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CSS transforms allows elements styled with CSS to be transformed in two-dimensional or three-dimensional space. This specification is the convergence of the CSS 2D transforms, CSS 3D transforms and SVG transforms specifications.
This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.
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This document was produced by the CSS Working Group (part of the Style Activity).
This document was produced by a group operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.
This specification replaces the former CSS 2D Transforms and CSS 3D Transforms specifications, as well as SVG Transforms.
The list of changes made to this specification is available.
transform
’ Property
transform
’ Attribute
transform
’ attribute specificity
transform
’ attribute
gradientTransform
’ and ‘patternTransform
’ attributes
transform
’ attribute
transform-origin
’ Property
transform-style
’ Property
perspective
’ Property
perspective-origin
’ Property
backface-visibility
’ Property
This section is not normative.
The CSS visual formatting model 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.
This coordinate space can be modified with the ‘
’ property. Using
transform, elements can be translated, rotated and scaled in two or three
dimensional space.
transform
Additional properties make working with transforms easier, and allow the author to control how nested three-dimensional transforms interact.
transform-origin
’ property
provides a convenient way to control the origin about which transforms on
an element are applied.
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".
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.
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.
Note that while some values of the ‘
’ 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.
transform
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 Visual formatting model from [CSS21]. Some values of these properties result in the creation of a containing block, and/or the creation of a stacking context.
Three-dimensional transforms can also affect the visual layering of elements, and thus override the back-to-front painting order described in Appendix E of [CSS21].
This specification follows the CSS property definition conventions from [CSS21]. Value types not defined in this specification are defined in CSS Level 2 Revision 1 [CSS21].
In addition to the property-specific values listed in their definitions, all properties defined in this specification also accept the inherit keyword as their property value. For readability it has not been repeated explicitly.
When used in this specification, terms have the meanings assigned in this section.
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 table wrapper box, not its table box.
A transformable element is an element in the HTML namespace which is
either a block-level
or atomic
inline-level element, or whose ‘
’ property computes to
‘display
’,
‘table-row
’, ‘table-row-group
’,
‘table-header-group
’, ‘table-footer-group
’, or
‘table-cell
’; or an element in the SVG
namespace (see [SVG11]) which has the attributes
‘table-caption
’, ‘transform
patternTransform
’ or ‘gradientTransform
’.
A matrix computed from the values of the ‘
’ and ‘perspective
’ properties as
described below.perspective-origin
A matrix computed from the values of the ‘
’ and ‘transform
’ properties as
described below.transform-origin
A matrix computed for elements in a 3D rendering context, as described below.
A containing block hierarchy of one or more levels, instantiated by
elements with a computed value for the ‘
’ property of
‘transform-style
’,
whose elements share a common three-dimensional coordinate system.preserve-3d
Specifying a value other than ‘
’ for the ‘none
’ property establishes a
new local coordinate system 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 transformation matrix.
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 current transformation matrix (CTM)
for the element.
transform
The coordinate space behaves as described in the coordinate system transformations section of the SVG 1.1 specification. This is a coordinate system with two axes: the X axis increases horizontally to the right; the Y axis increases vertically downwards. Three-dimensional transform functions extent this coordinate space into three dimensions, adding a Z axis perpendicular to the plane of the screen, that increases towards the viewer.
The transformation matrix is
computed from the ‘
’ and ‘transform
’ properties as
follows:
transform-origin
transform-origin
’
transform
’ property in turn
transform-origin
’
Transforms apply to transformable elements.
div { transform: translate(100px, 100px); }
This transform moves the element by 100 pixels in both the X and Y directions.
div { height: 100px; width: 100px; transform: translate(80px, 80px) scale(1.5, 1.5) rotate(45deg); }
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%
Note that an identical rendering can be obtained by nesting elements with the equivalent transforms:
<div style="transform: translate(80px, 80px)"> <div style="transform: scale(1.5, 1.5)"> <div style="transform: rotate(45deg)"></div> </div> </div>
In the HTML namespace, the transform property does not affect the flow
of the content surrounding the transformed element. However, the extent of
the overflow area takes into account transformed elements. This behavior
is similar to what happens when elements are offset via relative
positioning. Therefore, if the value of the ‘
’ property is ‘overflow
’ or ‘scroll
’, scrollbars will
appear as needed to see content that is transformed outside the visible
area.
auto
In the HTML namespace, any value other than ‘
’ 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.
none
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.
