Geometry Interfaces Module Level 1

W3C Working Draft,

This version:
https://www.w3.org/TR/2017/WD-geometry-1-20170529/
Latest published version:
https://www.w3.org/TR/geometry-1/
Editor's Draft:
https://drafts.fxtf.org/geometry/
Previous Versions:
Test Suite:
http://test.csswg.org/suites/geometry-1_dev/nightly-unstable/
Issue Tracking:
Legacy open bugs
GitHub Issues
Editor:
(Opera Software AS)
Former Editors:
(Adobe Systems Inc.)
(Adobe Systems Inc.)

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 https://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.

GitHub Issues are preferred for discussion of this specification. When filing an issue, please put the text “geometry” in the title, preferably like this: “[geometry] …summary of comment…”. All issues and comments are archived, and there is also a historical archive.

This document was published by the CSS Working Group and the SVG Working Group.

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 include 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 March 2017 W3C Process Document.

1. Introduction

This section is non-normative.

This specification describes several geometry interfaces for the representation of points, rectangles, quadrilaterals and transformation matrices with the dimension of 3x2 and 4x4.

The SVG interfaces SVGPoint, SVGRect and SVGMatrix are aliasing the here defined interfaces in favor for common interfaces used by SVG, Canvas 2D Context and CSS Transforms. [SVG11] [HTML] [CSS3-TRANSFORMS]

2. The DOMPoint interfaces

A 2D or a 3D point can be represented by the following WebIDL interfaces:

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double z = 0, optional unrestricted double w = 1),
 Exposed=(Window,Worker),
 Serializable]
interface DOMPointReadOnly {
    [NewObject] static DOMPointReadOnly fromPoint(optional DOMPointInit other);

    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double z;
    readonly attribute unrestricted double w;

    DOMPoint matrixTransform(optional DOMMatrixInit matrix);

    serializer = { attribute };
};

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double z = 0, optional unrestricted double w = 1),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGPoint]
interface DOMPoint : DOMPointReadOnly {
    [NewObject] static DOMPoint fromPoint(optional DOMPointInit other);

    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) and DOMPoint(x, y, z, w) constructors, when invoked, must run the following steps:

  1. Let point be a new DOMPointReadOnly or DOMPoint object as appropriate.

  2. Set point’s variables x coordinate to x, y coordinate to y, z coordinate to z and w perspective to w.

  3. Return point.

The fromPoint(other) static method on DOMPointReadOnly must create a DOMPointReadOnly from the dictionary other.

The fromPoint(other) static method on DOMPoint create a DOMPoint from the dictionary other.

To create a DOMPointReadOnly from a dictionary other, or to create a DOMPoint from a dictionary other, follow these steps:

  1. Let point be a new DOMPointReadOnly or DOMPoint as appropriate.

  2. Set point’s variables x coordinate to other’s x dictionary member, y coordinate to other’s y dictionary member, z coordinate to other’s z dictionary member and w perspective to other’s w dictionary member.

  3. Return point.

The x attribute, on getting, must return the x coordinate value. For the DOMPoint interface, setting the x attribute must set the x coordinate to the new value.

The y attribute, on getting, must return the y coordinate value. For the DOMPoint interface, setting the y attribute must set the y coordinate to the new value.

The z attribute, on getting, must return the z coordinate value. For the DOMPoint interface, setting the z attribute must set the z coordinate to the new value.

The w attribute, on getting, must return the w perspective value. For the DOMPoint interface, setting the w attribute must set the w perspective to the new value.

The matrixTransform(matrix) method, when invoked, must run the following steps:

  1. Create a new DOMPoint point initialized to x, y, z and w of the current point.

  2. Let matrixObject be the result of invoking create a DOMMatrix from the dictionary matrix.

  3. Post-multiply point with matrixObject.
  4. Return point.

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

In this example the method matrixTransform() on a DOMPoint instance is called with a DOMMatrix instance as argument.

var point = new DOMPoint(5, 4);
var matrix = new DOMMatrix([2, 0, 0, 2, 10, 10]);
var transformedPoint = point.matrixTransform(matrix);

The point variable is set to a new DOMPoint object with x coordinate initialized to 5 and y coordinate initialized to 4. This new DOMPoint is now scaled and the translated by matrix. This resulting transformedPoint has the x coordinate 20 and y coordinate 18.

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 dimension, the rectangle’s horizontal origin is the left edge; otherwise, it is the right edge. Similarly, when the rectangle has a non-negative height dimension, 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(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double width = 0, optional unrestricted double height = 0),
 Exposed=(Window,Worker),
 Serializable]
interface DOMRectReadOnly {
    [NewObject] static DOMRectReadOnly fromRect(optional DOMRectInit other);

    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;

    serializer = { attribute };
};

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double width = 0, optional unrestricted double height = 0),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGRect]
interface DOMRect : DOMRectReadOnly {
    [NewObject] static DOMRect fromRect(optional DOMRectInit other);

    inherit attribute unrestricted double x;
    inherit attribute unrestricted double y;
    inherit attribute unrestricted double width;
    inherit attribute unrestricted double height;
};

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

  1. Let rect be a new DOMRectReadOnly or DOMRect object as appropriate.

  2. Set rect’s variables x coordinate to x, y coordinate to y, width dimension to width and height dimension to height.

  3. Return rect.

The fromRect(other) static method on DOMRectReadOnly must create a DOMRectReadOnly from the dictionary other.

The fromRect(other) static method on DOMRect must create a DOMRect from the dictionary other.

To create a DOMRectReadOnly from a dictionary other, or to create a DOMRect from a dictionary other, follow these steps:

  1. Let rect be a new DOMRectReadOnly or DOMRect as appropriate.

  2. Set rect’s variables x coordinate to other’s x dictionary member, y coordinate to other’s y dictionary member, width dimension to other’s width dictionary member and height dimension to other’s height dictionary member.

  3. Return rect.

The x attribute, on getting, must return the x coordinate value. For the DOMRect interface, setting the x attribute must set the x coordinate to the new value.

The y attribute, on getting, it must return the y coordinate value. For the DOMRect interface, setting the y attribute must set the y coordinate to the new value.

