CSS Transforms Module Level 1

1. Introduction

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 transform property. Using transform, elements can be translated, rotated and scaled.

1.1. Module Interactions

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 [CSS2]. Some values of these properties result in the creation of a containing block, and/or the creation of a stacking context.

Transforms affect the rendering of backgrounds on elements with a value of fixed for the background-attachment property, which is specified in [CSS3BG].

Transforms affect the client rectangles returned by the Element Interface Extensions getClientRects() and getBoundingClientRect(), which are specified in [CSSOM-VIEW].

Transforms affect the computation of the scrollable overflow region as described by [CSS-OVERFLOW-3].

1.2. CSS Values

This specification follows the CSS property definition conventions from [CSS2] 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. Terminology {#terminology}

When used in this specification, terms have the meanings assigned in this section.

2. The Transform Rendering Model

This section is normative.

Specifying a value other than none for the transform 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.

The transformation matrix is computed from the transform and transform-origin properties as follows:

1. Start with the identity matrix.

2. Translate by the computed X and Y of transform-origin

3. Multiply by each of the transform functions in transform property from left to right

4. Translate by the negated computed X and Y values of transform-origin

div {
  transform-origin: 0 0;
  transform: translate(-10px, -20px) scale(2) rotate(45deg);
}

Transforms apply to transformable elements.

The coordinate space is a coordinate system with two axes: the X axis increases horizontally to the right; the Y axis increases vertically downwards.

Transformations are cumulative. That is, elements establish their local coordinate system within the coordinate system of their parent.

To map a point p_local with the coordinate pair x_local and y_local from the local coordinate system of an element into the parent’s coordinate system, post-multiply the transformation matrix TM of the element by p_local. The result is the mapped point p_parent with the coordinate pair x_parent and y_parent in the parent’s local coordinate system.

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.

The current transformation matrix is computed by post-multiplying all transformation matrices starting from the viewport coordinate system and ending with the transformation matrix of an element.

<svg xmlns="http://www.w3.org/2000/svg">
  <g transform="translate(-10, 20)">
    <g transform="scale(2)">
      <rect width="200" height="200" transform="rotate(45)"/>
    </g>
  </g>
</svg>

Note: Transformations do affect the visual rendering, but have no effect on the CSS layout other than affecting overflow. Transforms are also taken into account when computing client rectangles exposed via the Element Interface Extensions, namely getClientRects() and getBoundingClientRect(), which are specified in [CSSOM-VIEW].

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-origin: 50px 50px;
  transform: rotate(45deg);
}

The transform-origin property moves the point of origin by 50 pixels in both the X and Y directions. The transform rotates the element clockwise by 45° about the point of origin. After all transform functions were applied, the translation of the origin gets translated back by -50 pixels in both the X and Y directions.

div {
  height: 100px; width: 100px;
  transform: translate(80px, 80px) scale(1.5, 1.5) rotate(45deg);
}

The visual appearance is as if the div element gets translated by 80px to the bottom left direction, then scaled up by 150% and finally rotated by 45°.

Each <transform-function> can get represented by a corresponding 4x4 matrix. To map a point from the coordinate space of the div box to the coordinate space of the parent element, these transforms get multiplied in the reverse order:

1. The rotation matrix gets post-multiplied by the scale matrix.

2. The result of the previous multiplication is then post-multiplied by the translation matrix to create the accumulated transformation matrix.

3. Finally, the point to map gets pre-multiplied with the accumulated transformation matrix.

For more details see The Transform Function Lists.

Note: The 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>

For elements whose layout is governed by the CSS box model, the transform property does not affect the flow of the content surrounding the transformed element. However, the extent of the overflow area takes into account transformed elements. This behavior is similar to what happens when elements are offset via relative positioning. Therefore, if the value of the overflow property is scroll or auto, scrollbars will appear as needed to see content that is transformed outside the visible area. Specifically, transforms can extend (but do not shrink) the size of the overflow area, which is computed as the union of the bounds of the elements before and after the application of transforms.

For elements whose layout is governed by the CSS box model, any value other than none for the transform property results in the creation of a stacking context. Implementations must paint the layer it creates, within its parent stacking context, at the same stacking order that would be used if it were a positioned element with z-index: 0. If an element with a transform is positioned, the z-index property applies as described in [CSS2], except that auto is treated as 0 since a new stacking context is always created.

For elements whose layout is governed by the CSS box model, any value other than none for the transform property also causes the element to establish a containing block for all descendants. Its padding box will be used to layout for all of its absolute-position descendants, fixed-position descendants, and descendant fixed background attachments.

