Geometry Interfaces Module Level 1

W3C Candidate Recommendation, 25 November 2014

This version:: http://www.w3.org/TR/2014/CR-geometry-1-20141125/
Latest version:: http://www.w3.org/TR/geometry-1/
Editor's Draft:: http://dev.w3.org/fxtf/geometry/
Previous Versions:: http://www.w3.org/TR/2014/WD-geometry-1-20140918/
Feedback:: public-fx@w3.org with subject line “[geometry] … message topic …” (archives)
Test Suite:: http://test.csswg.org/suites/geometry-1_dev/nightly-unstable/
Editors:: Simon Pieters (Opera Software ASA); Dirk Schulze (Adobe Systems Inc.); Rik Cabanier (Adobe Systems Inc.)
Issues list:: Bugzilla (file a bug)

Abstract

This specification provides basic geometric interfaces to represent points, rectangles, quadrilaterals and transformation matrices that can be used by other modules or specifications.

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/.

This document was produced by the CSS Working Group (part of the Style Activity) and the SVG Working Group (part of the Graphics Activity) as a Candidate Recommendation.

A Candidate Recommendation is a document that has been widely reviewed and is ready for implementation. W3C encourages everybody to implement this specification and return comments to the (archived) public mailing list public-fx@w3.org (see instructions). When sending e-mail, please put the text “geometry” in the subject, preferably like this: “[geometry] …summary of comment…”

Publication as a Candidate Recommendation 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.

This document was produced by groups operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures (CSS) and a public list of any patent disclosures (SVG) made in connection with the deliverables of each group; these pages also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

This document is governed by the 1 August 2014 W3C Process Document.

A test suite and implementation report for Geometry Interfaces Module Level 1 will be developed during the Candidate Recommendation phase, which will last a minimum of six months, and at least until 6 May 2015. A preliminary implementation report is available, although there are few tests as yet. See the section “CR exit criteria” for more details.

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.

1. Introduction

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:

[Constructor(unrestricted double x, unrestricted double y,
             unrestricted double z, unrestricted double w),
 Exposed=(Window,Worker)]
interface DOMPointReadOnly {
    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double z;
    readonly attribute unrestricted double w;

    DOMPoint matrixTransform(DOMMatrixReadOnly matrix);
};

[Constructor(optional DOMPointInit point),
 Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double z = 0, optional unrestricted double w = 1),
 Exposed=(Window,Worker)]
interface DOMPoint : DOMPointReadOnly {
    inherit attribute unrestricted double x;
    inherit attribute unrestricted double y;
    inherit attribute unrestricted double z;
    inherit attribute unrestricted double w;
};

dictionary DOMPointInit {
    unrestricted double x = 0;
    unrestricted double y = 0;
    unrestricted double z = 0;
    unrestricted double w = 1;
};

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:

Set the the current object’s variables x coordinate to x, y coordinate to y, z coordinate to z and w perspective to w.
Return the new DOMPointReadOnly object.

The DOMPoint() constructor, when invoked, must run the following steps:

If invoked with a DOMPointInit argument

Let point be the argument.
Call the constructor of DOMPointReadOnly with the arguments x, y, z, w, where:
1. x is the x dictionary member of point.
2. y is the y dictionary member of point.
3. z is the z dictionary member of point.
4. w is the w dictionary member of point.
Return the new DOMPoint object.

Otherwise

Call the constructor of DOMPointReadOnly with the arguments x, y, z and w, respectively.
Return the new DOMPoint object.

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 DOMPoint point initialized to x, y, z and w of the current point.
Post-multiply point with matrix.
Return point.

matrixTransform() does not modify the current DOMPointReadOnly object and returns a new DOMPoint object.

In this example the method matrixTransform() on point is called with a DOMMatrix argument matrix.

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.
width dimension: The width of the rectangle. Can be negative.
height dimension: The height of the rectangle. Can be negative.