The width attribute, on getting, must return the width dimension value. For the DOMRect interface, setting the width attribute must set the width dimension to the new value.

The height attribute, on getting, must return the height dimension 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).

The right attribute, on getting, must return max(x coordinate, x coordinate + width dimension).

The bottom attribute, on getting, must return max(y coordinate, y coordinate + height dimension).

The left attribute, on getting, must return min(x coordinate, x coordinate + width dimension).

4. The DOMQuad interface

Objects implementing the DOMQuad interface represents a quadrilateral.

[Constructor(optional DOMPointInit p1, optional DOMPointInit p2,
             optional DOMPointInit p3, optional DOMPointInit p4),
 Exposed=(Window,Worker),
 Serializable]
interface DOMQuad {
    [NewObject] static DOMQuad fromRect(optional DOMRectInit other);
    [NewObject] static DOMQuad fromQuad(optional DOMQuadInit other);

    [SameObject] readonly attribute DOMPoint p1;
    [SameObject] readonly attribute DOMPoint p2;
    [SameObject] readonly attribute DOMPoint p3;
    [SameObject] readonly attribute DOMPoint p4;
    [NewObject] DOMRect getBounds();

    serializer = { attribute };
};

dictionary DOMQuadInit {
  DOMPointInit p1;
  DOMPointInit p2;
  DOMPointInit p3;
  DOMPointInit p4;
};

The following algorithms assume that DOMQuad objects have the internal member variables point 1, point 2, point 3, and point 4, which are DOMPoint objects. DOMQuad must be able to access and set the value of these variables. The author can modify these DOMPoint objects, which directly affects the quadrilateral.

An interface returning a DOMQuad 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 DOMQuad(p1, p2, p3, p4) constructor, when invoked, must run the following steps:

  1. Let point1 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p1.

  2. Let point2 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p2.

  3. Let point3 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p3.

  4. Let point4 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p4.

  5. Return a new DOMQuad with point 1 set to point1, point 2 set to point2, point 3 set to point3 and point 4 set to point4.

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 fromRect(other) static method on DOMQuad must create a DOMQuad from the DOMRectInit dictionary other.

To create a DOMQuad from a DOMRectInit dictionary other, follow these steps:

  1. Let x, y, width and height be the value of other’s x, y, width and height dictionary members, respectively.

  2. Let point1 be a new DOMPoint object with x coordinate set to x, y coordinate set to y, z coordinate set to 0 and w perspective set to 1.

  3. Let point2 be a new DOMPoint object with x coordinate set to x + width, y coordinate set to y, z coordinate set to 0 and w perspective set to 1.

  4. Let point3 be a new DOMPoint object with x coordinate set to x + width, y coordinate set to y + height, z coordinate set to 0 and w perspective set to 1.

  5. Let point4 be a new DOMPoint object with x coordinate set to x, y coordinate set to y + height, z coordinate set to 0 and w perspective set to 1.

  6. Return a new DOMQuad with point 1 set to point1, point 2 set to point2, point 3 set to point3 and point 4 set to point4.

The fromQuad(other) static method on DOMQuad must create a DOMQuad from the DOMQuadInit dictionary other.

To create a DOMQuad from a DOMQuadInit dictionary other, follow these steps:

  1. Let point1 be the result of invoking create a DOMPoint from the dictionary p1 dictionary member of other, if it exists.

  2. Let point2 be the result of invoking create a DOMPoint from the dictionary p2 dictionary member of other, if it exists.

  3. Let point3 be the result of invoking create a DOMPoint from the dictionary p3 dictionary member of other, if it exists.

  4. Let point4 be the result of invoking create a DOMPoint from the dictionary p4 dictionary member of other, if it exists.

  5. Return a new DOMQuad with point 1 set to point1, point 2 set to point2, point 3 set to point3 and point 4 set to point4.

The p1 attribute must return point 1.

The p2 attribute must return point 2.

The p3 attribute must return point 3.

The p4 attribute must return point 4.

The getBounds() method, when invoked, must run the following algorithm:

  1. Let bounds be a DOMRect object.

  2. Let left be the minimum of point 1’s x coordinate, point 2’s x coordinate, point 3’s x coordinate and point 4’s x coordinate.

  3. Let top be the minimum of point 1’s y coordinate, point 2’s y coordinate, point 3’s y coordinate and point 4’s y coordinate.

  4. Let right be the maximum of point 1’s x coordinate, point 2’s x coordinate, point 3’s x coordinate and point 4’s x coordinate.

  5. Let bottom be the maximum of point 1’s y coordinate, point 2’s y coordinate, point 3’s y coordinate and point 4’s y coordinate.

  6. Set x coordinate of bounds to left, y coordinate of bounds to top, width dimension of bounds to right - left and height dimension of bounds to bottom - top.

  7. Return bounds.

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 = DOMQuad.fromRect(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 bounding rectangle returned by the getBounds() method of the DOMQuad.

5. 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.

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
A 4x4 abstract matrix 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(optional (DOMString or sequence<unrestricted double>) init),
 Exposed=(Window,Worker),
 Serializable]
interface DOMMatrixReadOnly {
    [NewObject] static DOMMatrixReadOnly fromMatrix(optional DOMMatrixInit other);
    [NewObject] static DOMMatrixReadOnly fromFloat32Array(Float32Array array32);
    [NewObject] static DOMMatrixReadOnly fromFloat64Array(Float64Array array64);

