CSS Transforms Module Level 2
CSS Transforms Module Level 2
Editor’s Draft
30 November 2025
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Editors:
Tab Atkins Jr.
Google
L. David Baron
Google
Simon Fraser
Apple Inc
Dean Jackson
Apple Inc
Theresa O'Connor
Apple Inc
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Delta Spec:
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rules apply.
Abstract
CSS transforms allows elements styled with CSS to be transformed in two-dimensional or three-dimensional space.
This spec adds new transform functions and properties for three-dimensional transforms, and convenience functions for simple transforms.
CSS
is a language for describing the rendering of structured documents
(such as HTML and XML)
on screen, on paper, etc.
Status of this document
This is a public copy of the editors’ draft.
It is provided for discussion only and may change at any moment.
Its publication here does not imply endorsement of its contents by W3C.
Don’t cite this document other than as work in progress.
Please send feedback
by
filing issues in GitHub
(preferred),
including the spec code “css-transforms” in the title, like this:
“[css-transforms]
…summary of comment…
”.
All issues and comments are
archived
Alternately, feedback can be sent to the (
archived
) public mailing list
www-style@w3.org
This document is governed by the
18 August 2025 W3C Process Document
1.
Introduction
This specification is a delta spec that extends
[css-transforms-1]
to allow authors to transform elements in three-dimensional space.
New transform functions for the
transform
property allow three-dimensional transforms,
and additional properties make working with three-dimensional transforms easier,
and allow the author to control how nested three-dimensional transformed elements interact.
The
perspective
property allows the author to provide child elements with an extra perspective transformation. The
perspective-origin
property provides control over the origin at which perspective is applied, effectively changing the location of the "vanishing point".
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.
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.
Note:
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.
This specification also adds three convenience properties,
scale
translate
and
rotate
, that make it easier to describe and animate simple transforms.
1.1.
Module Interactions
The
3D transform functions
here extend the set of functions for the
transform
property.
Some values of
perspective
transform-style
and
backface-visibility
result in the creation of a
containing block for all descendants
, and/or the creation of a
stacking context
Three-dimensional transforms affect the visual layering of elements, and thus override the back-to-front painting order described in
Appendix E
of
[CSS21]
1.2.
Value Definitions
This specification follows the
CSS property definition conventions
from
[CSS21]
using the
value definition syntax
from
[CSS-VALUES-3]
Value types not defined in this specification are defined in CSS Values & Units
[CSS-VALUES-3]
Combination with other CSS modules may expand the definitions of these value types.
In addition to the property-specific values listed in their definitions,
all properties defined in this specification
also accept the
CSS-wide keywords
as their property value.
For readability they have not been repeated explicitly.
2.
Terminology
3D transformed element
An element whose computed value for the
transform
property includes one of the
3D transform functions
3D matrix
A 4x4 matrix which does not fulfill the requirements of an
2D matrix
identity transform function
In addition to the identity transform function in CSS Transforms,
examples for identity transform functions include
translate3d(0, 0, 0)
translateZ(0)
scaleZ(1)
rotate3d(1, 1, 1, 0)
rotateX(0)
rotateY(0)
rotateZ(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(none)
The value of m
34
becomes infinitesimal small
and the transform function is therefore assumed to be equal to the identity matrix.
perspective matrix
A matrix computed from the values of the
perspective
and
perspective-origin
properties as described
below
accumulated 3D transformation matrix
A matrix computed for an element relative to the root of its
3D rendering context
, as described
below
3D rendering context
A set of elements with a common ancestor which share a common three-dimensional coordinate system, as described
below
2.1.
Resolved value of
transform
The
transform
property is a
resolved value special case property
[CSSOM]
When the
computed value
is a
the
resolved value
is one
function or one
function
computed by the following algorithm:
Let
transform
be a 4x4 matrix initialized to the identity matrix. The elements
m11
m22
m33
and
m44
of
transform
must be set to
; all other elements of
transform
must be set to
Post-multiply all
s in
to
transform
Chose between
or
serialization:
If
transform
is a
2D matrix
Serialize
transform
to a
function.
Otherwise
Serialize
transform
to a
function.
For other computed values, the
resolved value
is the
computed value
3.
Two Dimensional Subset
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
three-dimensional transforms
and the properties
transform-style
perspective
perspective-origin
and
backface-visibility
must not be supported. Section
3D Transform Rendering
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
Mathematical Description of Transform Functions
is still effective but can be reduced by using a 3x3 transformation matrix where
equals m
11
equals m
12
equals m
21
equals m
22
equals m
41
and
equals m
42
(see A 2D 3x2 matrix with six parameter).
$$\begin{bmatrix} a & c & e \\ b & d & f \\ 0 & 0 & 1 \end{bmatrix}$$
3x3 matrix for two-dimensional transformations.
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.
div {
transform: scale(2) rotate(45deg);
transform: scale(2) rotate3d(0, 0, 1, 45deg);
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.
4.
The Transform Rendering Model
This specification extends
CSS Transforms 1
§ 2 The Transform Rendering Model
to account for the existence of three-dimensional transform functions, the Z value of
transform-origin
, the
perspective
property, and a new 3D rendering model that applies when the used value of the
transform-style
property is
preserve-3d
Three-dimensional transform functions conceptually extend the coordinate space into three dimensions, adding a Z axis perpendicular to the plane of the screen, that increases towards the viewer.
Demonstration of the initial coordinate space.
4.1.
3D Transform Rendering
Normally, elements render as flat planes, and are rendered into the same plane as their stacking context. 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 stacking context.
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.
describe how nested 3d-transformed elements render (perhaps with math)
This example doesn’t follow from the previous text.
This example shows the effect of three-dimensional transform applied to an element.
The transform is a 50° rotation about the vertical, Y axis. Note how this makes the blue box appear narrower, but not three-dimensional.
4.1.1.
Perspective
Perspective 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 appear smaller. The scaling is proportional to
/(
) where
, the value of
perspective
, is the distance from the drawing plane to the assumed position of the viewer’s eye.
The appearance of perspective can be applied to a 3d-transformed element in two ways. First, the element’s 'transform function list' can contain the
perspective()
function which computes into the element’s 'current transformation matrix'.
Second, the
perspective
and
perspective-origin
properties can be applied to an element to influence the rendering of its 3d-transformed children, giving them a shared perspective that provides the impression of them living in the same three-dimensional scene.
Diagrams showing how scaling depends on the
perspective
property and Z position. In the top diagram,
is half of
. In order to make it appear that the original circle (solid outline) appears at
(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.
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
Diagram showing the effect of moving the perspective origin upward.
The
perspective matrix
is computed as follows:
Start with the identity matrix.
Translate by the computed X and Y values of
perspective-origin
Multiply by the matrix that would be obtained from the
perspective()
transform function, where the length is provided by the value of the
perspective
property
Translate by the negated computed X and Y values of
perspective-origin
This example shows how perspective can be used to cause three-dimensional transforms to appear more realistic.
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.
4.1.2.
3D Rendering Contexts
This section specifies the rendering model for content that uses 3D-transforms and the
transform-style
property. In order to describe this model, we introduce the concept of a "3D rendering context".
