This specification provides basic geometric interfaces to represent points, rectangles, quadrilaterals and transformation matrices that can be used by other modules or specifications.
CSS is a language for describing the rendering of structured documents
(such as HTML and XML)
on screen, on paper, in speech, etc.
Status of this document
This section describes the status of this document at the time of
its publication. Other documents may supersede this document. A list of
current W3C publications and the latest revision of this technical report
can be found in the W3C technical reports
index at http://www.w3.org/TR/.
Publication as a Working Draft does not imply endorsement by the W3C
Membership. This is a draft document and may be updated, replaced or
obsoleted by other documents at any time. It is inappropriate to cite this
document as other than work in progress.
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The following features are at-risk, and may be dropped during the CR period:
The DOMRectList interface is at-risk. The authors of this specification await feedback from implementers if the item() function of DOMRectList is currently in use on legacy interfaces. If there is no/not enough content to justify DOMRectList, legacy interfaces must use sequences instead and DOMRectList will be removed from this specification.
This specification describes several geometry interfaces [WEBIDL] for the representation of points, rectangles, quadrilaterals and transformation matrices with the dimension of 3x2 and 4x4.
The SVG interfaces SVGPoint, SVGRect and SVGMatrix [SVG11] are aliasing the here defined interfaces in favor for common interfaces used by SVG, Canvas 2D Context [2DCONTEXT] and CSS Transforms [CSS3-TRANSFORMS].
2
The DOMPoint interfaces
A 2D or a 3D point can be represented by the following WebIDL interfaces:
The following algorithms assume that DOMPointReadOnly objects have the internal member variables x coordinate, y coordinate, z coordinate and w perspective. DOMPointReadOnly as well as the inheriting interface DOMPoint must be able to access and set the value of these variables.
An interface returning an DOMPointReadOnly object by an attribute or function may be able to modify internal member variable values. Such an interface must specify this ability explicitly in prose.
Internal member variables must not be exposed in any way.
The DOMPointReadOnly(x, y, z, w) constructor, when invoked, must run the following steps:
The x attribute, on getting, must return the x coordinate value of the object it was invoked on. For the DOMPoint interface, setting the x attribute must set the x coordinate value of the object it was invoked on to the new value.
The y attribute, on getting, must return the y coordinate value of the object it was invoked on. For the DOMPoint interface, setting the y attribute must set the y coordinate value of the object it was invoked on to the new value.
The z attribute, on getting, must return the z coordinate value of the object it was invoked on. For the DOMPoint interface, setting the z attribute must set the z coordinate value of the object it was invoked on to the new value.
The w attribute, on getting, must return the w perspective value of the object it was invoked on. For the DOMPoint interface, setting the w attribute must set the w perspective value of the object it was invoked on to the new value.
matrixTransform(matrix), when invoked, must run the following steps
Create a new DOMPointpoint initialized to x, y, z and w of the current point.
var point = new DOMPoint(5, 4);
var matrix = new DOMMatrix(2, 0, 0, 2, 10, 10);
var transformedPoint = point.matrixTransform(matrix);
point creates a new DOMPoint object initialized to the same attribute values as point. This new DOMPoint is now scaled and the translated by matrix. This resulting transformPoint has the attribute values x: 20 and y: 18.
For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGPoint whose value is the DOMPoint interface object.
3
The DOMRect interfaces
Objects implementing the DOMRectReadOnly interface represent a rectangle. The type of box is specified by the method or attribute that returns a DOMRect or DOMRectReadOnly object.
Rectangles have the following properties:
origin
When the rectangle has a non-negative width, the rectangle’s horizontal origin is the left edge; otherwise, it is the right edge. Similarly, when the rectangle has a non-negative height, the rectangle’s vertical origin is the top edge; otherwise, it is the bottom edge.
x coordinate
The horizontal distance between the viewport’s left edge and the rectangle’s origin.
y coordinate
The vertical distance between the viewport’s top edge and the rectangle’s origin.
An interface returning an DOMRectReadOnly object by an attribute or function may be able to modify internal member variable values. Such an interface must specify this ability explicitly in prose.
Internal member variables must not be exposed in any way.
The DOMRectReadOnly(x, y, width, height) constructor, when invoked, must run the following steps:
The x attribute, on getting, must return the x coordinate value of the object it was invoked on. For the DOMRect interface, setting the x attribute must set the x coordinate value of the object it was invoked on to the new value.