<style>
#container {
  width: 300px;
  height: 200px;
  border: 5px dashed black;
  padding: 5px;
  overflow: scroll;
}

#bloat {
  height: 1000px;
}

#child {
  right: 0;
  bottom: 0;
  width: 10%;
  height: 10%;
  background: green;
}
</style>

<div id="container" style="transform:translateX(5px);">
  <div id="bloat"></div>
  <div id="child" style="position:fixed;"></div>
</div>

<div id="container" style="position:relative; z-index:0; left:5px;">
  <div id="bloat"></div>
  <div id="child" style="position:absolute;"></div>
</div>

When the background of an element is propagated to the canvas (see CSS Backgrounds 3 § 2.11.1 The Canvas Background and the Root Element and CSS Backgrounds 3 § 2.11.2 The Canvas Background and the HTML <body> Element), that background is not affected by any transform specified for that element or for the root element.

For elements that are effected by a transform (i.e. have a transform applied to them, or to any of their ancestor elements) and do not have their background propagated to the canvas, a value of fixed for the background-attachment property is treated as if it had a value of scroll. The computed value of background-attachment is not affected.

3. The transform Property

A transformation is applied to the coordinate system an element renders into through the transform 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.

Any computed value other than none for the transform affects containing block and stacking context, as described in § 2 The Transform Rendering Model.

<transform-list> = <transform-function>+

3.1. Serialization of <transform-function>s

To serialize the <transform-function>s, serialize as per their individual grammars, in the order the grammars are written in, avoiding <calc()> expressions where possible, avoiding <calc()> transformations, omitting components when possible without changing the meaning, joining space-separated tokens with a single space, and following each serialized comma with a single space.

3.2. Resolved value of transform

The transform property is a resolved value special case property. [CSSOM]

When the computed value is a <transform-list>, the resolved value is one <matrix()> function computed by the following algorithm:

1. Let transform be a 4x4 matrix initialized to the identity matrix. The elements m11, m22, m33 and m44 of transform must be set to 1; all other elements of transform must be set to 0.

2. Post-multiply all <transform-function>s in <transform-list> to transform.

3. Serialize transform to a <matrix()> function.

For other computed values, the resolved value is the computed value.

4. The transform-origin Property

The values of the transform and transform-origin properties are used to compute the transformation matrix, as described above.

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 two or more values are defined and either no value is a keyword, or the only used keyword is center, then the first value represents the horizontal position (or offset) and the second represents the vertical position (or offset). A third value always represents the Z position (or offset) and must be of type <length>.

<length-percentage>

A percentage for the horizontal offset is relative to the width of the reference box. A percentage for the vertical offset is relative to the 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.

<length>

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.

right

Computes to 100% for the horizontal position.

bottom

Computes to 100% for the vertical position.

left

Computes to 0% for the horizontal position.

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.

For SVG elements without associated CSS layout box the initial used value is 0 0 as if the user agent style sheet contained:

*:not(svg), *:not(foreignObject) > svg {
    transform-origin: 0 0;
}

The transform-origin property is a resolved value special case property like height. [CSSOM]

5. Transform reference box: the transform-box property

All transformations defined by the transform and transform-origin property are relative to the position and dimensions of the reference box of the element. The reference box is specified by one of the following:

content-box

Uses the content box as reference box. The reference box of a table is the border box of its table wrapper box, not its table box.

border-box

Uses the border box as reference box. The reference box of a table is the border box of its table wrapper box, not its table box.

fill-box

Uses the object bounding box as reference box.

stroke-box

Uses the stroke bounding box as reference box.

view-box

Uses the nearest SVG viewport as reference box.

If a viewBox attribute is specified for the SVG viewport creating element:

• The reference box is positioned at the origin of the coordinate system established by the viewBox attribute.

• The dimension of the reference box is set to the width and height values of the viewBox attribute.

For the SVG pattern element, the reference box gets defined by the patternUnits attribute [SVG2].

For the SVG linearGradient and radialGradient elements, the reference box gets defined by the gradientUnits attribute [SVG2].

For the SVG clipPath element, the reference box gets defined by the clipPathUnits attribute [CSS-MASKING].

A reference box adds an additional offset to the origin specified by the transform-origin property.

For SVG elements without associated CSS layout box, the used value for content-box is fill-box and for border-box is stroke-box.

For elements with associated CSS layout box, the used value for fill-box is content-box and for stroke-box and view-box is border-box.

6. The SVG transform Attribute

6.1. SVG presentation attributes

The transform-origin CSS property is also a presentation attribute and extends the list of existing presentation attributes [SVG2].

SVG 2 defines the transform, patternTransform, gradientTransform attributes as presentation attributes, represented by the CSS transform property [SVG2].