3D rendering context
is a set of elements rooted in a common ancestor that, for the purposes of 3D-transform rendering, are considered to share a common three-dimensional coordinate system. The front-to-back rendering of elements in the a 3D rendering context depends on their z-position in that three-dimensional space, and, if the 3D transforms on those elements cause them to intersect, then they are rendered with intersection.
The position of each element in that three-dimensional space is determined by
accumulating
the transformation matrices up from the given element to the element that establishes the
3D rendering context
Elements establish and participate in 3D rendering contexts as follows:
3D rendering context
is established by a
transformable element
whose used value for
transform-style
is
preserve-3d
and which itself is not part of a 3D rendering context. An element that establishes a 3D rendering context also participates in that context.
An element whose used value for
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.
An element participates in a
3D rendering context
if its parent establishes or extends a
3D rendering context
Some CSS properties have values that are considered to force "grouping": they require that their element and its descendants are rendered as a group before being composited with other elements; these include opacity, filters and properties that affect clipping. The relevant property values are listed under
grouping property values
. Consequently, when used on an element with transform-style:preserve-3d, they change the used value to
flat
and prevent it from creating or extending a
3D rendering context
In a 3D rendering context, rendering and sorting of elements is done as follows:
The element establishing the 3D rendering context,
and each other 3D transformed element participating in the 3D rendering context,
is rendered into its own plane.
This plane includes
the element’s backgrounds, borders, other box decorations, content,
and descendant elements,
excluding any descendant elements that have their own plane (and their descendants).
This rendering is done according to
CSS 2.1,
Appendix E, Section E.2 Painting Order
Intersection is performed between this set of planes,
according to
Newell’s algorithm
with the planes transformed by the
accumulated 3D transformation matrix
Coplanar
3D transformed elements
are rendered in painting order.
is it OK to not pop 2D-transformed elements into their own planes?
Note:
This specification previously defined that
the background, borders, and other box decorations of the establishing element
were rendered behind the entire 3D scene.
This was changed in
#6238
However, if the definition of 3D Rendering Contexts is changed in the future,
it may be worth considering changing back.
Note that elements with transforms which have a negative z-component will render behind the content and untransformed descendants of the establishing element, and that
3D transformed elements
may interpenetrate with content and untransformed elements.
Note:
Because the 3D-transformed elements in a 3D rendering context can all depth-sort and intersect with each other, they are effectively rendered as if they were siblings. The effect of transform-style: preserve-3d can then be thought of as causing all the
3D transformed elements
in a 3D rendering context to be hoisted up into the establishing element, but still rendered with their
accumulated 3D transformation matrix
Lorem ipsum dolor sit amet, consectetaur adipisicing elit…
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, and the scene element adds perspective to the 3D rendering context. The children intersect with each other, and the orange element also intersects with the container.
This example shows how nested 3D transforms are rendered. 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 the same 3D rendering context. Thus the lime element only appears shorter; it does not "pop out" of the blue element.
4.1.3.
Transformed element hierarchies
By default,
transformed elements
do not create a
3D rendering context
and create a flattened representation of their content. However, since it is useful to construct hierarchies of transformed objects that share a common 3-dimensional space, this flattening behavior may be overridden by specifying a value of
preserve-3d
for the
transform-style
property. This allows descendants of the transformed element to share the same 3D rendering context. Non-3D-transformed descendants of such elements are rendered into the plane of the element in step C above, but 3D-transformed elements in the same 3D rendering context will "pop out" into their own planes.
This example is identical to the previous example, with the addition of
transform-style: preserve-3d
on the blue element. The blue element now extends the 3D rendering context of its container. 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.
4.1.4.
Accumulated 3D Transformation Matrix Computation
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:
Let
transform
be the identity matrix.
Let
current element
be the transformed element.
Let
parent element
be the parent element of the transformed element.
While
current element
is an element in the transformed element’s
3D rendering context
If
current element
has a value for
transform
which is not
none
, pre-multiply
current element
’s
transformation matrix
with the
transform
Compute a translation matrix which represents the offset (including the scroll offset) of
current element
from its
parent element
, and pre-multiply that matrix into the
transform
If
parent element
has a value for
perspective
which is not
none
, pre-multiply the
parent element
’s
perspective matrix
into the
transform
Let
current element
be the
parent element
Let
parent element
be the
current element
’s parent.
Note:
as described here, the
accumulated 3D transformation matrix
takes into account offsets (including the scroll offset) generated by the
visual formatting model
on the transformed element, and elements in its ancestor chain up to and including the element that establishes the its
3D rendering context
4.1.5.
Backface Visibility
Using three-dimensional transforms, it’s possible to transform an element such that its reverse side is visible. 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.
Visibility of the reverse side of an element is considered using the
accumulated 3D transformation matrix
, and is thus relative to the parent of the element that establishes the
3D rendering context
Note:
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 only the inside faces of the box.
This example shows how to make a "card" element that flips over when clicked. Note the "transform-style: preserve-3d" on #card which is necessary to avoid flattening when flipped.
what is the impact of backface-visibility on non-transformed or 2D-transformed elements? Do they get popped into their own planes and intersect?
4.2.
Processing of Perspective-Transformed Boxes
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
#912
The
accumulated 3D transformation matrix
is affected both by the
perspective
property, and by any perspective() transform function present in the value of the
transform
property.
This
accumulated 3D transformation matrix
is a 4×4 matrix, while the objects to be transformed are two-dimensional boxes. To transform each corner (
) of a box, the matrix must first be applied to (
, 0, 1), which will result in a four-dimensional point (
). This is transformed back to a three-dimensional point (
′,
′,
′) as follows:
If
> 0, (
′,
′,
′) = (
).
If
= 0, (
′,
′,
′) = (
).
is an implementation-dependent value that should be chosen so that
′ or
′ is much larger than the viewport size, if possible. For example, (5px, 22px, 0px, 0) might become (5000px, 22000px, 0px), with
= 1000, but this value of
would be too small for (0.1px, 0.05px, 0px, 0). This specification does not define the value of
exactly. Conceptually, (
′,
′,
′) is
infinitely far
in the direction (
).
If
< 0 for all four corners of the transformed box, the box is not rendered.
If
< 0 for one to three corners of the transformed box, the box must be replaced by a polygon that has any parts with
< 0 cut out. This will in general be a polygon with three to five vertices, of which exactly two will have
= 0 and the rest
> 0. These vertices are then transformed to three-dimensional points using the rules just stated. Conceptually, a point with
< 0 is "behind" the viewer, so should not be visible.
.transformed {
height: 100px;
width: 100px;
background: lime;
transform: perspective(50px) translateZ(100px);
All of the box’s corners have
-coordinates greater than the perspective. This means that the box is behind the viewer and will not display. Mathematically, the point (
) first becomes (
, 0, 1), then is translated to (
, 100, 1), and then applying the perspective results in (
, 100, −1). The
-coordinate is negative, so it does not display. An implementation that doesn’t handle the
< 0 case separately might incorrectly display this point as (−
, −
, −100), dividing by −1 and mirroring the box.
.transformed {
height: 100px;
width: 100px;
background: radial-gradient(yellow, blue);
transform: perspective(50px) translateZ(50px);
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.