[Constructor(unrestricted double x = 0, unrestricted double y = 0,
             unrestricted double width = 0, unrestricted double height = 0),
 Exposed=(Window,Worker)]
interface DOMRect : DOMRectReadOnly {
    inherit attribute unrestricted double x;
    inherit attribute unrestricted double y;
    inherit attribute unrestricted double width;
    inherit attribute unrestricted double height;
};

[Constructor(unrestricted double x, unrestricted double y,
             unrestricted double width, unrestricted double height),
 Exposed=(Window,Worker)]
interface DOMRectReadOnly {
    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double width;
    readonly attribute unrestricted double height;
    readonly attribute unrestricted double top;
    readonly attribute unrestricted double right;
    readonly attribute unrestricted double bottom;
    readonly attribute unrestricted double left;
};

dictionary DOMRectInit {
    unrestricted double x = 0;
    unrestricted double y = 0;
    unrestricted double width = 0;
    unrestricted double height = 0;
};

The following algorithms assume that DOMRectReadOnly objects have the internal member variables x coordinate, y coordinate, width dimension and height dimension. DOMRectReadOnly as well as the inheriting interface DOMRect must be able to access and set the value of these variables.

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:

Set the the current object’s variables x coordinate to x, y coordinate to y, width dimension to width and height dimension to height.
Return the new DOMRectReadOnly object.

The DOMRect(x, y, width, height) constructor, when invoked, must run the following steps:

Call the constructor of DOMRectReadOnly with x, y, width and height.
Return the new DOMRect object.

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.

The top attribute, on getting, must return min(y coordinate, y coordinate + height dimension) of the object it was invoked on.

The right attribute, on getting, must return max(x coordinate, x coordinate + width dimension) of the object it was invoked on.

The bottom attribute, on getting, must return max(y coordinate, y coordinate + height dimension) of the object it was invoked on.

The left attribute, on getting, must return min(x coordinate, x coordinate + width dimension) of the object it was invoked on.

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.

[Constructor(optional DOMPointInit p1, optional DOMPointInit p2,
             optional DOMPointInit p3, optional DOMPointInit p4),
 Constructor(optional DOMRectInit rect),
 Exposed=(Window,Worker)]
interface DOMQuad {
    [SameObject] readonly attribute DOMPoint p1;
    [SameObject] readonly attribute DOMPoint p2;
    [SameObject] readonly attribute DOMPoint p3;
    [SameObject] readonly attribute DOMPoint p4;
    [SameObject] readonly attribute DOMRectReadOnly bounds;
};

The DOMQuad() constructor, when invoked, must run the following steps:

If invoked with one argument

Let rect be the argument.
Let x, y, width and height be the value of rect’s x, y, width and height attributes, respectively.
Let point 1 be a new DOMPoint object with x set to x, y set to y, z set to zero and w set to one.
Let point 2 be a new DOMPoint object with x set to x + width, y set to y, z set to zero and w set to one.
Let point 3 be a new DOMPoint object with x set to x + width, y set to y + height, z set to zero and w set to one.
Let point 4 be a new DOMPoint object with x set to x, y set to y + height, z set to zero and w set to one.
Return a new DOMQuad with p1 set to point 1, p2 set to point 2, p3 set to point 3 and p4 set to point 4, and let the associated bounding rectangle be bounds.

Otherwise

Let p1, p2, p3 and p4 be the given arguments, in the same order.
Let point 1 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p1.
Let point 2 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p2.
Let point 3 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p3.
Let point 4 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p4.
Return a new DOMQuad with p1 set to point 1, p2 set to point 2, p3 set to point 3 and p4 set to point 4, and let the associated bounding rectangle be bounds.

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 bounds attribute must return the associated bounding rectangle of the quadrilateral it was invoked on.

DOMQuad objects have an associated bounding rectangle set to a DOMRectReadOnly object when created. DOMQuad objects must have read and write access to the internal member variables of the associated bounding rectangle. The associated bounding rectangle is live; whenever the objects for p1, p2, p3 or p4 change, the associated bounding rectangle must update its internal member variable values as appropriate to describe the new smallest bounding box of the four points.