The participation in the CSS cascade is determined by the specificity of presentation attributes in the SVG specification. According to SVG, user agents conceptually insert a new author style sheet for presentation attributes, which is the first in the author style sheet collection [SVG2].

This example shows the combination of the transform style property and the transform attribute.

<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 transform style property overrides the transform attribute. Therefore the container gets translated by 100px in both the horizontal and the vertical directions, instead of 200px.

6.2. Syntax of the SVG transform attribute

For backwards compatibility reasons, the syntax of the transform, patternTransform, gradientTransform attributes differ from the syntax of the transform CSS property. For the attributes, there is no support for additional <transform-function>s defined for the CSS transform property. Specifically, <translateX()>, <translateY()>, <scaleX()>, <scaleY()> and <skew()> are not supported by the transform, patternTransform, gradientTransform attributes.

The following list uses the Backus-Naur Form (BNF) to define values for the transform, patternTransform and gradientTransform attributes followed by an informative rail road diagram. The following notation is used:

• *: 0 or more

• +: 1 or more

• ?: 0 or 1

• (): grouping

• |: separates alternatives

• double quotes surround literals. Literals consists of letters [CSS-SYNTAX-3], left parenthesis and right parenthesis.

• <number-token> defined by the CSS Syntax module [CSS-SYNTAX-3].

Note: The syntax reflects implemented behavior in user agents and differs from the syntax defined by SVG 1.1.

left parenthesis (

U+0028 LEFT PARENTHESIS

right parenthesis )

U+0029 RIGHT PARENTHESIS

comma

U+002C COMMA.

wsp

Either a U+000A LINE FEED, U+000D CARRIAGE RETURN, U+0009 CHARACTER TABULATION, or U+0020 SPACE.

comma-wsp

(wsp+ comma? wsp*) | (comma wsp*)

translate

"translate" wsp* "(" wsp* number ( comma-wsp? number )? wsp* ")"

scale

"scale" wsp* "(" wsp* number ( comma-wsp? number )? wsp* ")"

rotate

"rotate" wsp* "(" wsp* number ( comma-wsp? number comma-wsp? number )? wsp* ")"

skewX

"skewX" wsp* "(" wsp* number wsp* ")"

skewY

"skewY" wsp* "(" wsp* number wsp* ")"

matrix

"matrix" wsp* "(" wsp*
    number comma-wsp?
    number comma-wsp?
    number comma-wsp?
    number comma-wsp?
    number comma-wsp?
    number wsp* ")"
  

transform

matrix
| translate
| scale
| rotate
| skewX
| skewY
  

transforms

transform
| transform comma-wsp? transforms
  

transform-list

wsp* transforms? wsp*

6.3. SVG transform functions

SVG transform functions of the transform, patternTransform, gradientTransform attributes defined by the syntax above are mapped to CSS <transform-function>s as follows:

The SVG transform function rotate with 3 values can not be mapped to a corresponding CSS <transform-function>. The 2 optional number values represent a horizontal translation value cx followed by a vertical translation value cy. Both number values get interpreted as CSS <length> types with px units and define the origin for rotation. The behavior is equivalent to an initial translation by cx, cy, a rotation defined by the first number value interpreted as <angle> type with deg unit followed by a translation by -cx, -cy.

A transform attribute can be the start or end value of a CSS Transition. If the value of a transform attribute is the start or end value of a CSS Transition and the SVG transform list contains at least one rotate transform function with 3 values, the individual SVG transform functions must get post-multiplied and the resulting matrix must get mapped to a <matrix()> CSS <transform-function> and used as start/end value of the CSS Transition.

6.4. User coordinate space

For the pattern element, the patternTransform attribute and transform property define an additional transformation in the pattern coordinate system. See patternUnits attribute for details [SVG2].

For the linearGradient and radialGradient elements, the gradientTransform attribute and transform property define an additional transformation in the gradient coordinate system. See gradientUnits attribute for details [SVG2].

For the clipPath element, the transform attribute and transform property define an additional transformation in the clipping path coordinate space. See clipPathUnits attribute for details [CSS-MASKING].

For all other transformable elements the transform attribute and transform property define a transformation in the current user coordinate system of the parent. All percentage values of the transform attribute are relative to the element’s reference box.

<svg xmlns="http://www.w3.org/2000/svg">
  <style>
  pattern {
    transform: 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="200" height="200" fill="url(#pattern-1)" />
</svg>

6.5. SVG DOM interface for the transform attribute

The SVG specification defines the "SVGAnimatedTransformList" interface in the SVG DOM to provide access to the animated and the base value of the SVG transform, gradientTransform and patternTransform attributes. To ensure backwards compatibility, this API must still be supported by user agents.

baseVal gives the author the possibility to access and modify the values of the SVG transform, patternTransform, gradientTransform attributes. To provide the necessary backwards compatibility to the SVG DOM, baseVal must reflect the values of this author style sheet. All modifications to SVG DOM objects of baseVal must affect this author style sheet immediately.

animVal represents the computed style of the transform 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 animVal can not be modified.