Mathematically, the point (
) first becomes (
, 0, 1), then is translated to (
, 50, 1), then becomes (
, 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.
.transformed {
height: 50px;
width: 50px;
background: lime;
border: 25px solid blue;
transform-origin: left;
transform: perspective(50px) rotateY(-45deg);
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
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.
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
= −0.4142 < 0, so we need to slice away the part of the box with
< 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.
Again, the rendered box is still finite, so the user can scroll to see the whole thing if they choose. 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.
The same basic procedure would apply if one or three vertices had
< 0. However, in that case the result of truncating the
< 0 part would be a triangle or pentagon instead of a quadrilateral.
5.
Individual Transform Properties: the
translate
scale
, and
rotate
properties
The
translate
rotate
, and
scale
properties
allow authors to specify simple transforms independently,
in a way that maps to typical user interface usage,
rather than having to remember the order in
transform
that keeps the actions of
translate()
rotate()
and
scale()
independent and acting in screen coordinates.
Name:
translate
Value:
none
Initial:
none
Applies to:
transformable elements
Inherited:
no
Percentages:
relative to the width of the
reference box
(for the first value) or the height (for the second value)
Computed value:
the keyword
none
or a pair of computed
values and an absolute length
Canonical order:
per grammar
Animation type:
by computed value, but see below for
none
The
translate
property accepts 1-3 values,
each specifying a translation against one axis,
in the order X, Y, then Z.
When the second or third values are missing,
they default to
0px
If the third value is omitted or zero,
this specifies a 2d translation,
equivalent to the
translate()
function.
Otherwise,
this specifies a 3d translation,
equivalent to the
translate3d()
function.
Note:
The
resolved value
of the
translate
property
is the
computed value
and thus
getComputedStyle()
includes percentage values in its results.
Name:
rotate
Value:
none
[ x
{3}
&&
Initial:
none
Applies to:
transformable elements
Inherited:
no
Percentages:
n/a
Computed value:
the keyword
none
, or an
with an axis consisting of a list of three
Canonical order:
per grammar
Animation type:
as SLERP, but see below for
none
The
rotate
property accepts an angle to rotate an element,
and optionally an axis to rotate it around.
The axis can be specified with either the
or
keywords,
which specify a rotation around that axis,
equivalent to the
rotateX()
rotateY()
and
rotateZ()
transform functions.
Alternately, the axis can be specified explicitly
by giving three numbers
representing the x, y, and z components of an origin-centered vector,
equivalent to the
rotate3d()
function.
There is no difference in behavior between
a rotation specified as an
alone
and a rotation specified as being around the z-axis
(whether by the
keyword or
by a vector whose first two components are zero
and third component is positive);
they are all 2d rotations equivalent to the
rotate()
function.
For example,
rotate: 30deg
rotate: z 30deg
, and
rotate: 0 0 1 30deg
are equivalent.
Name:
scale
Value:
none
{1,3}
Initial:
none
Applies to:
transformable elements
Inherited:
no
Percentages:
n/a
Computed value:
the keyword
none
, or a list of 3
Canonical order:
per grammar
Animation type:
by computed value, but see below for
none
The
scale
property accepts 1-3 values,
each specifying a scale along one axis,
in order X, Y, then Z.
If the Y value is not given,
then it defaults to being the same as the X value.
If the Z value is not given,
then it defaults to
If the third value is omitted,
, or
100%
this specifies a 2d scaling,
equivalent to the
scale()
function.
Otherwise,
this specifies a 3d scaling,
equivalent to the
scale3d()
function.
There is no difference in behavior between the third value being omitted
and the third value being
or
100%
is equivalent to a
for example
scale: 100%
is equivalent to
scale: 1
Numbers are used during serialization of specified and computed values.
All three properties accept
(and default to)
the value
none
which produces no transform at all.
In particular,
this value does
not
trigger the creation of a stacking context or
containing block for all descendants
while all other values
(including “identity” transforms like
translate: 0px
create a stacking context and
containing block for all descendants
per usual for transforms.
When
translate
rotate
or
scale
are animating or transitioning, and the from value or to
value (but not both) is
none
, the value
none
is replaced by the equivalent identity
value (
0px
for translate,
0deg
for rotate,
for scale).
5.1.
Serialization
Because these properties have two distinct modes of behavior
(no transform versus transform),
serialization must take this into account:
for
translate
If a translation is specified,
the property must serialize with one through three values.
(As usual, if the second and third values are
0px
, the default,
or if only the third value is
0px
then those
0px
values must be omitted when serializing).
It must serialize as the keyword
none
if and only if
none
was originally specified.
(An identity transform does not count;
it must serialize as
0px
.)
for
rotate
If a rotation about the z axis (that is, in 2D) is specified,
the property must serialize as just an
If any other rotation is specified,
the property must serialize with an axis specified.
If the axis is parallel with the x or y axes,
it must serialize as the appropriate keyword.
It must serialize as the keyword
none
if and only if
none
was originally specified.
(An identity transform does not count;
it must serialize as
0deg
.)
for
scale
If a scale is specified,
the property must serialize with only one through three values.
As usual, if the third value is 1, the default,
then it is omitted when serializing.
If the third value is omitted
and the second value is the same as the first (the default),
then the second value is also omitted when serializing.
It must serialize as the keyword
none
if and only if
none
was originally specified.
(An identity transform does not count;
it must serialize as
.)
6.
Current Transformation Matrix
The
transformation matrix
computation is amended to the following:
The transformation matrix is computed from the
transform
transform-origin
translate
rotate
scale
, and
offset
properties as follows:
Start with the identity matrix.
Translate by the computed X, Y, and Z values of
transform-origin
Translate by the computed X, Y, and Z values of
translate
Rotate by the computed
about the specified axis of
rotate
Scale by the computed X, Y, and Z values of
scale
Translate and rotate by the transform specified by
offset
Multiply by each of the transform functions in
transform
from left to right.
Translate by the negated computed X, Y and Z values of
transform-origin
7.
The
transform-style
Property
Name:
transform-style
Value:
flat
preserve-3d
Initial:
flat
Applies to:
transformable elements
Inherited:
no
Percentages:
N/A
Computed value:
specified keyword
Canonical order:
per grammar
Animation type:
discrete
Used value:
flat if a
grouping property
is present, specified keyword otherwise
A computed value of
preserve-3d
for
transform-style
on a
transformable element
establishes both a stacking context and
containing block for all descendants
If the used value is
preserve-3d
then it also establishes or extends a
3D rendering context
7.1.
Grouping property values
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 force the element to have a used style of
flat
for
preserve-3d
overflow
: any value other than
visible
or
clip
opacity
: any value less than 1.
filter
: any value other than
none
clip
: any value other than
auto
clip-path
: any value other than
none
isolation
: used value of
isolate
mask-image
: any value other than
none
mask-border-source
: any value other than
none
mix-blend-mode
: any value other than
normal
contain
paint
and any other property/value combination that causes
paint containment
Note: this includes any property that affect the
used value
of the
contain
property,
such as
content-visibility: hidden
8.
The
perspective
Property
Name:
perspective
Value:
none
Initial:
none
Applies to:
transformable elements
Inherited:
no
Percentages:
N/A
Computed value:
the keyword
none
or an absolute length
Canonical order:
per grammar
Animation type:
by computed value
Distance to the center of projection.