Fixed backgrounds are affected by any transform specified for the root element, and not by any other transforms.
Thus an element with a fixed background still acts like a "porthole" into an image that's fixed to the viewport, and transforms on the element affect the porthole, not the background behind it. On the other hand, transforming the root element will still transform everything on the page, rather than everything except for fixed backgrounds.
If the root element is transformed, the transformation applies to the
entire canvas, including any background specified for the root element.
Since the
background painting area for the root element 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
‘
’
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.
scale(0.5)
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.
Three-dimensional transforms can result in transformation matrices with a non-zero Z component, potentially lifting them off the plane of their containing block. Because of this, elements with three-dimensional transformations could potentially render in an front-to-back order that different from the normal CSS rendering order, and intersect with each other. Whether they do so depends on whether the element is a member of a 3D rendering context, as described below.
This description does not exactly match what WebKit implements. Perhaps it should be changed to match current implementations?
This example shows the effect of three-dimensional transform applied to an element.
<style> div { height: 150px; width: 150px; } .container { border: 1px solid black; } .transformed { transform: rotateY(50deg); } </style> <div class="container"> <div class="transformed"></div> </div>
The transform is a 50° rotation about the vertical, Y axis. Note how this makes the blue box appear narrower, but not three-dimensional.
The ‘
’ and ‘perspective
’ 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 d/(d
− Z) where d, the value of ‘perspective-origin
’, is the distance from
the drawing plane to the the assumed position of the viewer's eye.
perspective
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
The perspective matrix is computed as follows:
perspective-origin
’
perspective(<length>)
’ transform
function, where the length is provided by the value of the ‘perspective
’ property
perspective-origin
’
This example shows how perspective can be used to cause three-dimensional transforms to appear more realistic.
<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>
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.
An element with a three-dimensional transform that is not contained in a 3D rendering context 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.
An element with a three-dimensional transform that is contained in a 3D rendering context can visibly interact with other elements in that same 3D rendering context; the set of elements participating in the same 3D rendering context 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 3D rendering context through each element that is a containing block for the given element, as described below.
<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>
This example shows how nested 3D transforms are rendered in the absence
of ‘
’. 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".transform-style:
preserve-3d
Elements establish and participate in 3D rendering contexts as follows:
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.
transform-style
’ is ‘preserve-3d
’, and which
itself participates in a 3D
rendering context, extends that 3D rendering context rather than
establishing a new one.
The final value of the transform used to render an element in a 3D rendering context is computed by accumulating an accumulated 3D transformation matrix as follows:
<style> div { height: 150px; width: 150px; } .container { perspective: 500px; border: 1px solid black; } .transformed { transform-style: preserve-3d; transform: rotateY(50deg); background-color: blue; } .child { transform-origin: top left; transform: rotateX(40deg); background-color: lime; } </style>
This example is identical to the previous example, with the addition of
‘
’ 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.transform-style:
preserve-3d
Elements in the same 3D rendering context may intersect with each other. User agents must render intersection by subdividing the planes of intersecting elements as described by Newell's algorithm.
Untransformed elements in a 3D rendering context render on the Z=0 plane, yet may still intersect with transformed elements.
Within a 3D rendering context, 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 stacking context order.
<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>
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.
Using three-dimensional transforms, it's possible to transform an
element such that its reverse side is towards the viewer. 3D-tranformed
elements show the same content on both sides, so the reverse side looks
like a mirror-image of the front side (as if the element were projected
onto a sheet of glass). Normally, elements whose reverse side is towards
the viewer remain visible. However, the ‘
’ 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
’ 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.backface-visibility:
hidden
transform
’ Property A transformation is applied to the coordinate system an element renders
in through the ‘
’ property. This property
contains a list of transform functions.