The y attribute, on getting, it must return the y coordinate value of the object it was invoked on. For the DOMRect interface, setting the y attribute must set the y coordinate value of the object it was invoked on to the new value.
The width attribute, on getting, must return the width value of the object it was invoked on. For the DOMRect interface, setting the width attribute must set the width dimension value of the object it was invoked on to the new value.
The height attribute, on getting, must return the height value. For the DOMRect interface, setting the height attribute must set the height dimension value to the new value.
For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGRect whose value is the DOMRect interface object.
4
The DOMRectList Interface
[NoInterfaceObject,
ArrayClass]
interface DOMRectList {
readonly attribute unsigned long length;
getter DOMRect? item(unsigned long index);
};
The length attribute must return the total number of DOMRect objects associated with the object.
The item(index) method, when invoked, must return a null value when index is greater than or equal to the number of DOMRect objects associated with the DOMRectList. Otherwise, the DOMRect object at index must be returned. Indices are zero-based.
DOMRectList must be supported for legacy reasons. New interfaces must not use DOMRectList and may use Sequences [WEBIDL] instead.
5
The DOMQuad interface
Objects implementing the DOMQuad interface represents a quadrilateral.
Note: It is possible to pass DOMPoint/DOMPointReadOnly arguments as well. The passed arguments will be transformed to the correct object type internally following the WebIDL rules [WEBIDL].
The p1 attribute must return a DOMPoint that represents p1 of the quadrilateral it was invoked on. The author can modify the returned DOMPoint object, which directly affects the quadrilateral.
The p2 attribute must return a DOMPoint that represents p2 of the quadrilateral it was invoked on. The author can modify the returned DOMPoint object, which directly affects the quadrilateral.
The p3 attribute must return a DOMPoint that represents p3 of the quadrilateral it was invoked on. The author can modify the returned DOMPoint object, which directly affects the quadrilateral.
The p4 attribute must return a DOMPoint that represents p4 of the quadrilateral it was invoked on. The author can modify the returned DOMPoint object, which directly affects the quadrilateral.
The DOMMatrix and DOMMatrixReadOnly interfaces each represent a mathematical matrix with the purpose of describing transformations in a graphical context. The following sections describe the details of the interface.
A 4x4 matrix representing a DOMMatrix with items m11 to m44.
In the following sections, terms have the following meaning:
post-multiply
Term A post-multiplied by term B is equal to A · B.
pre-multiply
Term A pre-multiplied by term B is equal to B · A.
The following algorithms assume that DOMMatrixReadOnly objects have the internal member variables m11 element, m12 element, m13 element, m14 element, m21 element, m22 element, m23 element, m24 element, m31 element, m32 element, m33 element, m34 element, m41 element, m42 element, m43 element, m44 element and is2D. DOMMatrixReadOnly as well as the inheriting interface DOMMatrix must be able to access and set the value of these variables.
An interface returning an DOMMatrixReadOnly object by an attribute or function may be able to modify internal member variable values. Such an interface must specify this ability explicitly in prose.
Internal member variables must not be exposed in any way.
For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGMatrix whose value is the DOMMatrix interface object.
6.1 DOMMatrixReadOnly constructor
The DOMMatrixReadOnly(sequence<unrestricted double> numberSequence) constructor, when invoked, must run the following steps:
Let matrix be a 4x4 matrix as shown in the initial figure of this section. Post-multiply all matrices from left to right and set matrix to this product.
Call the constructor of DOMMatrixReadOnly with a sequence of numbers, the values being the 16 elements of matrix.
If 2dTransform is set to false
Call the constructor of DOMMatrixReadOnly with a sequence of numbers, the values being the elements m11, m12, 21, m22, m41 and m42 of matrix of matrix.
The following attributes m11 to m44 correspond to the 16 items of the matrix interfaces. For the DOMMatrix interface, if the attributes m31, m32, m13, m23, m43, m14, m24, m34 are set to something else than 0 or m33, m44 are set to something else than 1 set is2D to false.
The m11 attribute, on getting, must return the m11 element value of the object it was invoked on. For the DOMMatrix interface, setting the m11 attribute must set the m11 element value of the object it was invoked on to the new value.