Verify that projection is the distance to the center of projection.
As very small
values can produce bizarre rendering results
and stress the numerical accuracy of transform calculations,
values less than
1px
must be treated as
1px
for rendering purposes.
(This clamping does not affect the underlying value,
so
perspective: 0;
in a stylesheet
will still serialize back as
.)
none
No perspective transform is applied. The effect is mathematically similar to an infinite
value. All objects appear to be flat on the canvas.
The use of this property with any value other than
none
establishes a stacking context. It also establishes a
containing block for all descendants
, just like the
transform
property does.
We don’t really need to be a stacking context or containing block for perspective, but maybe webcompat means we can’t change this.
The values of the
perspective
and
perspective-origin
properties are used to compute the
perspective matrix
, as described above.
9.
The
perspective-origin
Property
The
perspective-origin
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.
Name:
perspective-origin
Value:
Initial:
50% 50%
Applies to:
transformable elements
Inherited:
no
Percentages:
refer to the size of the
reference box
Computed value:
see
background-position
Canonical order:
per grammar
Animation type:
by computed value
The values of the
perspective
and
perspective-origin
properties are used to compute the
perspective matrix
, as described above.
The values for
perspective-origin
represent an offset of the perspective origin from the top left corner of the
reference box
A percentage for the horizontal perspective offset is relative to the width of the
reference box
. A percentage for the vertical offset is relative to height of the
reference box
. The value for the horizontal and vertical offset represent an offset from the top left corner of the
reference box
A length value gives a fixed length as the offset. The value for the horizontal and vertical offset represent an offset from the top left corner of the
reference box
top
Computes to
0%
for the vertical position if one or two values are given, otherwise specifies the top edge as the origin for the next offset.
right
Computes to
100%
for the horizontal position if one or two values are given, otherwise specifies the right edge as the origin for the next offset.
bottom
Computes to
100%
for the vertical position if one or two values are given, otherwise specifies the bottom edge as the origin for the next offset.
left
Computes to
0%
for the horizontal position if one or two values are given, otherwise specifies the left edge as the origin for the next offset.
center
Computes to
50%
left 50%
) for the horizontal position if the horizontal position is not otherwise specified, or
50%
top 50%
) for the vertical position if it is.
The
perspective-origin
property is a
resolved value special case property like
height
[CSSOM]
10.
The
backface-visibility
Property
Name:
backface-visibility
Value:
visible
hidden
Initial:
visible
Applies to:
transformable elements
Inherited:
no
Percentages:
N/A
Computed value:
specified keyword
Canonical order:
per grammar
Animation type:
discrete
A computed value of
hidden
for
backface-visibility
on a
transformable element
that participates in a
3D rendering context
establishes both a stacking context and
containing block for all descendants
The visibility of an element with
backface-visibility: hidden
is determined as follows:
Compute the element’s
accumulated 3D transformation matrix
If the component of the matrix in row 3, column 3 is negative, then the element should be hidden. Otherwise it is visible.
Backface-visibility cannot be tested by only looking at m33. See
#917
Note:
The reasoning for this definition is as follows. Assume elements are rectangles in the
plane with infinitesimal thickness. The front of the untransformed element has coordinates like (
), and the back is (
, −
), for some very small
. We want to know if after the transformation, the front of the element is closer to the viewer than the back (higher
-value) or further away. The
-coordinate of the front will be m
13
+ m
23
+ m
33
+ m
43
, before accounting for perspective, and the back will be m
13
+ m
23
− m
33
+ 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.)
11.
SVG and 3D transform functions
This specification explicitly requires three-dimensional transform functions to apply to the
container elements
svg
, all
graphics elements
, all
graphics referencing elements
and the SVG
foreignObject
element.
Three-dimensional transform functions and the properties
perspective
perspective-origin
transform-style
and
backface-visibility
can not be used for the elements:
clipPath
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. The
clipPath
mask
pattern
elements 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
If the
vector-effect
property is set to
non-scaling-stroke
and an object is within a
3D rendering context
the property has no affect on stroking the object.
formally describe the syntax of the 3D transform functions in SVG,
as is done
for the 2-D functions
12.
The Transform Functions
The value of the
transform
property is a list of
. The set of allowed transform functions is given below. Wherever
is used in this specification, a
that is equal to zero is also allowed, which is treated the same as an angle of zero degrees. A percentage for horizontal translations is relative to the width of the
reference box
. A percentage for vertical translations is relative to the height of the
reference box
A percentage in a scale function is equivalent to a number, and serializes as a number in specified values.
For example,
scale3d(50%, 100%, 150%)
serializes as
scale3d(0.5, 1, 1.5)
12.1.
2D Transform Functions
The scale functions defined in
[css-transforms-1]
now support percentages.
scale()
= scale( [
#{1,2}
scaleX()
= scaleX( [
] )
scaleY()
= scaleY( [
] )
As
defined in css-transforms-1
, but also accepting percentages as
described above
12.2.
3D Transform Functions
In the following
3d transform functions
, a
behaves the same as
0deg
("Unitless 0" angles are preserved for legacy compat reasons.)
matrix3d()
= matrix3d(
#{16}
specifies a 3D transformation as a 4x4 homogeneous matrix of 16 values in column-major order.
translate3d()
= translate3d(
specifies a
3D translation
by the vector [tx,ty,tz], with tx, ty and tz being the first, second and third translation-value parameters respectively.
translateZ()
= translateZ(
specifies a
3D translation
by the vector [0,0,tz] with the given amount in the Z direction.
scale3d()
= scale3d( [
#{3}
specifies a
3D scale
operation by the [sx,sy,sz] scaling vector described by the 3 parameters.
scaleZ()
= scaleZ( [
] )
specifies a
3D scale
operation using the [1,1,sz] scaling vector, where sz is given as the parameter.
rotate3d()
= rotate3d(
] )
specifies a
3D rotation
by the angle specified in last parameter about the [x,y,z] direction vector described by the first three parameters. A direction vector that cannot be normalized, such as [0,0,0], will cause the rotation to not be applied.
Note:
the rotation is clockwise as one looks from the end of the vector toward the origin.
rotateX()
= rotateX( [
] )
same as
rotate3d(1, 0, 0,
rotateY()
= rotateY( [
] )
same as
rotate3d(0, 1, 0,
rotateZ()
= rotateZ( [
] )
same as
rotate3d(0, 0, 1,
, which is a 3d transform equivalent to the 2d transform
rotate(
perspective()
= perspective( [
none
] )
specifies a
perspective projection matrix
. This matrix scales points in X and Y based on their Z value, scaling points with positive Z values away from the origin, and those with negative Z values towards the origin. Points on the z=0 plane are unchanged. The parameter represents the distance of the z=0 plane from the viewer. Lower values give a more flattened pyramid and therefore a more pronounced perspective effect. For example, a value of 1000px gives a moderate amount of foreshortening and a value of 200px gives an extreme amount.
If the depth value is less than
1px
it must be treated as
1px
for the purpose of rendering,
for computing the
resolved value
of
transform
and when used as the endpoint of
interpolation
Note:
The intent of the above rules on values less than
1px
is
that they cover the cases where the
perspective()
function
needs to be converted into a matrix.