The associated bounding rectangle is computed as follows:

Let bounds be a DOMRectReadOnly object.
Let left be the minimum of p1.x, p2.x, p3.x and p4.x.
Let top be the minimum of p1.y, p2.y, p3.y and p4.y.
Let right be the maximum of p1.x, p2.x, p3.x and p4.x.
Let bottom be the maximum of p1.y, p2.y, p3.y and p4.y.
Let x coordinate of bounds be left, y coordinate of bounds be top, width dimension of bounds be right - left and height dimension of bounds be bottom - top.

In this example the DOMQuad constructor is called with arguments of type DOMPoint and DOMPointInit. Both arguments are accepted and can be used.

var point = new DOMPoint(2, 0);
var quad1 = new DOMQuad(point, {x: 12, y: 0}, {x: 2, y: 10}, {x: 12, y: 10});

The attribute values of the resulting DOMQuad quad1 above are also equal to the attribute values of the following DOMQuad quad2:

var rect = new DOMRect(2, 0, 10, 10);
var quad2 = new DOMQuad(rect);

This is an example of an irregular quadrilateral:

new DOMQuad({x: 40, y: 25}, {x: 180, y: 8}, {x: 210, y: 150}, {x: 10, y: 180});

An irregular quadrilateral represented by a DOMQuad. The four red colored circles represent the DOMPoint attributes p1 to p4. The dashed rectangle represents the associated bounding rectangle bounds of the DOMQuad.

6. The DOMMatrix interfaces

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.

[\begin{matrix} m_{11} & m_{21} & m_{31} & m_{41} \\ m_{12} & m_{22} & m_{32} & m_{42} \\ m_{13} & m_{23} & m_{33} & m_{43} \\ m_{14} & m_{24} & m_{34} & m_{44} \end{matrix}]

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.
multiply: Multiply term A by term B is equal to A · B.

[Constructor(sequence<unrestricted double> numberSequence),
 Exposed=(Window,Worker)]
interface DOMMatrixReadOnly {
    // These attributes are simple aliases for certain elements of the 4x4 matrix
    readonly attribute unrestricted double a;
    readonly attribute unrestricted double b;
    readonly attribute unrestricted double c;
    readonly attribute unrestricted double d;
    readonly attribute unrestricted double e;
    readonly attribute unrestricted double f;

    readonly attribute unrestricted double m11;
    readonly attribute unrestricted double m12;
    readonly attribute unrestricted double m13;
    readonly attribute unrestricted double m14;
    readonly attribute unrestricted double m21;
    readonly attribute unrestricted double m22;
    readonly attribute unrestricted double m23;
    readonly attribute unrestricted double m24;
    readonly attribute unrestricted double m31;
    readonly attribute unrestricted double m32;
    readonly attribute unrestricted double m33;
    readonly attribute unrestricted double m34;
    readonly attribute unrestricted double m41;
    readonly attribute unrestricted double m42;
    readonly attribute unrestricted double m43;
    readonly attribute unrestricted double m44;

    readonly attribute boolean is2D;
    readonly attribute boolean isIdentity;

    // Immutable transform methods
    DOMMatrix translate(unrestricted double tx,
                        unrestricted double ty,
                        optional unrestricted double tz = 0);
    DOMMatrix scale(unrestricted double scale,
                    optional unrestricted double originX = 0,
                    optional unrestricted double originY = 0);
    DOMMatrix scale3d(unrestricted double scale,
                      optional unrestricted double originX = 0,
                      optional unrestricted double originY = 0,
                      optional unrestricted double originZ = 0);
    DOMMatrix scaleNonUniform(unrestricted double scaleX,
                              optional unrestricted double scaleY = 1,
                              optional unrestricted double scaleZ = 1,
                              optional unrestricted double originX = 0,
                              optional unrestricted double originY = 0,
                              optional unrestricted double originZ = 0);
    DOMMatrix rotate(unrestricted double angle,
                     optional unrestricted double originX = 0,
                     optional unrestricted double originY = 0);
    DOMMatrix rotateFromVector(unrestricted double x,
                               unrestricted double y);
    DOMMatrix rotateAxisAngle(unrestricted double x,
                              unrestricted double y,
                              unrestricted double z,
                              unrestricted double angle);
    DOMMatrix skewX(unrestricted double sx);
    DOMMatrix skewY(unrestricted double sy);
    DOMMatrix multiply(DOMMatrix other);
    DOMMatrix flipX();
    DOMMatrix flipY();
    DOMMatrix inverse();