The m12 attribute, on getting, must return the m12 element value of the object it was invoked on. For the DOMMatrix interface, setting the m12 attribute must set the m12 element value of the object it was invoked on to the new value.
The m13 attribute, on getting, must return the m13 element value of the object it was invoked on. For the DOMMatrix interface, setting the m13 attribute must set the m13 element value of the object it was invoked on to the new value.
The m14 attribute, on getting, must return the m14 element value of the object it was invoked on. For the DOMMatrix interface, setting the m14 attribute must set the m14 element value of the object it was invoked on to the new value.
The m21 attribute, on getting, must return the m21 element value of the object it was invoked on. For the DOMMatrix interface, setting the m21 attribute must set the m21 element value of the object it was invoked on to the new value.
The m22 attribute, on getting, must return the m22 element value of the object it was invoked on. For the DOMMatrix interface, setting the m22 attribute must set the m22 element value of the object it was invoked on to the new value.
The m23 attribute, on getting, must return the m23 element value of the object it was invoked on. For the DOMMatrix interface, setting the m23 attribute must set the m23 element value of the object it was invoked on to the new value.
The m24 attribute, on getting, must return the m24 element value of the object it was invoked on. For the DOMMatrix interface, setting the m24 attribute must set the m24 element value of the object it was invoked on to the new value.
The m31 attribute, on getting, must return the m31 element value of the object it was invoked on. For the DOMMatrix interface, setting the m31 attribute must set the m31 element value of the object it was invoked on to the new value.
The m32 attribute, on getting, must return the m32 element value of the object it was invoked on. For the DOMMatrix interface, setting the m32 attribute must set the m32 element value of the object it was invoked on to the new value.
The m33 attribute, on getting, must return the m33 element value of the object it was invoked on. For the DOMMatrix interface, setting the m33 attribute must set the m33 element value of the object it was invoked on to the new value.
The m34 attribute, on getting, must return the m34 element value of the object it was invoked on. For the DOMMatrix interface, setting the m34 attribute must set the m34 element value of the object it was invoked on to the new value.
The m41 attribute, on getting, must return the m41 element value of the object it was invoked on. For the DOMMatrix interface, setting the m41 attribute must set the m41 element value of the object it was invoked on to the new value.
The m42 attribute, on getting, must return the m42 element value of the object it was invoked on. For the DOMMatrix interface, setting the m42 attribute must set the m42 element value of the object it was invoked on to the new value.
The m43 attribute, on getting, must return the m43 element value of the object it was invoked on. For the DOMMatrix interface, setting the m43 attribute must set the m43 element value of the object it was invoked on to the new value.
The m44 attribute, on getting, must return the m44 element value of the object it was invoked on. For the DOMMatrix interface, setting the m44 attribute must set the m44 element value of the object it was invoked on to the new value.
The following attributes a to f correspond to the 2D components of the matrix interfaces.
The following methods do not modify the current matrix.
transformPoint(point)
The point argument is post-multiplied to the current matrix and returns the resulting point. The passed argument does not get modified.
Note: Even if is2D of the current matrix may return true, a 4x4 matrix multiplication must be performed if the z attribute of point is not 0 or the w attribute of point is not 1.
Return a DOMString in the form of a CSS Transforms <matrix()> function where a is a attribute, b is b attribute, c is c attribute, d is d attribute, e is e attribute, f is f attribute, [CSS3-TRANSFORMS].
Otherwise
Return a DOMString in the form of a CSS Transforms <matrix3d()> function where m11 to m44 are set to m11 to m44 attributes [CSS3-TRANSFORMS].
In this example, a matrix is created and several 2D transformation methods are called:
var matrix = new DOMMatrix();
matrix.scaleSelf(2);
matrix.translateSelf(20,20);
Calling matrix.toString() returns the DOMString:
"matrix(2, 0, 0, 2, 20, 20)"
In the following example, a matrix is created and several 3D transformation methods are called:
var matrix = new DOMMatrix();
matrix.scale3dSelf(2);
For 3D operations, the stringifier returns a DOMString representing a 3D matrix.
Calling matrix.toString() after the snippet above returns the DOMString:
The following methods modify the current matrix, so that each method returns the matrix where it was invoked on. The primary benefit of this is allowing content creators to chain method calls.