12.3.
Transform function primitives and derivatives
Some transform functions can be represented by more generic transform functions. These transform functions are called derived transform functions, and the generic transform functions are called primitive transform functions. Three-dimensional primitives and their derived transform functions are:
translate3d()
for
translateZ()
and
scale3d()
for
scaleZ()
and
rotate3d()
for
rotateX()
rotateY()
and
rotateZ()
For derived transform functions that have a two-dimensional primitive and a three-dimensional primitive, the context decides about the used primitive. See
Interpolation of primitives and derived transform functions
13.
Interpolation of Matrices
When interpolating between two matrices, each matrix is decomposed into the corresponding translation, rotation, scale, skew and (for a
3D matrix
) perspective values. Each corresponding component of the decomposed matrices gets interpolated numerically and recomposed back to a matrix in a final step.
13.1.
Interpolation of 3D matrices
13.1.1.
Decomposing a 3D matrix
The pseudo code below is based upon the "unmatrix" method in "Graphics Gems II, edited by Jim Arvo", but modified to use Quaternions instead of Euler angles to avoid the problem of Gimbal Locks.
The following pseudocode works on a 4x4 homogeneous matrix:
Input: matrix ; a 4x4 matrix
Output: translation ; 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
quaternion ; a 4 component vector
Returns false if the matrix cannot be decomposed, true if it can
// 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)
else
// No perspective.
perspective[0] = perspective[1] = perspective[2] = 0
perspective[3] = 1
// Next take care of translation
for (i = 0; i < 3; i++)
translate[i] = matrix[3][i]
// 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[i] *= -1;
row[i][0] *= -1
row[i][1] *= -1
row[i][2] *= -1
// Now, get the rotations out
quaternion[0] = 0.5 * sqrt(max(1 + row[0][0] - row[1][1] - row[2][2], 0))
quaternion[1] = 0.5 * sqrt(max(1 - row[0][0] + row[1][1] - row[2][2], 0))
quaternion[2] = 0.5 * sqrt(max(1 - row[0][0] - row[1][1] + row[2][2], 0))
quaternion[3] = 0.5 * sqrt(max(1 + row[0][0] + row[1][1] + row[2][2], 0))
if (row[2][1] > row[1][2])
quaternion[0] = -quaternion[0]
if (row[0][2] > row[2][0])
quaternion[1] = -quaternion[1]
if (row[1][0] > row[0][1])
quaternion[2] = -quaternion[2]
return true
13.1.2.
Interpolation of decomposed 3D matrix values
Each component of the decomposed values translation, scale, skew and perspective of the source matrix get linearly interpolated with each corresponding component of the destination matrix.
Note:
For instance,
translate[0]
of the source matrix and
translate[0]
of the destination matrix are interpolated numerically, and the result is used to set the translation of the animating element.
Quaternions of the decomposed source matrix are interpolated with quaternions of the decomposed destination matrix using the spherical linear interpolation (Slerp) as described by the pseudo code below:
Input: quaternionA ; a 4 component vector
quaternionB ; a 4 component vector
t ; interpolation parameter with 0 <= t <= 1
Output: quaternionDst ; a 4 component vector
product = dot(quaternionA, quaternionB)
// Clamp product to -1.0 <= product <= 1.0
product = min(product, 1.0)
product = max(product, -1.0)
if (abs(product) == 1.0)
quaternionDst = quaternionA
return
theta = acos(product)
w = sin(t * theta) / sqrt(1 - product * product)
for (i = 0; i < 4; i++)
quaternionA[i] *= cos(t * theta) - product * w
quaternionB[i] *= w
quaternionDst[i] = quaternionA[i] + quaternionB[i]
return
13.1.3.
Recomposing to a 3D matrix
After interpolation, the resulting values are used to transform the elements user space. One way to use these values is to recompose them into a 4x4 matrix. This can be done following the pseudo code below:
Input: translation ; 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
quaternion ; a 4 component vector
Output: matrix ; a 4x4 matrix
Supporting functions (matrix is a 4x4 matrix):
matrix multiply(matrix a, matrix b) returns the 4x4 matrix product of a * b
// apply perspective
for (i = 0; i < 4; i++)
matrix[i][3] = perspective[i]
// apply translation
for (i = 0; i < 4; i++)
for (j = 0; j < 3; j++)
matrix[3][i] += translation[j] * matrix[j][i]
// apply rotation
x = quaternion[0]
y = quaternion[1]
z = quaternion[2]
w = quaternion[3]
// Construct a composite rotation matrix from the quaternion values
// rotationMatrix is a identity 4x4 matrix initially
rotationMatrix[0][0] = 1 - 2 * (y * y + z * z)
rotationMatrix[0][1] = 2 * (x * y - z * w)
rotationMatrix[0][2] = 2 * (x * z + y * w)
rotationMatrix[1][0] = 2 * (x * y + z * w)
rotationMatrix[1][1] = 1 - 2 * (x * x + z * z)
rotationMatrix[1][2] = 2 * (y * z - x * w)
rotationMatrix[2][0] = 2 * (x * z - y * w)
rotationMatrix[2][1] = 2 * (y * z + x * w)
rotationMatrix[2][2] = 1 - 2 * (x * x + y * y)
matrix = multiply(matrix, rotationMatrix)
// apply skew
// temp is a identity 4x4 matrix initially
if (skew[2])
temp[2][1] = skew[2]
matrix = multiply(matrix, temp)
if (skew[1])
temp[2][1] = 0
temp[2][0] = skew[1]
matrix = multiply(matrix, temp)
if (skew[0])
temp[2][0] = 0
temp[1][0] = skew[0]
matrix = multiply(matrix, temp)
// apply scale
for (i = 0; i < 3; i++)
for (j = 0; j < 4; j++)
matrix[i][j] *= scale[i]
return
14.
Interpolation of primitives and derived transform functions
Two transform functions with the same name and the same number of arguments are interpolated numerically without a former conversion. The calculated value will be of the same transform function type with the same number of arguments. Special rules apply to
and
The transform functions
matrix3d()
and
perspective()
get converted into 4x4 matrices first and interpolated as defined in section
Interpolation of Matrices
afterwards.
For interpolations with the primitive
rotate3d()
, the direction vectors of the transform functions get normalized first. If the normalized vectors are not equal and both rotation angles are non-zero the transform functions get converted into 4x4 matrices first and interpolated as defined in section
Interpolation of Matrices
afterwards. Otherwise the rotation angle gets interpolated numerically and the rotation vector of the non-zero angle is used or (0, 0, 1) if both angles are zero.
The two transform functions
translate(0)
and
translate(100px)
are of the same type, have the same number of arguments and therefore can get interpolated numerically.
translateX(100px)
is not of the same type and
translate(100px, 0)
does not have the same number of arguments, therefore these transform functions can not get interpolated without a former conversion step.
Two different types of transform functions that share the same primitive, or transform functions of the same type with different number of arguments can be interpolated. Both transform functions need a former conversion to the common primitive first and get interpolated numerically afterwards. The computed value will be the primitive with the resulting interpolated arguments.