The final transformation value for a coordinate system is obtained by
converting each function in the list to its corresponding matrix like
defined in Mathematical Description of
Transform Functions, then multiplying the matrices.
transform
Name: | transform |
Value: | none | <transform-function> [ <transform-function> ]* |
Initial: | none |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | refer to the size of the element's bounding box |
Media: | visual |
Computed value: | As specified, but with relative lengths converted into absolute lengths. |
Any value other than ‘
’ 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.none
transform
’ Attribute The SVG 1.1
specification did not specify the attributes ‘
’, ‘transform
gradientTransform
’ or ‘patternTransform
’ as presentation
attributes. In order to improve the integration of SVG and HTML,
this specification makes these SVG attributes ‘presentation attributes
’ and makes the ‘
’ property one that
applies to transformable
elements in the SVG namespace.
transform
This specification will also introduce the new presentation attributes
‘
’, ‘transform-origin
’, ‘perspective
’, ‘perspective-origin
’ and ‘transform-style
’. All new
introduced presentation attributes are animatable.
backface-visibility
transform
’ attribute specificitySince the previously named SVG attributes become presentation attributes, their participation in the CSS cascade is determined by the specificity of presentation attributes, as explained in the SVG specification.
This example shows the combination of the ‘
’ style property and the
‘transform
’ presentation attribute.
transform
<svg xmlns="http://www.w3.org/2000/svg"> <style> .container { transform: translate(100px, 100px); } </style> <g class="container" transform="translate(200 200)"> <rect width="100" height="100" fill="blue" /> </g> </svg>
Because of the participation to the CSS cascade, the ‘
’ style property
overrides the ‘transform
’ presentation attribute.
Therefore the container gets translated by ‘transform
’ in both the horizontal and the
vertical directions, instead of ‘100px
’.200px
transform
’ attribute To provide backwards compatibility, the syntax of the ‘
’ presentation attribute
differs from the syntax of the ‘transform
’ style
property as shown in the example above. However, the syntax used for the
‘transform
’ style property can be
used for a ‘transform
’ presentation attribute
value. Authors are advised to follow the rules of CSS Values
and Units Module. Therefore an author should write ‘transform
’ instead of ‘transform="translate(200px,
200px)"
’ because the
second example with the spaces before the ‘transform="translate (200 200)"
’, the missing comma between the arguments
and the values without the explicit unit notation would be valid for the
attribute only.
(
The value for the ‘transform
’ attribute consists of a
transform list with zero or more transform functions using functional notation. If the transform
list consists of more than one transform function, these functions are
separated by optional whitespace, an optional comma (‘,
’) and optional whitespace. The transform list can
have optional whitespace characters before and after the list.
The syntax starts with the name of the function followed by optional
whitespace characters followed by a left parenthesis followed by optional
whitespace followed by the argument(s) to the notation followed by
optional whitespace followed by a right parenthesis. If a function takes
more than one argument, the arguments are either separated by a comma
(‘,
’) with optional whitespace characters
before and after the comma, or by one or more whitespace characters.
Arguments of transform functions consist of data types in the sense of CSS Values and Units Module. The definitions of data types in CSS Values and Units Module are enhanced as follows:
A translation-value or length can be a <number> without an unit identifier. In this case the number gets interpreted as "user unit". A user unit in the the initial coordinate system is equivalent to the parent environment's notion of a pixel unit.
An angle can be a <number> without an unit identifier. In this case the number gets interpreted as a value in degrees.
SVG supports scientific notations for numbers. Therefore a number gets parsed like described in SVG Basic data types for SVG attributes.
gradientTransform
’
and ‘patternTransform
’ attributes SVG specifies the attributes ‘gradientTransform
’ and ‘patternTransform
’. This specification makes
both attributes presentation attributes. Both attributes use the same syntax as the SVG ‘
’
attribute. This specification does not introduce corresponding CSS style
properties. Both, the ‘transform
gradientTransform
’ and the ‘patternTransform
’ attribute, are presentation
attributes for the ‘transform
’ property.
For backwards compatibility with existing SVG content, this
specification supports all transform functions defined by The
‘
’
attribute in SVG 1.1. Therefore the two-dimensional transform function
‘transform
’ is extended as
follows:
rotate(<angle>)
rotate(<angle>[, <translation-value>,
<translation-value>])
transform-origin
’ property. If the
optional translation values are specified, the transform origin is
translated by that amount (using the current transformation matrix) for
the duration of the rotate operation. For example ‘rotate(90deg, 100px,
100px)
’ would elements cause to appear rotated
one-quarter of a turn in the clockwise direction after a translation of
100 pixel in the vertical and horizontal direction.
User agents are just required to support the two optional arguments for translation on elements in the SVG namespace.
This specification explicitly requires three-dimensional transform
functions to apply to the container
elements: ‘a
’,
‘g
’, ‘svg
’, all graphics
elements, all graphics
referencing elements and the SVG ‘foreignObject
’ element.