The following code example:
var matrix = new DOMMatrix();
matrix.translateSelf(20, 20);
matrix.scaleSelf(2);
matrix.translateSelf(-20, -20);
is equivalent to:
var matrix = new DOMMatrix();
matrix.translateSelf(20, 20).scaleSelf(2).translateSelf(-20, -20);
Note: Authors who use chained method calls are recommended to use mutable transformation methods to avoid unnecessary memory allocations due to creation of intermediate DOMMatrix objects in User Agents.
multiplySelf(other)
The other matrix gets post-multiplied to the current matrix.
If is2D of other is false, set is2D of the current matrix to false.
Return the current matrix.
preMultiplySelf(other)
The other matrix gets pre-multiplied to the current matrix.
If is2D of other is false, set is2D of the current matrix to false.
Return the current matrix.
translateSelf(tx, ty, tz)
Post-multiply a translation transformation on the current matrix. The 3D translation matrix is described in CSS Transforms [CSS3-TRANSFORMS].
If tz is specified and not 0, set is2D of the current matrix to false.
Post-multiply a uniform 2D scale transformation (m11 = m22 = scale) on the current matrix. The 2D scale matrix is described in CSS Transforms with sx = sy = scale. [CSS3-TRANSFORMS].
Post-multiply a uniform 3D scale transformation (m11 = m22 = m33 = scale) on the current matrix. The 3D scale matrix is described in CSS Transforms with sx = sy = sz = scale. [CSS3-TRANSFORMS].
Post-multiply a non-uniform scale transformation on the current matrix. The 3D scale matrix is described in CSS Transforms with sx = scaleX, sy = scaleY and sz = scaleZ. [CSS3-TRANSFORMS].
Post-multiply a rotation transformation on the current matrix with the specified rotation angle in degrees. The 2D rotation matrix is described in CSS Transforms with alpha = angle in degrees. [CSS3-TRANSFORMS].
Post-multiply a rotation transformation on the current matrix. The rotation angle is determined by the angle between the vector (1,0)T and (x,y)T in the clockwise direction. If x and y should both be zero, the angle is specified as zero. The 2D rotation matrix is described in CSS Transforms where alpha is the angle between the vector (1,0)T and (x,y)T in degrees [CSS3-TRANSFORMS].
Return the current matrix.
rotateAxisAngleSelf(x, y, z, angle)
Post-multiply a rotation transformation on the current matrix around the specified vector x, y, z by the specified rotation angle in degrees. The 3D rotation matrix is described in CSS Transforms with alpha = angle in degrees [CSS3-TRANSFORMS].
If x or y are not 0, set is2D of the current matrix to false.
Return the current matrix.
skewXSelf(sx)
Post-multiply a skewX transformation on the current matrix by the specified angle sx in degrees. The 2D skewX matrix is described in CSS Transforms with alpha = sx in degrees [CSS3-TRANSFORMS].
Return the current matrix.
skewYSelf(sy)
Post-multiply a skewX transformation on the current matrix by the specified angle sy in degrees. The 2D skewY matrix is described in CSS Transforms with beta = sy in degrees [CSS3-TRANSFORMS].
Return the current matrix.
invertSelf()
Invert the current matrix.
If the current matrix is not invertible set all attributes to NaN and set is2D to false.
The editors would like to thank Robert O’Callahan for contributing to this specification. Many thanks to Dean Jackson for his initial proposal of DOMMatrix. Thanks to Brian Birtles, Benoit Jacob, Cameron McCormack, Kari Pihkala, Adenilson Cavalcanti, Boris Zbarsky and Max Vujovic for their careful reviews, comments, and corrections.
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 <strong class="advisement">, like
this:
UAs MUST provide an accessible alternative.
Conformance classes
Conformance to this specification
is defined for three conformance classes:
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.
Experimental implementations
To avoid clashes with future CSS features, the CSS2.1 specification
reserves a prefixed
syntax for proprietary and experimental extensions to CSS.
Prior to a specification reaching the Candidate Recommendation stage
in the W3C process, all implementations of a CSS feature are considered
experimental. The CSS Working Group recommends that implementations
use a vendor-prefixed syntax for such features, including those in
W3C Working Drafts. This avoids incompatibilities with future changes
in the draft.
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.