    DOMPoint            transformPoint(optional DOMPointInit point);
    Float32Array        toFloat32Array();
    Float64Array        toFloat64Array();
                        stringifier;
};

[Constructor,
 Constructor(DOMString transformList),
 Constructor(DOMMatrixReadOnly other),
 Constructor(Float32Array array32),
 Constructor(Float64Array array64),
 Constructor(sequence<unrestricted double> numberSequence),
 Exposed=(Window,Worker)]
interface DOMMatrix : DOMMatrixReadOnly {
    // These attributes are simple aliases for certain elements of the 4x4 matrix
    inherit attribute unrestricted double a;
    inherit attribute unrestricted double b;
    inherit attribute unrestricted double c;
    inherit attribute unrestricted double d;
    inherit attribute unrestricted double e;
    inherit attribute unrestricted double f;

    inherit attribute unrestricted double m11;
    inherit attribute unrestricted double m12;
    inherit attribute unrestricted double m13;
    inherit attribute unrestricted double m14;
    inherit attribute unrestricted double m21;
    inherit attribute unrestricted double m22;
    inherit attribute unrestricted double m23;
    inherit attribute unrestricted double m24;
    inherit attribute unrestricted double m31;
    inherit attribute unrestricted double m32;
    inherit attribute unrestricted double m33;
    inherit attribute unrestricted double m34;
    inherit attribute unrestricted double m41;
    inherit attribute unrestricted double m42;
    inherit attribute unrestricted double m43;
    inherit attribute unrestricted double m44;

    // Mutable transform methods
    DOMMatrix multiplySelf(DOMMatrix other);
    DOMMatrix preMultiplySelf(DOMMatrix other);
    DOMMatrix translateSelf(unrestricted double tx,
                     unrestricted double ty,
                     optional unrestricted double tz = 0);
    DOMMatrix scaleSelf(unrestricted double scale,
                 optional unrestricted double originX = 0,
                 optional unrestricted double originY = 0);
    DOMMatrix scale3dSelf(unrestricted double scale,
                   optional unrestricted double originX = 0,
                   optional unrestricted double originY = 0,
                   optional unrestricted double originZ = 0);
    DOMMatrix scaleNonUniformSelf(unrestricted double scaleX,
                           optional unrestricted double scaleY = 1,
                           optional unrestricted double scaleZ = 1,
                           optional unrestricted double originX = 0,
                           optional unrestricted double originY = 0,
                           optional unrestricted double originZ = 0);
    DOMMatrix rotateSelf(unrestricted double angle,
                  optional unrestricted double originX = 0,
                  optional unrestricted double originY = 0);
    DOMMatrix rotateFromVectorSelf(unrestricted double x,
                            unrestricted double y);
    DOMMatrix rotateAxisAngleSelf(unrestricted double x,
                           unrestricted double y,
                           unrestricted double z,
                           unrestricted double angle);
    DOMMatrix skewXSelf(unrestricted double sx);
    DOMMatrix skewYSelf(unrestricted double sy);
    DOMMatrix invertSelf();

    DOMMatrix setMatrixValue(DOMString transformList);
};

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.

The DOMMatrix and DOMMatrixReadOnly interfaces replace the SVGMatrix interface from SVG [SVG11].