Three-dimensional transform functions and the properties ‘
’, ‘perspective
’, ‘perspective-origin
’ and ‘transform-style
’ can not be
used for the elements: ‘backface-visibility
clipPath
’,
‘mask
’, ‘linearGradient
’, ‘radialGradient
’ and ‘pattern
’. If a transform list includes a
three-dimensional transform function, the complete transform list must be
ignored. The values of every previously named property must be ignored. Transformable elements that
are contained by one of these elements can have three-dimensional
transform functions. Before a ‘clipPath
’, ‘mask
’ or ‘pattern
’ element can get applied to a target
element, user agents must take the drawn results as static images in
analogue of "flattening" the elements and taking the rendered content as a
two-dimensional canvas.
Percentage or fractional values in SVG are either relative to the elements viewport units or to the element's object bounding box units as specified in SVG 1.1. To align with HTML, all percentage values for all properties defined in this specification are relative to the object bounding box units.
If an SVG element does not provide a bounding box (like for the
‘pattern
’, ‘mask
’ or ‘clipPath
’ elements), the bounding box is
treated as if the position x, y and the dimensions width and height are
zero. Percentage values or keywords won't affect the rendering and are
treated as if zero was specified.
The ‘
’ property on the
pattern in the following example specifies a ‘transform-origin
’ translation of the origin in the
horizontal and vertical dimension. The ‘50%
’
property specifies a translation as well, but in absolute lengths.transform
<svg xmlns="http://www.w3.org/2000/svg"> <style> pattern { transform: translate(50px, 50px) rotate(45deg); transform-origin: 50% 50%; } </style> <defs> <pattern id="pattern-1"> <rect id="rect1" width="100" height="100" fill="blue" /> </pattern> </defs> <rect width="100" height="100" fill="url(#pattern-1)" /> </svg>
An SVG ‘pattern
’ element
doesn't have a bounding box. Therefore the relative values of the
‘
’ property don't
affect the rendering and are treated as if zero was specified. The
translation on the ‘transform-origin
’ property is in absolute
coordinates and translate the coordinate system by 50 pixels in each
direction.transform
transform
’ attribute The SVG specification defines the ‘
’ interface
in the SVG DOM to provide access to the animated and the base value of the
SVG ‘SVGAnimatedTransformList
transform
’, ‘gradientTransform
’ and ‘patternTransform
’ attributes. To ensure
backwards compatibility, this API must still be supported by user agents.
The ‘
’ property contributes to
the CSS cascade. According to SVG 1.1 user agents conceptually insert a new
author style sheet for presentation attributes, which is the first in
the author style sheet collection. ‘transform
’ gives the author the
possibility to access and modify the values of the SVG ‘baseVal
’ attribute. To provide
the necessary backwards compatibility to the SVG DOM, ‘transform
’ must reflect
the values of this author style sheet. All modifications to SVG DOM
objects of ‘baseVal
’ must affect this author style
sheet immediately.
baseVal
‘
’ represents the computed style
of the ‘animVal
’ property. Therefore it
includes all applied CSS3
Transitions, CSS3
Animations or SVG Animations if any of
those are underway. The computed style and SVG DOM objects of ‘transform
’ can not be
modified.
animVal
The attribute ‘
’ of ‘type
SVGTransform
’ must return ‘
’ for Transform Functions or unit types that are
not supported by this interface. If a two-dimensional transform function
is not supported, the attribute ‘SVG_TRANSFORM_UNKNOWN
’ must return a 3x2
‘matrix
’ with the corresponding
values as described in the section Mathematical Description of Transform
Functions.
SVGMatrix
animate
’ and ‘set
’ element The SVG 1.1 specification did not allow animations of the ‘
’ attribute using the SVG
‘transform
animate
’ element or the SVG ‘set
’ element. This specification
explicitly allows the animation of the presentation attributes ‘
’, ‘transform
gradientTransform
’ and ‘patternTransform
’ for the ‘animate
’ and ‘set
’ elements. SVG animation must run the same
animation steps as described in section Transitions
and Animations between Transform Values.
attributeName
’ attribute SVG 1.1 Animation
defines the ‘attributeName
’ attribute to specify the
name of the target attribute. For the presentation attributes ‘gradientTransform
’ and ‘patternTransform
’ it will also be possible to
use the value ‘transform
’. The same ‘transform
’ property
will get animated.
