix" name='DOM-CSSMatrix-matrix'>a-f</a></code> of type <code>float</code>
</dt>
<dd>
Each of these attributes represents one of the values in the 3x2 matrix.<br>
</dd>
</dl>
</dd> <!-- Attributes -->
<dt>
<b>Methods</b>
</dt>
<dd>
<dl>
<!-- ===================================================== -->
<dt>
<code class='method-name'><a id="DOM-CSSMatrix-setMatrixValue" name='DOM-CSSMatrix-setMatrixValue'>setMatrixValue</a></code>
</dt>
<dd>
<div class='method'>
The <code>setMatrixValue</code> method replaces the existing matrix with one computed from parsing the passed string
as though it had been assigned to the transform property in a CSS style rule.
<div class='parameters'>
<b>Parameters</b>
<div class='paramtable'>
<dl>
<dt>
<code class='parameter-name'>string</code> of type <code>DOMString</code>
</dt>
<dd>
The string to parse.<br>
</dd>
</dl>
</div>
</div><!-- parameters -->
<div class='return-value'>
<b>No Return Value</b>
</div>
<div>
<b>Exceptions</b>
<div class='returnvalue'>
<dl>
<dt>
<code>DOMException SYNTAX_ERR</code>
</dt>
<dd>
Thrown when the provided string can not be
parsed into a CSSMatrix.
</dd>
</dl>
</div>
</div>
</div>
</dd> <!-- setMatrixValue -->
<!-- ===================================================== -->
<dt>
<code class='method-name'><a id="DOM-CSSMatrix-multiply" name='DOM-CSSMatrix-multiply'>multiply</a></code>
</dt>
<dd>
<div class='method'>
The <code>multiply</code> method returns a new CSSMatrix which is the result of this matrix multiplied by the passed matrix, with the passed matrix to the right. This matrix is not modified.
<div class='parameters'>
<b>Parameters</b>
<div class='paramtable'>
<dl>
<dt>
<code class='parameter-name'>secondMatrix</code> of type <code>CSSMatrix</code>
</dt>
<dd>
The matrix to multiply.<br>
</dd>
</dl>
</div>
</div><!-- parameters -->
<div class='return-value'>
<b>Return Value</b>
<div class='returnvalue'>
<dl>
<dt>
<code>CSSMatrix</code>
</dt>
<dd>
The result matrix.<br>
</dd>
</dl>
</div>
</div>
<div>
<b>No Exceptions</b>
</div>
</div>
</dd> <!-- multiply() -->
<!-- ===================================================== -->
<dt>
<code class='method-name'><a id="DOM-CSSMatrix-inverse" name='DOM-CSSMatrix-inverse'>inverse</a></code>
</dt>
<dd>
<div class='method'>
The <code>inverse</code> method returns a new matrix which is the inverse of this matrix. This matrix is not modified.
<div class='parameters'>
<b>No Parameters</b>
</div><!-- parameters -->
<div class='return-value'>
<b>Return Value</b>
<div class='returnvalue'>
<dl>
<dt>
<code>CSSMatrix</code>
</dt>
<dd>
The inverted matrix.<br>
</dd>
</dl>
</div>
</div>
<div>
<b>Exceptions</b>
<div class='returnvalue'>
<dl>
<dt>
<code>DOMException NOT_SUPPORTED_ERR</code>
</dt>
<dd>
Thrown when the CSSMatrix can not be
inverted.
</dd>
</dl>
</div>
</div>
</div><!-- ======================================================================================================= -->
</dd> <!-- inverse() -->
<!-- ===================================================== -->
<dt>
<code class='method-name'><a id="DOM-CSSMatrix-translate" name='DOM-CSSMatrix-translate'>translate</a></code>
</dt>
<dd>
<div class='method'>
The <code>translate</code> method returns a new matrix which is this matrix multiplied by a translation matrix containing the passed values. This matrix is not modified.
<div class='parameters'>
<b>Parameters</b>
<div class='paramtable'>