    // 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
    [NewObject] DOMMatrix translate(optional unrestricted double tx = 0,
                                    optional unrestricted double ty = 0,
                                    optional unrestricted double tz = 0);
    [NewObject] DOMMatrix scale(optional unrestricted double scaleX = 1,
                                optional unrestricted double scaleY,
                                optional unrestricted double scaleZ = 1,
                                optional unrestricted double originX = 0,
                                optional unrestricted double originY = 0,
                                optional unrestricted double originZ = 0);
    [NewObject] DOMMatrix scale3d(optional unrestricted double scale = 1,
                                  optional unrestricted double originX = 0,
                                  optional unrestricted double originY = 0,
                                  optional unrestricted double originZ = 0);
    [NewObject] DOMMatrix rotate(optional unrestricted double rotX = 0,
                                 optional unrestricted double rotY,
                                 optional unrestricted double rotZ);
    [NewObject] DOMMatrix rotateFromVector(optional unrestricted double x = 0,
                                           optional unrestricted double y = 0);
    [NewObject] DOMMatrix rotateAxisAngle(optional unrestricted double x = 0,
                                          optional unrestricted double y = 0,
                                          optional unrestricted double z = 0,
                                          optional unrestricted double angle = 0);
    [NewObject] DOMMatrix skewX(optional unrestricted double sx = 0);
    [NewObject] DOMMatrix skewY(optional unrestricted double sy = 0);
    [NewObject] DOMMatrix multiply(optional DOMMatrixInit other);
    [NewObject] DOMMatrix flipX();
    [NewObject] DOMMatrix flipY();
    [NewObject] DOMMatrix inverse();

    [NewObject] DOMPoint transformPoint(optional DOMPointInit point);
    [NewObject] Float32Array toFloat32Array();
    [NewObject] Float64Array toFloat64Array();

    [Exposed=Window] stringifier;
    serializer = { attribute };
};

[Constructor(optional (DOMString or sequence<unrestricted double>) init),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=(SVGMatrix,WebKitCSSMatrix)]
interface DOMMatrix : DOMMatrixReadOnly {
    [NewObject] static DOMMatrix fromMatrix(optional DOMMatrixInit other);
    [NewObject] static DOMMatrix fromFloat32Array(Float32Array array32);
    [NewObject] static DOMMatrix fromFloat64Array(Float64Array array64);

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

    [Exposed=Window] DOMMatrix setMatrixValue(DOMString transformList);
};

dictionary DOMMatrixInit {
    unrestricted double a;
    unrestricted double b;
    unrestricted double c;
    unrestricted double d;
    unrestricted double e;
    unrestricted double f;
    unrestricted double m11;
    unrestricted double m12;
    unrestricted double m13 = 0;
    unrestricted double m14 = 0;
    unrestricted double m21;
    unrestricted double m22;
    unrestricted double m23 = 0;
    unrestricted double m24 = 0;
    unrestricted double m31 = 0;
    unrestricted double m32 = 0;
    unrestricted double m33 = 1;
    unrestricted double m34 = 0;
    unrestricted double m41;
    unrestricted double m42;
    unrestricted double m43 = 0;
    unrestricted double m44 = 1;
    boolean is2D;
};

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 is 2D. 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]

5.1. DOMMatrixInit dictionary

To validate and fixup a DOMMatrixInit dictionary dict, run the following steps:

  1. If if at least one of the following conditions are true for dict, throw a TypeError exception and abort these steps.

  2. If m11 is not present then set it to the value of member a, or value 1 if a is also not present.

  3. If m12 is not present then set it to the value of member b, or value 0 if b is also not present.

  4. If m21 is not present then set it to the value of member c, or value 0 if c is also not present.

  5. If m22 is not present then set it to the value of member d, or value 1 if d is also not present.

  6. If m41 is not present then set it to the value of member e, or value 0 if e is also not present.

  7. If m42 is not present then set it to the value of member f, or value 0 if f is also not present.

  8. If is2D is not present and at least one of m13, m14, m23, m24, m31, m32, m34, m43 are present with a value other than 0 or -0, or at least one of m33, m44 are present with a value other than 1, set is2D to false.

  9. If is2D is still not present, set it to true.

The SameValueZero comparison algorithm returns true for two NaN values, and also for 0 and -0. [ECMA-262]

5.2. Parsing a string into an abstract matrix

To parse a string into an abstract matrix, given a string transformList, means to run the following steps. It will either return a 4x4 abstract matrix and a boolean 2dTransform, or failure.

  1. If transformList is the empty string, set it to the string "matrix(1, 0, 0, 1, 0, 0)".

  2. Parse transformList into parsedValue given the grammar for the CSS transform property. The result will be a <transform-list>, the keyword none, or failure. If parsedValue is failure, or any <transform-function> has <length> values without absolute length units, or any keyword other than none is used, then return failure. [CSS3-SYNTAX] [CSS3-TRANSFORMS]

  3. If parsedValue is none, set parsedValue to a <transform-list> containing a single identity matrix.

  4. Let 2dTransform track the 2D/3D dimension status of parsedValue.

    If parsedValue consists of any three-dimensional transform functions

    Set 2dTransform to false.

    Otherwise

    Set 2dTransform to true.

  5. Transform all <transform-function>s to 4x4 abstract matrices by following the “Mathematical Description of Transform Functions”. [CSS3-TRANSFORMS]

  6. Let matrix be a 4x4 abstract matrix as shown in the initial figure of this section. Post-multiply all matrices from left to right and set matrix to this product.

  7. Return matrix and 2dTransform.

5.3. Creating DOMMatrixReadOnly and DOMMatrix objects

To create a 2d matrix of type type being either DOMMatrixReadOnly or DOMMatrix, with a sequence init of 6 elements, follow these steps:

  1. Let matrix be a new instance of type.

  2. Set m11 element, m12 element, m21 element, m22 element, m41 element and m42 element to the values of init in order starting with the first value.

  3. Set m13 element, m14 element, m23 element, m24 element, m31 element, m32 element, m34 element, and m43 element to 0.

  4. Set m33 element and m44 element to 1.

  5. Set is 2D to true.

  6. Return matrix

To create a 3d matrix with type being either DOMMatrixReadOnly or DOMMatrix, with a sequence init of 16 elements, follow these steps:

  1. Let matrix be a new instance of type.

  2. Set m11 element to m44 element to the values of init in column-major order.

  3. Set is 2D to false.

  4. Return matrix

The DOMMatrixReadOnly(init) and the DOMMatrix(init) constructors must follow these steps:

If init is omitted
Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with the sequence [1, 0, 0, 1, 0, 0].
If init is a DOMString
  1. If current global object is not a Window object, then throw a TypeError exception.

  2. Parse init into an abstract matrix, and let matrix and 2dTransform be the result. If the result is failure, then throw a "SyntaxError" DOMException.