In this example the gradient transformation of the linear gradient gets animated.
<linearGradient gradientTransform="scale(2)"> <animate attributeName="gradientTransform" from="scale(2)" to="scale(4)" dur="3s" additive="sum"/> <animate attributeName="transform" from="translate(0, 0)" to="translate(100px, 100px)" dur="3s" additive="sum"/> </linearGradient>
The ‘linearGradient
’ element
specifies the ‘gradientTransform
’
presentation attribute. The two ‘animate
’ elements address the target
attribute ‘gradientTransform
’ and
‘
’. Even so all animations
apply to the same gradient transformation by taking the value of the
‘transform
gradientTransform
’ presentation
attribute, applying the scaling of the first animation and applying the
translation of the second animation one after the other.
animateTransform
’ element This specification introduces new transform functions that are not
supported by SVG 1.1
Animation. The SVG ‘
’ attribute gets extended by
all transform functions listed in 2D
Transform Functions, 3D
Transform Functions and SVG
Transform Functions.
type
The attributes ‘from
’,
‘by
’ and ‘to
’ of the ‘animateTransform
’ element take the argument(s)
to the functional notation and follow the syntax of
the SVG ‘transform
’ attribute.
The ‘values
’ attribute of the
‘animateTransform
’ element
consists of a semicolon-separated list of values, where each individual
value is expressed as described above for ‘from
’, ‘by
’ and ‘to
’ attributes.
transform-origin
’ PropertyName: | transform-origin |
Value: | [ <percentage> | <length> | left | center | right | top |
bottom] | [ [ <percentage> | <length> | left | center | right ] && [ <percentage> | <length> | top | center | bottom ] ] <length>? |
Initial: | 0 0 for SVG elements without associated CSS layout box, 50% 50% for all other elements |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | refer to the size of the element's bounding box |
Media: | visual |
Computed value: | For <length> the absolute value, otherwise a percentage |
The values of the ‘
’ and ‘transform
’ properties are
used to compute the transformation
matrix, as described above.
transform-origin
If only one value is specified, the second value is assumed to be
‘center
’. If one or two values are
specified, the third value is assumed to be ‘0px
’.
If at least one of the first two values is not a keyword, then the first value represents the horizontal position (or offset) and the second represents the vertical position (or offset). The third value always represents the Z position (or offset).
<percentage> and <length> for the first two values represent an offset of the transform origin from the top left corner of the element's bounding box.
For SVG elements without an associated CSS layout box the <length> values represent an offset from the point of origin of the element's local coordinate space.
The resolved
value of ‘
’ is the used value
(i.e., percentages are resolved to absolute lengths).transform-origin
transform-style
’ PropertyName: | transform-style |
Value: | flat | preserve-3d |
Initial: | flat |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | N/A |
Media: | visual |
Computed value: | Same as specified value. |
A value of ‘
’ for ‘preserve-3d
’ establishes a
stacking context.
transform-style
The following CSS property values require the user agent to create a
flattened representation of the descendant elements before they can be
applied, and therefore override the behavior of ‘
’: ‘transform-style
’:
preserve-3d
overflow
’: any value other than
‘visible
’.
opacity
’: any value other than 1.
filter
’: any value other than
‘none
’.Should this affect the computed value of transform-style?
The values of the ‘
’ and ‘transform
’ properties are
used to compute the transformation
matrix, as described above.transform-origin
perspective
’ PropertyName: | perspective |
Value: | none | <length> |
Initial: | none |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | N/A |
Media: | visual |
Computed value: | Absolute length or "none". |
If the value is ‘
’, no perspective transform is applied.
Lengths must be positive.
none
The use of this property with any value other than ‘
’ establishes a stacking
context. It also establishes a containing block (somewhat similar to
‘none
’), just like the ‘position:
relative
’ property does.
transform
The values of the ‘
’ and ‘perspective
’ properties are
used to compute the perspective
matrix, as described above.perspective-origin
perspective-origin
’ Property The ‘
’ property
establishes the origin for the perspective property. It effectively sets
the X and Y position at which the viewer appears to be looking at the
children of the element.
perspective-origin
Name: | perspective-origin |
Value: | [ <percentage> | <length> | left | center | right | top |
bottom] | [ [ <percentage> | <length> | left | center | right ] && [ <percentage> | <length> | top | center | bottom ] ] |
Initial: | 50% 50% |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | refer to the size of the element's bounding box |
Media: | visual |
Computed value: | For <length> the absolute value, otherwise a percentage. |
The values of the ‘
’ and ‘perspective
’ properties are
used to compute the perspective
matrix, as described above.
perspective-origin
If only one value is specified, the second value is assumed to be
‘center
’.