The following example describes a transition from
translateX(100px)
to
translateY(100px)
in 3 seconds on hovering over the div box. Both transform functions derive from the same primitive
translate()
and therefore can be interpolated.
div
transform
translateX
100
px
);
div:hover
transform
translateY
100
px
);
transition
transform
For the time of the transition both transform functions get transformed to the common primitive.
translateX(100px)
gets converted to
translate(100px, 0)
and
translateY(100px)
gets converted to
translate(0, 100px)
. Both transform functions can then get interpolated numerically.
If both transform functions share a primitive in the two-dimensional space, both transform functions get converted to the two-dimensional primitive. If one or both transform functions are three-dimensional transform functions, the common three-dimensional primitive is used.
In this example a two-dimensional transform function gets animated to a three-dimensional transform function. The common primitive is
translate3d()
div
transform
translateX
100
px
);
div:hover
transform
translateZ
100
px
);
transition
transform
First
translateX(100px)
gets converted to
translate3d(100px, 0, 0)
and
translateZ(100px)
to
translate3d(0, 0, 100px)
respectively. Then both converted transform functions get interpolated numerically.
15.
Addition and accumulation of transform lists
Addition
of two transform lists
and
is defined as
list
concatenation
such that
result
is equal to
appended
to
Accumulation
of two transform lists
and
follows the same steps as interpolation
with regards to matching transform functions including
padding lists with
identity transform functions
converting
none
to an
identity transform function
and converting both arguments to matrices as necessary (see
CSS Transforms 1
§ 9 Interpolation of Transforms
).
However, instead of interpolating the individual parameters,
they are combined using arithmetic addition—except in the case of parameters whose value is one in the
identity transform function
(e.g. scale parameters and matrix elements
m11
m22
m33
, and
m44
),
which combine using
accumulation for one-based values
as follows:
result
- 1
The above definition preserves the intent of
accumulation
which is that
acts as
a delta from
and allows an animation such as:
div
animate
transform
'scale(1)'
'scale(2)'
},
duration
1000
easing
'ease'
);
to produce the expected behavior when extended as follows:
div
animate
transform
'scale(1)'
'scale(2)'
},
duration
1000
easing
'ease'
iterations
iterationComposite
'accumulate'
);
15.1.
Neutral element for addition
Some animations require a neutral element for addition. For transform functions this is a scalar or a list of scalars of 0. Examples of neutral elements for transform functions are
translate(0)
translate3d(0, 0, 0)
translateX(0)
translateY(0)
translateZ(0)
scale(0)
scaleX(0)
scaleY(0)
scaleZ(0)
rotate(0)
rotate3d(v
, v
, v
, 0)
(where
is a context dependent vector),
rotateX(0)
rotateY(0)
rotateZ(0)
skew(0, 0)
skewX(0)
skewY(0)
matrix(0, 0, 0, 0, 0, 0)
matrix3d(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
and
perspective(none)
Note:
Animations to or from the neutral element of additions
matrix3d()
and
perspective()
fall back to discrete animations (See
§ 13 Interpolation of Matrices
).
16.
Mathematical Description of Transform Functions
Mathematically, all transform functions can be represented as 4x4 transformation matrices of the following form:
$$\begin{bmatrix} m11 & m21 & m31 & m41 \\ m12 & m22 & m32 & m42 \\ m13 & m23 & m33 & m43 \\ m14 & m24 & m34 & m44 \end{bmatrix}$$
One translation unit on a matrix is equivalent to 1 pixel in the local coordinate system of the element.
A 3D translation with the parameters
tx
ty
and
tz
is equivalent to the matrix:
$$\begin{bmatrix} 1 & 0 & 0 & tx \\ 0 & 1 & 0 & ty \\ 0 & 0 & 1 & tz \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
A 3D scaling with the parameters
sx
sy
and
sz
is equivalent to the matrix:
$$\begin{bmatrix} sx & 0 & 0 & 0 \\ 0 & sy & 0 & 0 \\ 0 & 0 & sz & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
A 3D rotation with the vector [x,y,z] and the parameter
alpha
is equivalent to the matrix:
$$\begin{bmatrix} 1 - 2 \cdot (y^2 + z^2) \cdot sq & 2 \cdot (x \cdot y \cdot sq - z \cdot sc) & 2 \cdot (x \cdot z \cdot sq + y \cdot sc) & 0 \\ 2 \cdot (x \cdot y \cdot sq + z \cdot sc) & 1 - 2 \cdot (x^2 + z^2) \cdot sq & 2 \cdot (y \cdot z \cdot sq - x \cdot sc) & 0 \\ 2 \cdot (x \cdot z \cdot sq - y \cdot sc) & 2 \cdot (y \cdot z \cdot sq + x \cdot sc) & 1 - 2 \cdot (x^2 + y^2) \cdot sq & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
where:
$$sc = \sin (\alpha/2) \cdot \cos (\alpha/2)$$
$$sq = \sin^2 (\alpha/2)$$
and where x, y, and z have been normalized
(that is,
where the x, y, and z values given
have been divided by
the square root of the sum of their squares).
Note that this means that a rotation around the X axis simplifies to:
$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 - 2 \cdot sq & -2 \cdot sc & 0 \\ 0 & 2 \cdot sc & 1 - 2 \cdot sq & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
a rotation around the Y axis simplifies to:
$$\begin{bmatrix} 1 - 2 \cdot sq & 0 & 2 \cdot sc & 0 \\ 0 & 1 & 0 & 0 \\ -2 \cdot sc & 0 & 1 - 2 \cdot sq & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
and a rotation around the Z axis simplifies to:
$$\begin{bmatrix} 1 - 2 \cdot sq & -2 \cdot sc & 0 & 0 \\ 2 \cdot sc & 1 - 2 \cdot sq & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
A perspective projection matrix with the parameter
is equivalent to the matrix:
$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -1/d & 1 \end{bmatrix}$$
If the parameter
is
none
it is treated as infinity
(and the resulting matrix is the identity matrix).
17.
The SVG
transform
Attribute
This specification will also introduce the new presentation attributes
transform-origin
perspective
perspective-origin
transform-style
and
backface-visibility
Values on new introduced presentation attributes get parsed following the syntax rules on
SVG Data Types
[SVG11]
18.
SVG Animation
18.1.
The
animate
and
set
element
The introduce presentation attributes
perspective
perspective-origin
transform-style
and
backface-visibility
are animatable.
transform-style
and
backface-visibility
are non-additive.
19.
More Issues
Per
the WG resolved to add a formula for decomposing a transform into a unified "scale"
(the spec already defines how to decompose it into scaleX/Y/Z),
for use by things like SVG’s non-scaling stroke spec.
Formula is defined here.
20.
Privacy Considerations
No new privacy considerations have been reported on this specification.
21.
Security Considerations
No new security considerations have been reported on this specification.
Changes
Recent Changes
Substantive changes since
9 November 2021 WD
None yet
Substantive changes since
3 March 2020 WD
The specification no longer requires maintaining state for whether individual transform properties have 2D or 3D values, but instead requires that any value that can be expressed as 2D is treated as 2D (see
#3305
).
Note:
An analogous change is intended for transform functions, but it has not been made yet.
The
scale
property and
scale()
scaleX()
and
scaleY()
functions now support percentages (see
#3399
).