  3. If 2dTransform is true
    Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers, the values being the elements m11, m12, m21, m22, m41 and m42 of matrix.
    Otherwise
    Return the result of invoking create a 3d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers, the values being the 16 elements of matrix.
If init is a sequence with 6 elements
Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with the sequence init.
If init is a sequence with 16 elements
Return the result of invoking create a 3d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with the sequence init.
Otherwise
Throw a TypeError exception.

The fromMatrix(other) static method on DOMMatrixReadOnly must create a DOMMatrixReadOnly from the dictionary other.

The fromMatrix(other) static method on DOMMatrix must create a DOMMatrix from the dictionary other.

To create a DOMMatrixReadOnly from a dictionary other or to create a DOMMatrix from a dictionary other, follow these steps:

  1. Validate and fixup other.
  2. If the is2D dictionary member of other is true

    Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers, the values being the 6 elements m11, m12, m21, m22, m41 and m42 of other in the given order.

    Otherwise

    Return the result of invoking create a 3d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers, the values being the 16 elements m11, m12, m13, ..., m44 of other in the given order.

The fromFloat32Array(array32) static method on DOMMatrixReadOnly and the fromFloat32Array(array32) static method on DOMMatrix must follow these steps:

If array32 has 6 elements

Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers taking the values from array32 in the provided order.

If array32 has 16 elements

Return the result of invoking create a 3d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers taking the values from array32 in the provided order.

Otherwise

Throw a TypeError exception.

The fromFloat64Array(array64) static method on DOMMatrixReadOnly and the fromFloat64Array(array64) static method on DOMMatrix must follow these steps:

If array64 has 6 elements

Return the result of invoking create a 2d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers taking the values from array64 in the provided order.

If array32 has 16 elements

Return the result of invoking create a 3d matrix of type DOMMatrixReadOnly or DOMMatrix as appropriate, with a sequence of numbers taking the values from array64 in the provided order.

Otherwise

Throw a TypeError exception.

5.4. DOMMatrix attributes

The following attributes m11 to m44 correspond to the 16 items of the matrix interfaces.

The m11 and a attributes, on getting, must return the m11 element value. For the DOMMatrix interface, setting the m11 or the a attribute must set the m11 element to the new value.

The m12 and b attributes, on getting, must return the m12 element value. For the DOMMatrix interface, setting the m12 or the b attribute must set the m12 element to the new value.

The m13 attribute, on getting, must return the m13 element value. For the DOMMatrix interface, setting the m13 attribute must set the m13 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m14 attribute, on getting, must return the m14 element value. For the DOMMatrix interface, setting the m14 attribute must set the m14 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m21 and c attributes, on getting, must return the m21 element value. For the DOMMatrix interface, setting the m21 or the c attribute must set the m21 element to the new value.

The m22 and d attributes, on getting, must return the m22 element value. For the DOMMatrix interface, setting the m22 or the d attribute must set the m22 element to the new value.

The m23 attribute, on getting, must return the m23 element value. For the DOMMatrix interface, setting the m23 attribute must set the m23 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m24 attribute, on getting, must return the m24 element value. For the DOMMatrix interface, setting the m24 attribute must set the m24 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m31 attribute, on getting, must return the m31 element value. For the DOMMatrix interface, setting the m31 attribute must set the m31 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m32 attribute, on getting, must return the m32 element value. For the DOMMatrix interface, setting the m32 attribute must set the m32 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m33 attribute, on getting, must return the m33 element value. For the DOMMatrix interface, setting the m33 attribute must set the m33 element to the new value and, if the new value is not 1, set is 2D to false.

The m34 attribute, on getting, must return the m34 element value. For the DOMMatrix interface, setting the m34 attribute must set the m34 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m41 and e attributes, on getting, must return the m41 element value. For the DOMMatrix interface, setting the m41 or the e attribute must set the m41 element to the new value.

The m42 and f attributes, on getting, must return the m42 element value. For the DOMMatrix interface, setting the m42 or the f attribute must set the m42 element to the new value.

The m43 attribute, on getting, must return the m43 element value. For the DOMMatrix interface, setting the m43 attribute must set the m43 element to the new value and, if the new value is not 0 or -0, set is 2D to false.

The m44 attribute, on getting, must return the m44 element value. For the DOMMatrix interface, setting the m44 attribute must set the m44 element to the new value and, if the new value is not 1, set is 2D to false.

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.

The is2D attribute must return the value of is 2D.

The isIdentity attribute must return true if m12 element, m13 element, m14 element, m21 element, m23 element, m24 element, m31 element, m32 element, m34 element, m41 element, m42 element, m43 element are 0 or -0 and m11 element, m22 element, m33 element, m44 element are 1. Otherwise it must return false.

Every DOMMatrixReadOnly object must be flagged with a boolean is 2D. This flag indicates that:

  1. The current matrix was initialized as a 2D matrix. See individual creators for more details.

  2. Only 2D transformation operations were applied. Each mutable or immutable transformation method defines if is 2D must be set to false.

Is 2D 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.

5.5. Immutable transformation methods

The following methods do not modify the current matrix and return a new DOMMatrix object.

translate(tx, ty, tz)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a translateSelf() transformation on result with the arguments tx, ty, tz.

  3. Return result.

The current matrix is not modified.

scale(scaleX, scaleY, scaleZ, originX, originY, originZ)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a scaleSelf() transformation on result with the arguments scaleX, scaleY, scaleZ, originX, originY, originZ.

  3. Return result.

The current matrix is not modified.

scale3d(scale, originX, originY, originZ)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a scale3dSelf() transformation on result with the arguments scale, originX, originY, originZ.

  3. Return result.

The current matrix is not modified.

rotate(rotX, rotY, rotZ)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a rotateSelf() transformation on result with the arguments rotX, rotY, rotZ.

  3. Return result.

The current matrix is not modified.

rotateFromVector(x, y)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a rotateFromVectorSelf() transformation on result with the arguments x, y.

  3. Return result.

The current matrix is not modified.

rotateAxisAngle(x, y, z, angle)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a rotateAxisAngleSelf() transformation on result with the arguments x, y, z, angle.