If at least one of the two values is not a keyword, then the first value represents the horizontal position (or offset) and the second represents the vertical position (or offset).
<percentage> and <length> values represent an offset of the perspective origin from the top left corner of the element's bounding box.
The resolved
value of ‘
’ is the used value
(i.e., percentages are resolved to absolute lengths).perspective-origin
backface-visibility
’ Property The ‘
’ property
determines whether or not the "back" side of a transformed element is
visible when facing the viewer. With an identity transform, the front side
of an element faces the viewer. Applying a rotation about Y of 180 degrees
(for instance) would cause the back side of the element to face the
viewer.backface-visibility
This property is useful when you place two elements back-to-back, as you would to create a playing card. Without this property, the front and back elements could switch places at times during an animation to flip the card. Another example is creating a box out of 6 elements, but where you want to see the inside faces of the box. This is useful when creating the backdrop for a 3 dimensional stage.
Name: | backface-visibility |
Value: | visible | hidden |
Initial: | visible |
Applies to: | transformable elements |
Inherited: | no |
Percentages: | N/A |
Media: | visual |
Computed value: | Same as specified value. |
The visibility of an element with ‘
’ is determined
as follows:
backface-visibility: hidden
The reasoning for this definition is as follows. Assume elements are rectangles in the x–y plane with infinitesimal thickness. The front of the untransformed element has coordinates like (x, y, ε), and the back is (x, y, −ε), for some very small ε. We want to know if after the transformation, the front of the element is closer to the viewer than the back (higher z-value) or further away. The z-coordinate of the front will be M_{13}x + M_{23}y + M_{33}ε + M_{43}, before accounting for perspective, and the back will be M_{13}x + M_{23}y − M_{33}ε + M_{43}. The first quantity is greater than the second if and only if M_{33} > 0. (If it equals zero, the front and back are equally close to the viewer. This probably means something like a 90-degree rotation, which makes the element invisible anyway, so we don't really care whether it vanishes.)
The value of the transform
property is a list of
<transform-functions>. The set of allowed transform
functions is given below. For <transform-functions> the
type <translation-value> is defined as a
<length> or <percentage> value, and the
<angle> type is defined by CSS Values and Units Module.
Wherever <angle> is used in this specification, a
<number> that is equal to zero is also allowed, which is
treated the same as an angle of zero degrees.
matrix(<number>, <number>,
<number>, <number>, <number>, <number>)
translate(<translation-value>[,
<translation-value>])
translateX(<translation-value>)
translateY(<translation-value>)
scale(<number>[, <number>])
scaleX(<number>)
scaleY(<number>)
rotate(<angle>)
transform-origin
’ property. For
example, ‘rotate(90deg)
’ would cause elements to
appear rotated one-quarter of a turn in the clockwise direction.
skewX(<angle>)
skewY(<angle>)
matrix3d(<number>, <number>,
<number>, <number>, <number>, <number>,
<number>, <number>, <number>, <number>,
<number>, <number>, <number>, <number>,
<number>, <number>)
translate3d(<translation-value>,
<translation-value>, <length>)
translateZ(<length>)
scale3d(<number>, <number>,
<number>)
scaleZ(<number>)
rotate3d(<number>, <number>,
<number>, <angle>)
rotateX(<angle>)
rotate3d(1, 0, 0, <angle>)
.
rotateY(<angle>)
rotate3d(0, 1, 0, <angle>)
.
rotateZ(<angle>)
rotate3d(0, 0, 1, <angle>)
,
which is also the same as rotate(<angle>)
.
perspective(<length>)
If a list of <transform-functions> is provided, then the net effect is as if each transform function had been specified separately in the order provided. For example,
<div style="transform:translate(-10px,-20px) scale(2) rotate(45deg) translate(5px,10px)"/>
is functionally equivalent to:
<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>
That is, in the absence of other styling that affects position and dimensions, a nested set of transforms is equivalent to a single list of transform functions, applied from the outside in. The resulting transform is the matrix multiplication of the list of transforms.