Fix multiple definitions to be consistent with the spec’s definition for a 3D Rendering Context:
Define that borders, backgrounds, and box decorations of an element establishing a 3D Rendering Context are rendered at z=0 in its 3D scene, rather than behind its 3D scene (see
#6238
).
Define
accumulated 3D transformation matrix
to include the
transform
of the establishing element and the
perspective
of its parent (see
#6191
).
Define that paint containment is a grouping property (see
#6202
).
Add support for a
none
argument to
perspective()
(see
#6488
).
Define that clamping of values of
perspective()
also applies to resolved values and interpolation (see
#6320
and
#6346
).
Clarify that the effects of
preserve-3d
only affect
transformable elements
(see
#6430
).
Fixed the
neutral element for addition
for
perspective()
to be
perspective(none)
Added a note that the resolved value of
translate
includes percentages (see
#2124
).
Describe 3D sorting more precisely, to explain which descendants are included, and not limit Appendix E reference to steps 1-7 (see
#926
).
Conformance
Document conventions
Conformance requirements are expressed with a combination of
descriptive assertions and RFC 2119 terminology. The key words “MUST”,
“MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”,
“RECOMMENDED”, “MAY”, and “OPTIONAL” in the normative parts of this
document are to be interpreted as described in RFC 2119.
However, for readability, these words do not appear in all uppercase
letters in this specification.
All of the text of this specification is normative except sections
explicitly marked as non-normative, examples, and notes.
[RFC2119]
Examples in this specification are introduced with the words “for example”
or are set apart from the normative text with
class="example"
like this:
This is an example of an informative example.
Informative notes begin with the word “Note” and are set apart from the
normative text with
class="note"
, like this:
Note, this is an informative note.
Advisements are normative sections styled to evoke special attention and are
set apart from other normative text with
, like
this:
UAs MUST provide an accessible alternative.
Tests
Tests relating to the content of this specification
may be documented in “Tests” blocks like this one.
Any such block is non-normative.
Conformance classes
Conformance to this specification
is defined for three conformance classes:
style sheet
CSS
style sheet
renderer
UA
that interprets the semantics of a style sheet and renders
documents that use them.
authoring tool
UA
that writes a style sheet.
A style sheet is conformant to this specification
if all of its statements that use syntax defined in this module are valid
according to the generic CSS grammar and the individual grammars of each
feature defined in this module.
A renderer is conformant to this specification
if, in addition to interpreting the style sheet as defined by the
appropriate specifications, it supports all the features defined
by this specification by parsing them correctly
and rendering the document accordingly. However, the inability of a
UA to correctly render a document due to limitations of the device
does not make the UA non-conformant. (For example, a UA is not
required to render color on a monochrome monitor.)
An authoring tool is conformant to this specification
if it writes style sheets that are syntactically correct according to the
generic CSS grammar and the individual grammars of each feature in
this module, and meet all other conformance requirements of style sheets
as described in this module.
Partial implementations
So that authors can exploit the forward-compatible parsing rules to
assign fallback values, CSS renderers
must
treat as invalid (and
ignore
as appropriate
) any at-rules, properties, property values, keywords,
and other syntactic constructs for which they have no usable level of
support. In particular, user agents
must not
selectively
ignore unsupported component values and honor supported values in a single
multi-value property declaration: if any value is considered invalid
(as unsupported values must be), CSS requires that the entire declaration
be ignored.
Implementations of Unstable and Proprietary Features
To avoid clashes with future stable CSS features,
the CSSWG recommends
following best practices
for the implementation of
unstable
features and
proprietary extensions
to CSS.
Non-experimental implementations
Once a specification reaches the Candidate Recommendation stage,
non-experimental implementations are possible, and implementors should
release an unprefixed implementation of any CR-level feature they
can demonstrate to be correctly implemented according to spec.
To establish and maintain the interoperability of CSS across
implementations, the CSS Working Group requests that non-experimental
CSS renderers submit an implementation report (and, if necessary, the
testcases used for that implementation report) to the W3C before
releasing an unprefixed implementation of any CSS features. Testcases
submitted to W3C are subject to review and correction by the CSS
Working Group.
Further information on submitting testcases and implementation reports
can be found from on the CSS Working Group’s website at
Questions should be directed to the
public-css-testsuite@w3.org
mailing list.
Index
Terms defined by this specification
3D matrix
, in § 2
3D rendering context
, in § 2
3D transformed element
, in § 2
3d transform functions
, in § 12.2
accumulated 3D transformation matrix
, in § 2
accumulation for one-based values
, in § 15
backface-visibility
, in § 10
bottom
, in § 9
center
, in § 9
identity transform function
, in § 2
left
, in § 9
, in § 9
, in § 8
matrix3d()
, in § 12.2
none
value for perspective
, in § 8
value for perspective()
, in § 12.2
value for translate, rotate, scale
, in § 5
, in § 9
perspective
, in § 8
perspective()
, in § 12.2
perspective matrix
, in § 2
perspective-origin
, in § 9
right
, in § 9
rotate
, in § 5
rotate3d()
, in § 12.2
rotateX()
, in § 12.2
rotateY()
, in § 12.2
rotateZ()
, in § 12.2
scale
, in § 5
scale()
, in § 12.1
scale3d()
, in § 12.2
scaleX()
, in § 12.1
scaleY()
, in § 12.1
scaleZ()
, in § 12.2
top
, in § 9
, in § 12
transform-style
, in § 7
translate
, in § 5
translate3d()
, in § 12.2
translateZ()
, in § 12.2
, in § 5
, in § 5
, in § 5
Terms defined by reference
[COMPOSITING-2]
defines the following terms:
isolation
mix-blend-mode
[CSS-BACKGROUNDS-3]
defines the following terms:
background-position
[CSS-CASCADE-5]
defines the following terms:
computed value
used value
[CSS-COLOR-4]
defines the following terms:
opacity
[CSS-CONTAIN-2]
defines the following terms:
contain
content-visibility
paint
paint containment
[CSS-MASKING-1]
defines the following terms:
clip
clip-path
clipPath
mask
mask-border-source
mask-image
[CSS-OVERFLOW-3]
defines the following terms:
clip
overflow
visible
[CSS-TRANSFORMS-1]
defines the following terms:
2D matrix
containing block for all descendants
matrix()
reference box
rotate()
transform
transform-origin
transformable element
transformation matrix
transformed element
translate()
translateX()
translateY()
[CSS-VALUES-4]
defines the following terms:
&&
CSS-wide keywords
value accumulation
value addition
{A,B}
{A}
[CSS-VALUES-5]
defines the following terms:
[CSS21]
defines the following terms:
auto
stacking context
[CSSOM]
defines the following terms:
getComputedStyle(elt)
resolved value
resolved value special case property
resolved value special case property like height
[FILTER-EFFECTS-1]
defines the following terms:
filter
[HTML]
defines the following terms:
[INFRA]
defines the following terms:
append
list
[MOTION-1]
defines the following terms:
offset
[SVG-ANIMATIONS]
defines the following terms:
animate
set
[SVG2]
defines the following terms:
container element
foreignObject
graphics element
graphics referencing element
linearGradient
pattern
radialGradient
svg
vector-effect
References
Normative References
[COMPOSITING-2]
Compositing and Blending Module Level 2
. Editor's Draft. URL:
[CSS-BACKGROUNDS-3]
Elika Etemad; Brad Kemper.