  3. Return result.

The current matrix is not modified.

skewX(sx)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a skewXSelf() transformation on result with the argument sx.

  3. Return result.

The current matrix is not modified.

skewY(sy)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a skewYSelf() transformation on result with the argument sy.

  3. Return result.

The current matrix is not modified.

multiply(other)
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a multiplySelf() transformation on result with the argument other.

  3. Return result.

The current matrix is not modified.

flipX()
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Post-multiply result with new DOMMatrix([-1, 0, 0, 1, 0, 0]).
  3. Return result.

The current matrix is not modified.

flipY()
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Post-multiply result with new DOMMatrix([1, 0, 0, -1, 0, 0]).
  3. Return result.

The current matrix is not modified.

inverse()
  1. Let result be the resulting matrix initialized to the values of the current matrix.

  2. Perform a invertSelf() transformation on result.

  3. Return result.

The current matrix is not modified.

The following methods do not modify the current matrix.

transformPoint(point)

Let pointObject be the result of invoking create a DOMPoint from the dictionary point. pointObject is post-multiplied to the current matrix and returns the resulting point. The passed argument does not get modified.

Even if is2D of the current matrix returns true, a 4x4 matrix multiplication will be performed if the z attribute of point is not 0 or -0 or the w attribute of point is not 1.

toFloat32Array()

Returns the serialized 16 elements m11 to m44 of the current matrix in column-major order as Float32Array.

toFloat64Array()

Returns the serialized 16 elements m11 to m44 of the current matrix in column-major order as Float64Array.

stringification behavior
  1. If one or more of m11 element through m44 element are a non-finite value, then throw an "InvalidStateError" DOMException.

    The CSS syntax cannot represent NaN or Infinity values.

  2. Let string be the empty string.

  3. If is 2D is true, then:

    1. Append "matrix(" to string.

    2. Append ! ToString(m11 element) to string.

    3. Append ", " to string.

    4. Append ! ToString(m12 element) to string.

    5. Append ", " to string.

    6. Append ! ToString(m21 element) to string.

    7. Append ", " to string.

    8. Append ! ToString(m22 element) to string.

    9. Append ", " to string.

    10. Append ! ToString(m41 element) to string.

    11. Append ", " to string.

    12. Append ! ToString(m42 element) to string.

    13. Append ")" to string.

    The string will be in the form of a a CSS Transforms <matrix()> function. [CSS3-TRANSFORMS]

  4. Otherwise:

    1. Append "matrix3d(" to string.

    2. Append ! ToString(m11 element) to string.

    3. Append ", " to string.

    4. Append ! ToString(m12 element) to string.

    5. Append ", " to string.

    6. Append ! ToString(m13 element) to string.

    7. Append ", " to string.

    8. Append ! ToString(m14 element) to string.

    9. Append ", " to string.

    10. Append ! ToString(m21 element) to string.

    11. Append ", " to string.

    12. Append ! ToString(m22 element) to string.

    13. Append ", " to string.

    14. Append ! ToString(m23 element) to string.

    15. Append ", " to string.

    16. Append ! ToString(m24 element) to string.

    17. Append ", " to string.

    18. Append ! ToString(m41 element) to string.

    19. Append ", " to string.

    20. Append ! ToString(m42 element) to string.

    21. Append ", " to string.

    22. Append ! ToString(m43 element) to string.

    23. Append ", " to string.

    24. Append ! ToString(m44 element) to string.

    25. Append ")" to string.

    The string will be in the form of a a CSS Transforms <matrix3d()> function. [CSS3-TRANSFORMS]

  5. Return string.

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);
console.assert(matrix.toString() ===
               "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);
console.assert(matrix.toString() ===
               "matrix3d(2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1)");

For 3D operations, the stringifier returns a string representing a 3D matrix.

This example will throw an exception because there are non-finite values in the matrix.

var matrix = new DOMMatrix([NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN]);
var string = matrix + " Batman!";

5.6. Mutable transformation methods

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);

Authors who use chained method calls are advised to use mutable transformation methods to avoid unnecessary memory allocations due to creation of intermediate DOMMatrix objects in user agents.

multiplySelf(other)
  1. Let otherObject be the result of invoking create a DOMMatrix from the dictionary other.

  2. The otherObject matrix gets post-multiplied to the current matrix.

  3. If is 2D of otherObject is false, set is 2D of the current matrix to false.

  4. Return the current matrix.

preMultiplySelf(other)
  1. Let otherObject be the result of invoking create a DOMMatrix from the dictionary other.

  2. The otherObject matrix gets pre-multiplied to the current matrix.

  3. If is 2D of otherObject is false, set is 2D of the current matrix to false.

  4. Return the current matrix.

translateSelf(tx, ty, tz)
  1. Post-multiply a translation transformation on the current matrix. The 3D translation matrix is described in CSS Transforms. [CSS3-TRANSFORMS]

  2. If tz is specified and not 0 or -0, set is 2D of the current matrix to false.

  3. Return the current matrix.

scaleSelf(scaleX, scaleY, scaleZ, originX, originY, originZ)
  1. Perform a translateSelf() transformation on the current matrix with the arguments originX, originY, originZ.

  2. If scaleY is missing, set scaleY to the value of scaleX.

  3. 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]

  4. Negate originX, originY and originZ.

  5. Perform a translateSelf() transformation on the current matrix with the arguments originX, originY, originZ.

  6. If scaleZ is not 1 or originZ is not 0 or -0, set is 2D of the current matrix to false.

  7. Return the current matrix.

scale3dSelf(scale, originX, originY, originZ)
  1. Apply a translateSelf() transformation to the current matrix with the arguments originX, originY, originZ.

  2. 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]

  3. Apply a translateSelf() transformation to the current matrix with the arguments -originX, -originY, -originZ.

  4. If scale is not 1, set is 2D of the current matrix to false.

  5. Return the current matrix.

rotateSelf(rotX, rotY, rotZ)
  1. If rotY and rotZ are both missing, set rotZ to the value of rotX and set rotX and rotY to 0.