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.
from
’ and
‘to
’ transforms are both single
functions of the same type:
from
’ and
‘to
’ transforms are "none":
from
’ or
‘to
’ transforms is "none":
none
’ is replaced by
an equivalent identity function list for the corresponding transform
function list.
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)".
The identity functions are translate(0), translate3d(0, 0, 0), translateX(0), translateY(0), translateZ(0), scale(1), scale3d(1, 1, 1), scaleX(1), scaleY(1), scaleZ(1), rotate(0), rotate3d(1, 1, 1, 0), rotateX(0), rotateY(0), rotateZ(0), 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).
from
’ and
‘to
’ transforms have the same
number of transform functions and corresponding functions in each
transform list are of the same type:
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.
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.
Input: matrix ; a 4x4 matrix Output: translation ; a 3 component vector rotation ; Euler angles, represented as a 3 component vector scale ; a 3 component vector skew ; skew factors XY,XZ,YZ represented as a 3 component vector perspective ; a 4 component vector Returns false if the matrix cannot be decomposed, true if it can Supporting functions (point is a 3 component vector, matrix is a 4x4 matrix): double determinant(matrix) returns the 4x4 determinant of the matrix matrix inverse(matrix) returns the inverse of the passed matrix matrix transpose(matrix) returns the transpose of the passed matrix point multVecMatrix(point, matrix) multiplies the passed point by the passed matrix and returns the transformed point double length(point) returns the length of the passed vector point normalize(point) normalizes the length of the passed point to 1 double dot(point, point) returns the dot product of the passed points double cos(double) returns the cosine of the passed angle in radians double asin(double) returns the arcsine in radians of the passed value double atan2(double y, double x) returns the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value Decomposition also makes use of the following function: point combine(point a, point b, double ascl, double bscl) result[0] = (ascl * a[0]) + (bscl * b[0]) result[1] = (ascl * a[1]) + (bscl * b[1]) result[2] = (ascl * a[2]) + (bscl * b[2]) return result // Normalize the matrix. if (matrix[3][3] == 0) return false for (i = 0; i < 4; i++) for (j = 0; j < 4; j++) matrix[i][j] /= matrix[3][3] // perspectiveMatrix is used to solve for perspective, but it also provides // an easy way to test for singularity of the upper 3x3 component. perspectiveMatrix = matrix for (i = 0; i < 3; i++) perspectiveMatrix[i][3] = 0 perspectiveMatrix[3][3] = 1 if (determinant(perspectiveMatrix) == 0) return false // First, isolate perspective. if (matrix[0][3] != 0 || matrix[1][3] != 0 || matrix[2][3] != 0) // rightHandSide is the right hand side of the equation. rightHandSide[0] = matrix[0][3]; rightHandSide[1] = matrix[1][3]; rightHandSide[2] = matrix[2][3]; rightHandSide[3] = matrix[3][3]; // Solve the equation by inverting perspectiveMatrix and multiplying // rightHandSide by the inverse. inversePerspectiveMatrix = inverse(perspectiveMatrix) transposedInversePerspectiveMatrix = transposeMatrix4(inversePerspectiveMatrix) perspective = multVecMatrix(rightHandSide, transposedInversePerspectiveMatrix) // Clear the perspective partition matrix[0][3] = matrix[1][3] = matrix[2][3] = 0 matrix[3][3] = 1 else // No perspective. perspective[0] = perspective[1] = perspective[2] = 0 perspective[3] = 1 // Next take care of translation translate[0] = matrix[3][0] matrix[3][0] = 0 translate[1] = matrix[3][1] matrix[3][1] = 0 translate[2] = matrix[3][2] matrix[3][2] = 0 // Now get scale and shear. 