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:

If numberSequence has 6 elements

Set m11 element, m12 element, m21 element, m22 element, m41 element, m42 element to the values of numberSequence in order starting with the first value. Furthermore, set m31 element, m32 element, m13 element, m23 element, m43 element, m14 element, m24 element, m34 element to 0 and m33 element, m44 element to 1.
Set is2D to true.
Return the new DOMMatrixReadOnly object.

If numberSequence has 16 elements

Set m11 element to m44 element to the values of numberSequence in column-major order.
Set is2D to false.
Return the new DOMMatrixReadOnly object.

Otherwise

Throw a TypeError exception.

6.2. DOMMatrix constructors

The DOMMatrix() constructor, when invoked, must run the following steps:

If invoked with no arguments

Call the constructor of DOMMatrixReadOnly with a sequence of numbers: 1, 0, 0, 1, 0, 0.
Return the new DOMMatrix object.

If invoked with a DOMString argument transformList

Parse transformList by following the syntax description in “Syntax of the SVG ‘transform’ attribute” [CSS3-TRANSFORMS] to a <transform-list>. If parsing is not successful or any <transform-function> has <length> values without absolute length units, throw a SyntaxError exception.
Let 2dTransform track the 2D/3D dimension status of the <transform-list>.

If the <transform-list> consists of any 3D Transform functions

Set 2dTransform to false.

Otherwise

Set 2dTransform to true.
Transform all <transform-function>s to 4x4 matrices by following the “Mathematical Description of Transform Functions” [CSS3-TRANSFORMS].
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 as follows

If 2dTransform is set to true

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.
Return the new DOMMatrix object.

If invoked with a DOMMatrixReadOnly argument other

If the is2D attribute of other returns true: Call the constructor of DOMMatrixReadOnly with a sequence of numbers, the values being the 16 elements m11 element, m12 element, m13 element, ..., m44 element of other in the given order.
Otherwise: Call the constructor of DOMMatrixReadOnly with a sequence of numbers, the values being the 6 elements m11 element, m12 element, m21 element, m22 element, m41 element and m42 element of other in the given order.

If invoked with a Float32Array argument array32

If array32 has 6 elements

If array32 has 16 elements

Call the constructor of DOMMatrixReadOnly with a sequence of numbers taking the values from array32 in the provided order.
Return the new DOMMatrix object.

Otherwise

Throw a TypeError exception.

If invoked with a Float64Array argument array64

If array64 has 6 elements

If array64 has 16 elements

Call the constructor of DOMMatrixReadOnly with sequence of numbers taking the values from array64 in the provided order.
Return the new DOMMatrix object.

Otherwise

Throw a TypeError exception.

If invoked with a sequence<unrestricted double> argument numberSequence

If array64 has 6 elements

If array64 has 16 elements

Call the constructor of DOMMatrixReadOnly with numberSequence as argument.
Return the new DOMMatrix object.

Otherwise

Throw a TypeError exception.

6.3. DOMMatrix attributes

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 a attribute is an alias to the m11 attribute.

The b attribute is an alias to the m12 attribute.

The c attribute is an alias to the m21 attribute.

The d attribute is an alias to the m22 attribute.

The e attribute is an alias to the m41 attribute.

The f attribute is an alias to the m42 attribute.

The following attributes provide status information about DOMMatrixReadOnly.

is2D

Every DOMMatrixReadOnly object must be flagged with a boolean is2D. This flag indicates that

The current matrix was initialized as a 2D matrix. See individual constructors for more details.
Only 2D transformation operations were applied. Each mutable or immutable transformation method defines if is2D must be set to false.

is2D can never be set to true when it was set to false before on a DOMMatrix object with the exception of calling the setMatrixValue() method.

Returns the value of is2D.

isIdentity

Returns true if m12, m13, m14, m21, m23, m24, m31, m32, m34, m41, m42, m43 are 0 and m11, m22, m33, m44 are 1. Otherwise returns false.