CSS Backgrounds and Borders Module Level 3
. URL:
[CSS-CASCADE-5]
Elika Etemad; Miriam Suzanne; Tab Atkins Jr..
CSS Cascading and Inheritance Level 5
. URL:
[CSS-COLOR-4]
Tab Atkins Jr.; Chris Lilley; Lea Verou.
CSS Color Module Level 4
. URL:
[CSS-CONTAIN-2]
Tab Atkins Jr.; Florian Rivoal; Vladimir Levin.
CSS Containment Module Level 2
. URL:
[CSS-MASKING-1]
Dirk Schulze; Brian Birtles; Tab Atkins Jr..
CSS Masking Module Level 1
. URL:
[CSS-OVERFLOW-3]
Elika Etemad; Florian Rivoal.
CSS Overflow Module Level 3
. URL:
[CSS-TRANSFORMS-1]
Simon Fraser; et al.
CSS Transforms Module Level 1
. URL:
[CSS-VALUES-3]
Tab Atkins Jr.; Elika Etemad.
CSS Values and Units Module Level 3
. URL:
[CSS-VALUES-4]
Tab Atkins Jr.; Elika Etemad.
CSS Values and Units Module Level 4
. URL:
[CSS-VALUES-5]
Tab Atkins Jr.; Elika Etemad; Miriam Suzanne.
CSS Values and Units Module Level 5
. URL:
[CSS21]
Bert Bos; et al.
Cascading Style Sheets Level 2 Revision 1 (CSS 2.1) Specification
. URL:
[CSSOM]
Daniel Glazman; Emilio Cobos Álvarez.
CSS Object Model (CSSOM)
. URL:
[FILTER-EFFECTS-1]
Dirk Schulze; Dean Jackson.
Filter Effects Module Level 1
. URL:
[HTML]
Anne van Kesteren; et al.
HTML Standard
. Living Standard. URL:
[INFRA]
Anne van Kesteren; Domenic Denicola.
Infra Standard
. Living Standard. URL:
[MOTION-1]
Tab Atkins Jr.; Dirk Schulze; Jihye Hong.
Motion Path Module Level 1
. URL:
[RFC2119]
S. Bradner.
Key words for use in RFCs to Indicate Requirement Levels
. March 1997. Best Current Practice. URL:
[SVG-ANIMATIONS]
SVG Animations Level 2
. Editor's Draft. URL:
[SVG11]
Erik Dahlström; et al.
Scalable Vector Graphics (SVG) 1.1 (Second Edition)
. 16 August 2011. REC. URL:
[SVG2]
Amelia Bellamy-Royds; et al.
Scalable Vector Graphics (SVG) 2
. URL:
Property Index
Name
Value
Initial
Applies to
Inh.
%ages
Animation type
Canonical order
Computed value
Used value
backface-visibility
visible | hidden
visible
transformable elements
no
N/A
discrete
per grammar
specified keyword
perspective
none |
none
transformable elements
no
N/A
by computed value
per grammar
the keyword none or an absolute length
perspective-origin
50% 50%
transformable elements
no
refer to the size of the reference box
by computed value
per grammar
see background-position
rotate
none |
none
transformable elements
no
n/a
as SLERP, but see below for none
per grammar
the keyword none, or an
scale
none | [
none
transformable elements
no
n/a
by computed value, but see below for none
per grammar
the keyword none, or a list of 3
transform-style
flat | preserve-3d
flat
transformable elements
no
N/A
discrete
per grammar
specified keyword
flat if a grouping property is present, specified keyword otherwise
translate
none |
none
transformable elements
no
relative to the width of the reference box (for the first value) or the height (for the second value)
by computed value, but see below for none
per grammar
the keyword none or a pair of computed
Issues Index
describe how nested 3d-transformed elements render (perhaps with math)
This example doesn’t follow from the previous text.
is it OK to not pop 2D-transformed elements into their own planes?
what is the impact of backface-visibility on non-transformed or 2D-transformed elements? Do they get popped into their own planes and intersect?
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
#912
Verify that projection is the distance to the center of projection.
We don’t really need to be a stacking context or containing block for perspective, but maybe webcompat means we can’t change this.
Backface-visibility cannot be tested by only looking at m33. See
#917
formally describe the syntax of the 3D transform functions in SVG,
as is done
for the 2-D functions
Per
the WG resolved to add a formula for decomposing a transform into a unified "scale"
(the spec already defines how to decompose it into scaleX/Y/Z),
for use by things like SVG’s non-scaling stroke spec.
Formula is defined here.
MDN
backface-visibility
In all current engines.
Firefox
16+
Safari
15.4+
Chrome
36+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
37+
Samsung Internet
Opera Mobile
MDN
perspective-origin
In all current engines.
Firefox
16+
Safari
9+
Chrome
36+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
9+
Chrome for Android
Android WebView
4.4+
Samsung Internet
Opera Mobile
MDN
perspective
In all current engines.
Firefox
16+
Safari
9+
Chrome
36+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
9+
Chrome for Android
Android WebView
4.4+
Samsung Internet
Opera Mobile
MDN
rotate
In all current engines.
Firefox
72+
Safari
14.1+
Chrome
104+
Opera
Edge
104+
Edge (Legacy)
IE
None
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
Samsung Internet
Opera Mobile
scale
In all current engines.
Firefox
72+
Safari
14.1+
Chrome
104+
Opera
Edge
104+
Edge (Legacy)
IE
None
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
Samsung Internet
Opera Mobile
translate
In all current engines.
Firefox
72+
Safari
14.1+
Chrome
104+
Opera
Edge
104+
Edge (Legacy)
IE
None
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
Samsung Internet
Opera Mobile
MDN
transform-style
In all current engines.
Firefox
16+
Safari
9+
Chrome
36+
Opera
Edge
79+
Edge (Legacy)
12+
IE
None
Firefox for Android
iOS Safari
9+
Chrome for Android
Android WebView
4.4+
Samsung Internet
Opera Mobile
MDN
transform
In all current engines.
Firefox
16+
Safari
9+
Chrome
36+
Opera
23+
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
9+
Chrome for Android
Android WebView
4.4+
Samsung Internet
Opera Mobile
24+
transform-function
In all current engines.
Firefox
3.5+
Safari
3.1+
Chrome
1+
Opera
10.5+
Edge
79+
Edge (Legacy)
12+
IE
9+
Firefox for Android
iOS Safari
3.2+
Chrome for Android
Android WebView
2+
Samsung Internet
Opera Mobile
11+
MDN
transform-function/matrix3d
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
10+
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/perspective
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/rotate3d
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/rotateX
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/rotateY
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/rotateZ
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/scale3d
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/scaleZ
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/translate3d
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile
MDN
transform-function/translateZ
In all current engines.
Firefox
10+
Safari
4+
Chrome
12+
Opera
Edge
79+
Edge (Legacy)
12+
IE
10+
Firefox for Android
iOS Safari
Chrome for Android
Android WebView
3+
Samsung Internet
Opera Mobile