'row' is a 3 element array of 3 component vectors for (i = 0; i < 3; i++) row[i][0] = matrix[i][0] row[i][1] = matrix[i][1] row[i][2] = matrix[i][2] // Compute X scale factor and normalize first row. scale[0] = length(row[0]) row[0] = normalize(row[0]) // Compute XY shear factor and make 2nd row orthogonal to 1st. skew[0] = dot(row[0], row[1]) row[1] = combine(row[1], row[0], 1.0, -skew[0]) // Now, compute Y scale and normalize 2nd row. scale[1] = length(row[1]) row[1] = normalize(row[1]) skew[0] /= scale[1]; // Compute XZ and YZ shears, orthogonalize 3rd row skew[1] = dot(row[0], row[2]) row[2] = combine(row[2], row[0], 1.0, -skew[1]) skew[2] = dot(row[1], row[2]) row[2] = combine(row[2], row[1], 1.0, -skew[2]) // Next, get Z scale and normalize 3rd row. scale[2] = length(row[2]) row[2] = normalize(row[2]) skew[1] /= scale[2] skew[2] /= scale[2] // At this point, the matrix (in rows) is orthonormal. // Check for a coordinate system flip. If the determinant // is -1, then negate the matrix and the scaling factors. pdum3 = cross(row[1], row[2]) if (dot(row[0], pdum3) < 0) for (i = 0; i < 3; i++) { scale[0] *= -1; row[i][0] *= -1 row[i][1] *= -1 row[i][2] *= -1 // Now, get the rotations ou rotate[1] = asin(-row[0][2]); if (cos(rotate[1]) != 0) rotate[0] = atan2(row[1][2], row[2][2]); rotate[2] = atan2(row[0][1], row[0][0]); else rotate[0] = atan2(-row[2][0], row[1][1]); rotate[2] = 0; return true;
Once decomposed, each component of each returned value of the source matrix is linearly interpolated with the corresponding component of the destination matrix. For instance, the translate[0] and translate[1] values are interpolated numerically, and the result is used to set the translation of the animating element.
This section is not normative.
After interpolation the resulting values are used to position the
element. One way to use these values is to recompose them into a 4x4
matrix. This can be done using the transform functions of the ‘transform
’ property.
This can be done by the following pseudo code. The values passed in are
the output of the Unmatrix function above:
matrix3d(1,0,0,0, 0,1,0,0, 0,0,1,0, perspective[0], perspective[1], perspective[2], perspective[3]) translate3d(translation[0], translation[1], translation[2]) rotateX(rotation[0]) rotateY(rotation[1]) rotateZ(rotation[2]) matrix3d(1,0,0,0, 0,1,0,0, 0,skew[2],1,0, 0,0,0,1) matrix3d(1,0,0,0, 0,1,0,0, skew[1],0,1,0, 0,0,0,1) matrix3d(1,0,0,0, skew[0],1,0,0, 0,0,1,0, 0,0,0,1) scale3d(scale[0], scale[1], scale[2])
Mathematically, all transform functions can be represented as 4x4 transformation matrices of the following form:
A 2D 3x2 matrix with six parameters a, b, c, d, e and f is equivalent to to the matrix:
A 2D translation with the parameters tx and ty is equivalent to a 3D translation where tz has zero as a value.
A 2D scaling with the parameters sx and sy is equivalent to a 3D scale where sz has one as a value.
A 2D rotation with the parameter alpha is equivalent to a 3D rotation with vector [0,0,1] and parameter alpha.
A 2D skew transformation along the X axis with the parameter alpha is equivalent to the matrix:
A 2D skew transformation along the Y axis with the parameter beta is equivalent to the matrix:
A 3D translation with the parameters tx, ty and tz is equivalent to the matrix:
A 3D scaling with the parameters sx, sy and sz is equivalent to the matrix:
A 3D rotation with the vector [x,y,z] and the parameter alpha is equivalent to the matrix:
where:
A perspective projection matrix with the parameter d is equivalent to the matrix:
Property | Values | Initial | Applies to | Inh. | Percentages | Media |
---|---|---|---|---|---|---|
backface-visibility | visible | hidden | visible | transformable elements | no | N/A | visual |
perspective | none | <length> | none | transformable elements | no | N/A | visual |
perspective-origin | [ <percentage> | <length> | left | center | right | top | bottom] | [ [ <percentage> | <length> | left | center | right ] && [ <percentage> | <length> | top | center | bottom ] ] | 50% 50% | transformable elements | no | refer to the size of the element's bounding box | visual |
transform | none | <transform-function> [ <transform-function> ]* | none | transformable elements | no | refer to the size of the element's bounding box | visual |
transform-origin | [ <percentage> | <length> | left | center | right | top | bottom] | [ [ <percentage> | <length> | left | center | right ] && [ <percentage> | <length> | top | center | bottom ] ] <length>? | 0 0 for SVG elements without associated CSS layout box, 50% 50% for all other elements | transformable elements | no | refer to the size of the element's bounding box | visual |
transform-style | flat | preserve-3d | flat | transformable elements | no | N/A | visual |