  2. If rotY is still missing, set rotY to 0.

  3. If rotZ is still missing, set rotZ to 0.

  4. If rotX or rotY are not 0 or -0, set is 2D of the current matrix to false.

  5. Post-multiply a rotation transformation on the current matrix around the vector 0, 0, 1 by the specified rotation rotZ in degrees. The 3D rotation matrix is described in CSS Transforms with alpha = rotZ in degrees. [CSS3-TRANSFORMS]

  6. Post-multiply a rotation transformation on the current matrix around the vector 0, 1, 0 by the specified rotation rotY in degrees. The 3D rotation matrix is described in CSS Transforms with alpha = rotY in degrees. [CSS3-TRANSFORMS]

  7. Post-multiply a rotation transformation on the current matrix around the vector 1, 0, 0 by the specified rotation rotX in degrees. The 3D rotation matrix is described in CSS Transforms with alpha = rotX in degrees. [CSS3-TRANSFORMS]

  8. Return the current matrix.

rotateFromVectorSelf(x, y)
  1. 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 0 or -0, the angle is specified as 0. 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]

  2. Return the current matrix.

rotateAxisAngleSelf(x, y, z, angle)
  1. 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]

  2. If x or y are not 0 or -0, set is 2D of the current matrix to false.

  3. Return the current matrix.

skewXSelf(sx)
  1. 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]

  2. Return the current matrix.

skewYSelf(sy)
  1. 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]

  2. Return the current matrix.

invertSelf()
  1. Invert the current matrix.

  2. If the current matrix is not invertible set all attributes to NaN and set is 2D to false.

  3. Return the current matrix.

setMatrixValue(transformList)
  1. Parse transformList into an abstract matrix, and let matrix and 2dTransform be the result. If the result is failure, then throw a "SyntaxError" DOMException.

  2. Set is 2D to the value of 2dTransform.

  3. Set m11 element through m44 element to the element values of matrix in column-major order.

  4. Return the current matrix.

6. Structured serialization

DOMPointReadOnly, DOMPoint, DOMRectReadOnly, DOMRect, DOMQuad, DOMMatrixReadOnly, and DOMMatrix objects are serializable objects. [HTML]

The serialization steps for DOMPointReadOnly and DOMPoint, given value and serialized, are:

  1. Set serialized.[[X]] to value’s x coordinate.

  2. Set serialized.[[Y]] to value’s y coordinate.

  3. Set serialized.[[Z]] to value’s z coordinate.

  4. Set serialized.[[W]] to value’s w perspective.

Their deserialization steps, given serialized and value, are:

  1. Set value’s x coordinate to serialized.[[X]].
  2. Set value’s y coordinate to serialized.[[Y]].
  3. Set value’s z coordinate to serialized.[[Z]].
  4. Set value’s w perspective to serialized.[[W]].

The serialization steps for DOMRectReadOnly and DOMRect, given value and serialized, are:

  1. Set serialized.[[X]] to value’s x coordinate.

  2. Set serialized.[[Y]] to value’s y coordinate.

  3. Set serialized.[[Width]] to value’s width dimension.

  4. Set serialized.[[Height]] to value’s height dimension.

Their deserialization steps, given serialized and value, are:

  1. Set value’s x coordinate to serialized.[[X]].
  2. Set value’s y coordinate to serialized.[[Y]].
  3. Set value’s width dimension to serialized.[[Width]].
  4. Set value’s height dimension to serialized.[[Height]].

The serialization steps for DOMQuad, given value and serialized, are:

  1. Set serialized.[[P1]] to the sub-serialization of value’s point 1.

  2. Set serialized.[[P2]] to the sub-serialization of value’s point 2.

  3. Set serialized.[[P3]] to the sub-serialization of value’s point 3.

  4. Set serialized.[[P4]] to the sub-serialization of value’s point 4.

Their deserialization steps, given serialized and value, are:

  1. Set value’s point 1 to the sub-deserialization of serialized.[[P1]].

  2. Set value’s point 2 to the sub-deserialization of serialized.[[P2]].

  3. Set value’s point 3 to the sub-deserialization of serialized.[[P3]].

  4. Set value’s point 4 to the sub-deserialization of serialized.[[P4]].

The serialization steps for DOMMatrixReadOnly and DOMMatrix, given value and serialized, are:

  1. If value’s is 2D is true:

    1. Set serialized.[[M11]] to value’s m11 element.

    2. Set serialized.[[M12]] to value’s m12 element.

    3. Set serialized.[[M21]] to value’s m21 element.

    4. Set serialized.[[M22]] to value’s m22 element.

    5. Set serialized.[[M41]] to value’s m41 element.

    6. Set serialized.[[M42]] to value’s m42 element.

    7. Set serialized.[[Is2D]] to true.

    It is possible for a 2D DOMMatrix or DOMMatrixReadOnly to have -0 for some of the other elements, e.g., the m13 element, which will not be roundtripped by this algorithm.

  2. Otherwise:

    1. Set serialized.[[M11]] to value’s m11 element.

    2. Set serialized.[[M12]] to value’s m12 element.

    3. Set serialized.[[M13]] to value’s m13 element.

    4. Set serialized.[[M14]] to value’s m14 element.

    5. Set serialized.[[M21]] to value’s m21 element.

    6. Set serialized.[[M22]] to value’s m22 element.

    7. Set serialized.[[M23]] to value’s m23 element.

    8. Set serialized.[[M24]] to value’s m24 element.

    9. Set serialized.[[M31]] to value’s m31 element.

    10. Set serialized.[[M32]] to value’s m32 element.

    11. Set serialized.[[M33]] to value’s m33 element.

    12. Set serialized.[[M34]] to value’s m34 element.

    13. Set serialized.[[M41]] to value’s m41 element.

    14. Set serialized.[[M42]] to value’s m42 element.

    15. Set serialized.[[M43]] to value’s m43 element.

    16. Set serialized.[[M44]] to value’s m44 element.

    17. Set serialized.[[Is2D]] to false.

    Their deserialization steps, given serialized and value, are:

    1. If serialized.[[Is2D]] is true:

      1. Set value’s m11 element to serialized.[[M11]].

      2. Set value’s m12 element to serialized.[[M12]].

      3. Set value’s m13 element to 0.

      4. Set value’s m14 element to 0.

      5. Set value’s m21 element to serialized.[[M21]].

      6. Set value’s m22 element to serialized.[[M22]].

      7. Set value’s m23 element to 0.

      8. Set value’s m24 element to 0.

      9. Set value’s m31 element to 0.

      10. Set value’s m32 element to 0.

      11. Set value’s m33 element to 1.

      12. Set value’s m34 element to 0.

      13. Set value’s m41 element to serialized.[[M41]].

      14. Set value’s m42 element to serialized.[[M42]].

      15. Set value’s m43 element to 0.

      16. Set value’s m44 element to 1.

      17. Set value’s is 2D to true.

    2. Otherwise:

      1. Set value’s m11 element to serialized.[[M11]].

      2. Set value’s m12 element to serialized.[[M12]].

      3. Set value’s m13 element to serialized.[[M13]].

      4. Set value’s m14 element to serialized.[[M14]].

      5. Set value’s m21 element to serialized.[[M21]].

      6. Set value’s m22 element to serialized.[[M22]].

      7. Set value’s m23 element to serialized.[[M23]].

      8. Set value’s m24 element to serialized.[[M24]].

      9. Set value’s m31 element to serialized.[[M31]].

      10. Set value’s m32 element to serialized.[[M32]].

      11. Set value’s m33 element to serialized.[[M33]].

      12. Set value’s m34 element to serialized.[[M34]].

      13. Set value’s m41 element to serialized.[[M41]].

      14. Set value’s m42 element to serialized.[[M42]].

      15. Set value’s m43 element to serialized.[[M43]].

      16. Set value’s m44 element to serialized.[[M44]].

      17. Set value’s is 2D to false.

    7. Privacy and Security Considerations

    The DOMMatrix and DOMMatrixReadOnly interfaces have entry-points to parsing a string with CSS syntax. Therefore the privacy and security considerations of the CSS Syntax specification applies. [CSS3-SYNTAX]

    This could potentially be used to exploit bugs in the CSS parser in a user agent.

    There are no other known security or privacy impacts of the interfaces defined in this specification. However, other specifications that have APIs that use the interfaces defined in this specification could potentially introduce security or privacy issues.

    For example, the getBoundingClientRect() API defined in CSSOM View returns a DOMRect that could be used to measure the size of an inline element containing some text of a particular font, which exposes information about whether the user has that font installed. That information, if used to test many common fonts, can then be personally-identifiable information. [CSSOM-VIEW]

    8. Historical

    This section is non-normative.

    The interfaces in this specification are intended to replace earlier similar interfaces found in various specifications as well as proprietary interfaces found in some user agents. This section attempts to enumerate these interfaces.

    8.1. CSSOM View

    Earlier revisions of CSSOM View defined a ClientRect interface, which is replaced by DOMRect. Implementations conforming to this specification will not support ClientRect. [CSSOM-VIEW]

    8.2. SVG

    Earlier revisions of SVG defined SVGPoint, SVGRect, SVGMatrix, which are defined in this specifications as aliases to DOMPoint, DOMRect, DOMMatrix, respectively. [SVG11]

    8.3. Non-standard

    Some user agents supported a WebKitPoint interface. Implementations conforming to this specification will not support WebKitPoint.

    Several user agents supported a WebKitCSSMatrix interface, which is also widely used on the Web. It is defined in this specification as an alias to DOMMatrix.

    Some user agents supported a MSCSSMatrix interface. Implementations conforming to this specification will not support MSCSSMatrix.

    Changes since last publication

    This section is non-normative.

    The following changes were made since the 18 September 2014 Working Draft.

    The following changes were made since the 26 June 2014 Last Call Public Working Draft.

    • DOMPointReadOnly got a constructor taking 4 arguments.

    • DOMRectReadOnly got a constructor taking 4 arguments.

    • DOMMatrixReadOnly got a constructor taking a sequence of numbers as argument.

    • DOMRectList turned to an ArrayClass. The interfaces can just be used for legacy interfaces.

    • Put DOMRectList on at-Risk awaiting browser feedback.

    • All interfaces are described in the sense of internal elements to describe the read-only/writable and inheriting behavior.

    • Replace IndexSizeError exception with TypeError.

    The following changes were made since the 22 May 2014 First Public Working Draft.

    Acknowledgments

    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 Adenilson Cavalcanti, Benoit Jacob, Boris Zbarsky, Brian Birtles, Cameron McCormack, Domenic Denicola, Kari Pihkala, Max Vujovic, Mike Taylor, Peter Hall, Philip Jägenstedt, and Timothy Loh 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:

style sheet
A CSS style sheet.
renderer
A UA that interprets the semantics of a style sheet and renders documents that use them.
authoring tool
A 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 https://www.w3.org/Style/CSS/Test/. Questions should be directed to the public-css-testsuite@w3.org mailing list.

Index

Terms defined by this specification

Terms defined by reference

References

Normative References

[CSS-TRANSFORMS-2]
CSS Transforms Module Level 2 URL: https://drafts.csswg.org/css-transforms-2/
[CSS-VALUES-3]
Tab Atkins Jr.; Elika Etemad. CSS Values and Units Module Level 3. URL: https://www.w3.org/TR/css-values-3/
[CSS3-SYNTAX]
Tab Atkins Jr.; Simon Sapin. CSS Syntax Module Level 3. URL: https://www.w3.org/TR/css-syntax-3/
[CSS3-TRANSFORMS]
Simon Fraser; et al. CSS Transforms Module Level 1. URL: https://www.w3.org/TR/css-transforms-1/
[ECMA-262]
ECMAScript Language Specification. URL: https://tc39.github.io/ecma262/
[HTML]
Anne van Kesteren; et al. HTML Standard. Living Standard. URL: https://html.spec.whatwg.org/multipage/
[RFC2119]
S. Bradner. Key words for use in RFCs to Indicate Requirement Levels. March 1997. Best Current Practice. URL: https://tools.ietf.org/html/rfc2119
[WEBIDL]
Cameron McCormack; Boris Zbarsky; Tobie Langel. Web IDL. URL: https://heycam.github.io/webidl/