7. The Transform Functions

The value of the transform property is a list of <transform-function>. The set of allowed transform functions is given below. In the following functions, a <zero> behaves the same as 0deg ("unitless 0" angles are preserved for legacy compat). 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.

7.1. 2D Transform Functions

matrix() = matrix( <number>#{6} )

specifies a 2D transformation in the form of a transformation matrix of the six values a, b, c, d, e, f.

translate() = translate( <length-percentage> , <length-percentage>? )

specifies a 2D translation by the vector [tx, ty], where tx is the first translation-value parameter and ty is the optional second translation-value parameter. If <ty> is not provided, ty has zero as a value.

translateX() = translateX( <length-percentage> )

specifies a translation by the given amount in the X direction.

translateY() = translateY( <length-percentage> )

specifies a translation by the given amount in the Y direction.

scale() = scale( <number> , <number>? )

specifies a 2D scale operation by the [sx,sy] scaling vector described by the 2 parameters. If the second parameter is not provided, it takes a value equal to the first. For example, scale(1, 1) would leave an element unchanged, while scale(2, 2) would cause it to appear twice as long in both the X and Y axes, or four times its typical geometric size.

scaleX() = scaleX( <number> )

specifies a 2D scale operation using the [sx,1] scaling vector, where sx is given as the parameter.

scaleY() = scaleY( <number> )

specifies a 2D scale operation using the [1,sy] scaling vector, where sy is given as the parameter.

rotate() = rotate( [ <angle> | <zero> ] )

specifies a 2D rotation by the angle specified in the parameter about the origin of the element, as defined by the transform-origin property. For example, rotate(90deg) would cause elements to appear rotated one-quarter of a turn in the clockwise direction.

skew() = skew( [ <angle> | <zero> ] , [ <angle> | <zero> ]? )

specifies a 2D skew by [ax,ay] for X and Y. If the second parameter is not provided, it has a zero value.

skew() exists for compatibility reasons, and should not be used in new content. Use skewX() or skewY() instead, noting that the behavior of skew() is different from multiplying skewX() with skewY().

skewX() = skewX( [ <angle> | <zero> ] )

specifies a 2D skew transformation along the X axis by the given angle.

skewY() = skewY( [ <angle> | <zero> ] )

specifies a 2D skew transformation along the Y axis by the given angle.

7.2. 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. Two-dimensional primitives and their derived transform functions are:

translate()

for <translateX()>, <translateY()> and <translate()>.

scale()

for <scaleX()>, <scaleY()> and <scale()>.

8. The Transform Function Lists

If a list of <transform-function>s is provided, then the net effect is as if each transform function had been specified separately in the order provided.

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 coordinate system of the ancestor to the local coordinate system of a given element. The resulting transform is the matrix multiplication of the list of transforms.

<div style="transform: translate(-10px, -20px) scale(2) rotate(45deg)"/>

<div style="transform: translate(-10px, -20px)" id="root">
  <div style="transform: scale(2)">
    <div style="transform: rotate(45deg)">
    </div>
  </div>
</div>

If a transform function causes the current transformation matrix of an object to be non-invertible, the object and its content do not get displayed.

<style>
.box {
  transform: scale(0);
}
</style>

<div class="box">
  Not visible
</div>

9. Interpolation of Transforms

Interpolation of transform function lists is performed as follows:

• If both V_a and V_b are none:

  • V_result is none.

• Treating none as a list of zero length, if V_a or V_b differ in length:

  • extend the shorter list to the length of the longer list, setting the function at each additional position to the identity transform function matching the function at the corresponding position in the longer list. Both transform function lists are then interpolated following the next rule.

  For example, if V_a is scale(2) and V_b is none then the value scale(1) will be used for V_b and interpolation will proceed using the next rule. Similarly, if V_a is scale(1) and V_b is scale(2) rotate(50deg) then the interpolation will be performed as if V_a were scale(1) rotate(0).
• Let V_result be an empty list. Beginning at the start of V_a and V_b, compare the corresponding functions at each position:

  • While the functions have either the same name, or are derivatives of the same primitive transform function, interpolate the corresponding pair of functions as described in § 10 Interpolation of primitives and derived transform functions and append the result to V_result.

  • If the pair do not have a common name or primitive transform function, post-multiply the remaining transform functions in each of V_a and V_b respectively to produce two 4x4 matrices.