Informative References

[CSSOM-VIEW]
Simon Pieters. CSSOM View Module. URL: https://www.w3.org/TR/cssom-view-1/
[SVG11]
Erik Dahlström; et al. Scalable Vector Graphics (SVG) 1.1 (Second Edition). 16 August 2011. REC. URL: https://www.w3.org/TR/SVG11/

IDL Index

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double z = 0, optional unrestricted double w = 1),
 Exposed=(Window,Worker),
 Serializable]
interface DOMPointReadOnly {
    [NewObject] static DOMPointReadOnly fromPoint(optional DOMPointInit other);

    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double z;
    readonly attribute unrestricted double w;

    DOMPoint matrixTransform(optional DOMMatrixInit matrix);

    serializer = { attribute };
};

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double z = 0, optional unrestricted double w = 1),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGPoint]
interface DOMPoint : DOMPointReadOnly {
    [NewObject] static DOMPoint fromPoint(optional DOMPointInit other);

    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;
};

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double width = 0, optional unrestricted double height = 0),
 Exposed=(Window,Worker),
 Serializable]
interface DOMRectReadOnly {
    [NewObject] static DOMRectReadOnly fromRect(optional DOMRectInit other);

    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;

    serializer = { attribute };
};

[Constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
             optional unrestricted double width = 0, optional unrestricted double height = 0),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGRect]
interface DOMRect : DOMRectReadOnly {
    [NewObject] static DOMRect fromRect(optional DOMRectInit other);

    inherit attribute unrestricted double x;
    inherit attribute unrestricted double y;
    inherit attribute unrestricted double width;
    inherit attribute unrestricted double height;
};

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

[Constructor(optional DOMPointInit p1, optional DOMPointInit p2,
             optional DOMPointInit p3, optional DOMPointInit p4),
 Exposed=(Window,Worker),
 Serializable]
interface DOMQuad {
    [NewObject] static DOMQuad fromRect(optional DOMRectInit other);
    [NewObject] static DOMQuad fromQuad(optional DOMQuadInit other);

    [SameObject] readonly attribute DOMPoint p1;
    [SameObject] readonly attribute DOMPoint p2;
    [SameObject] readonly attribute DOMPoint p3;
    [SameObject] readonly attribute DOMPoint p4;
    [NewObject] DOMRect getBounds();

    serializer = { attribute };
};

dictionary DOMQuadInit {
  DOMPointInit p1;
  DOMPointInit p2;
  DOMPointInit p3;
  DOMPointInit p4;
};

[Constructor(optional (DOMString or sequence<unrestricted double>) init),
 Exposed=(Window,Worker),
 Serializable]
interface DOMMatrixReadOnly {
    [NewObject] static DOMMatrixReadOnly fromMatrix(optional DOMMatrixInit other);
    [NewObject] static DOMMatrixReadOnly fromFloat32Array(Float32Array array32);
    [NewObject] static DOMMatrixReadOnly fromFloat64Array(Float64Array array64);

    // 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
    [NewObject] DOMMatrix translate(optional unrestricted double tx = 0,
                                    optional unrestricted double ty = 0,
                                    optional unrestricted double tz = 0);
    [NewObject] DOMMatrix scale(optional unrestricted double scaleX = 1,
                                optional unrestricted double scaleY,
                                optional unrestricted double scaleZ = 1,
                                optional unrestricted double originX = 0,
                                optional unrestricted double originY = 0,
                                optional unrestricted double originZ = 0);
    [NewObject] DOMMatrix scale3d(optional unrestricted double scale = 1,
                                  optional unrestricted double originX = 0,
                                  optional unrestricted double originY = 0,
                                  optional unrestricted double originZ = 0);
    [NewObject] DOMMatrix rotate(optional unrestricted double rotX = 0,
                                 optional unrestricted double rotY,
                                 optional unrestricted double rotZ);
    [NewObject] DOMMatrix rotateFromVector(optional unrestricted double x = 0,
                                           optional unrestricted double y = 0);
    [NewObject] DOMMatrix rotateAxisAngle(optional unrestricted double x = 0,
                                          optional unrestricted double y = 0,
                                          optional unrestricted double z = 0,
                                          optional unrestricted double angle = 0);
    [NewObject] DOMMatrix skewX(optional unrestricted double sx = 0);
    [NewObject] DOMMatrix skewY(optional unrestricted double sy = 0);
    [NewObject] DOMMatrix multiply(optional DOMMatrixInit other);
    [NewObject] DOMMatrix flipX();
    [NewObject] DOMMatrix flipY();
    [NewObject] DOMMatrix inverse();

    [NewObject] DOMPoint transformPoint(optional DOMPointInit point);
    [NewObject] Float32Array toFloat32Array();
    [NewObject] Float64Array toFloat64Array();

    [Exposed=Window] stringifier;
    serializer = { attribute };
};

[Constructor(optional (DOMString or sequence<unrestricted double>) init),
 Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=(SVGMatrix,WebKitCSSMatrix)]
interface DOMMatrix : DOMMatrixReadOnly {
    [NewObject] static DOMMatrix fromMatrix(optional DOMMatrixInit other);
    [NewObject] static DOMMatrix fromFloat32Array(Float32Array array32);
    [NewObject] static DOMMatrix fromFloat64Array(Float64Array array64);

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

    [Exposed=Window] DOMMatrix setMatrixValue(DOMString transformList);
};

dictionary DOMMatrixInit {
    unrestricted double a;
    unrestricted double b;
    unrestricted double c;
    unrestricted double d;
    unrestricted double e;
    unrestricted double f;
    unrestricted double m11;
    unrestricted double m12;
    unrestricted double m13 = 0;
    unrestricted double m14 = 0;
    unrestricted double m21;
    unrestricted double m22;
    unrestricted double m23 = 0;
    unrestricted double m24 = 0;
    unrestricted double m31 = 0;
    unrestricted double m32 = 0;
    unrestricted double m33 = 1;
    unrestricted double m34 = 0;
    unrestricted double m41;
    unrestricted double m42;
    unrestricted double m43 = 0;
    unrestricted double m44 = 1;
    boolean is2D;
};