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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:

[Exposed=(Window,Worker),
 Serializable]
interface DOMPointReadOnly {
    constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
            optional unrestricted double z = 0, optional unrestricted double w = 1);

    [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;

    [NewObject] DOMPoint matrixTransform(optional DOMMatrixInit matrix = {});

    [Default] object toJSON();
};

[Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGPoint]
interface DOMPoint : DOMPointReadOnly {
    constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
            optional unrestricted double z = 0, optional unrestricted double w = 1);

    [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:

Let point be a new DOMPointReadOnly or DOMPoint object as appropriate.
Set point’s variables x coordinate to x, y coordinate to y, z coordinate to z and w perspective to w.
Return point.

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

The fromPoint(other) static method on DOMPoint must 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:

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

Let matrixObject be the result of invoking create a DOMMatrix from the dictionary matrix.
Return the result of invoking transform a point with a matrix, given the current point and matrixObject. The current point does not get modified.

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.

2.1. Transforming a point with a matrix

To transform a point with a matrix, given point and matrix:

Let x be point’s x coordinate.
Let y be point’s y coordinate.
Let z be point’s z coordinate.
Let w be point’s w perspective.
Let pointVector be a new column vector with the elements being x, y, z, and w, respectively.
$[\begin{matrix} x \\ y \\ z \\ w \end{matrix}]$
Set pointVector to pointVector pre-multiplied by matrix.
Let transformedPoint be a new DOMPoint object.
Set transformedPoint’s x coordinate to pointVector’s first element.
Set transformedPoint’s y coordinate to pointVector’s second element.
Set transformedPoint’s z coordinate to pointVector’s third element.
Set transformedPoint’s w perspective to pointVector’s fourth element.
Return transformedPoint.

Note: If matrix’s is 2D is true, point’s z coordinate is 0 or -0, and point’s w perspective is 1, then this is a 2D transformation. Otherwise this is a 3D transformation.

3. The DOMRect interfaces

Objects implementing the DOMRectReadOnly interface represent a rectangle.

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.

[Exposed=(Window,Worker),
 Serializable]
interface DOMRectReadOnly {
    constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
            optional unrestricted double width = 0, optional unrestricted double height = 0);

    [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;

    [Default] object toJSON();
};

[Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=SVGRect]
interface DOMRect : DOMRectReadOnly {
    constructor(optional unrestricted double x = 0, optional unrestricted double y = 0,
            optional unrestricted double width = 0, optional unrestricted double height = 0);

    [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:

Let rect be a new DOMRectReadOnly or DOMRect object as appropriate.
Set rect’s variables x coordinate to x, y coordinate to y, width dimension to width and height dimension to height.
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:

Let rect be a new DOMRectReadOnly or DOMRect as appropriate.
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.
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 the NaN-safe minimum of the y coordinate and the sum of the y coordinate and the height dimension.

The right attribute, on getting, must return the NaN-safe maximum of the x coordinate and the sum of the x coordinate and the width dimension.

The bottom attribute, on getting, must return the NaN-safe maximum of the y coordinate and the sum of the y coordinate and the height dimension.

The left attribute, on getting, must return the NaN-safe minimum of the x coordinate and the sum of the x coordinate and the width dimension.

4. The DOMRectList interface

[Exposed=Window]
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 null 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 only exists for compatibility with legacy Web content. When specifying a new API, DOMRectList must not be used. Use sequence<DOMRect> instead. [WEBIDL]

5. The DOMQuad interface

Objects implementing the DOMQuad interface represents a quadrilateral.

[Exposed=(Window,Worker),
 Serializable]
interface DOMQuad {
    constructor(optional DOMPointInit p1 = {}, optional DOMPointInit p2 = {},
            optional DOMPointInit p3 = {}, optional DOMPointInit p4 = {});

    [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();

    [Default] object toJSON();
};

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:

Let point1 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p1.
Let point2 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p2.
Let point3 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p3.
Let point4 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p4.
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.

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 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:

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

Let point1 be the result of invoking create a DOMPoint from the dictionary p1 dictionary member of other, if it exists.
Let point2 be the result of invoking create a DOMPoint from the dictionary p2 dictionary member of other, if it exists.
Let point3 be the result of invoking create a DOMPoint from the dictionary p3 dictionary member of other, if it exists.
Let point4 be the result of invoking create a DOMPoint from the dictionary p4 dictionary member of other, if it exists.
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:

Let bounds be a DOMRect object.
Let left be the NaN-safe minimum of point 1’s x coordinate, point 2’s x coordinate, point 3’s x coordinate and point 4’s x coordinate.
Let top be the NaN-safe minimum of point 1’s y coordinate, point 2’s y coordinate, point 3’s y coordinate and point 4’s y coordinate.
Let right be the NaN-safe maximum of point 1’s x coordinate, point 2’s x coordinate, point 3’s x coordinate and point 4’s x coordinate.
Let bottom be the NaN-safe maximum of point 1’s y coordinate, point 2’s y coordinate, point 3’s y coordinate and point 4’s y coordinate.
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.
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: 12, y: 10}, {x: 2, y: 10});

The attribute values of the resulting DOMQuad quad1 above are also equivalent 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.

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 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.

[Exposed=(Window,Worker),
 Serializable]
interface DOMMatrixReadOnly {
    constructor(optional (DOMString or sequence<unrestricted double>) init);

    [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 scaleNonUniform(optional unrestricted double scaleX = 1,
                                          optional unrestricted double scaleY = 1);
    [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;
    [Default] object toJSON();
};

[Exposed=(Window,Worker),
 Serializable,
 LegacyWindowAlias=(SVGMatrix,WebKitCSSMatrix)]
interface DOMMatrix : DOMMatrixReadOnly {
    constructor(optional (DOMString or sequence<unrestricted double>) init);

    [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 DOMMatrix2DInit {
    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 m21;
    unrestricted double m22;
    unrestricted double m41;
    unrestricted double m42;
};

dictionary DOMMatrixInit : DOMMatrix2DInit {
    unrestricted double m13 = 0;
    unrestricted double m14 = 0;
    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 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]

6.1. DOMMatrix2DInit and DOMMatrixInit dictionaries

To validate and fixup (2D) a DOMMatrix2DInit or DOMMatrixInit dictionary dict, run the following steps:

If if at least one of the following conditions are true for dict, then throw a TypeError exception and abort these steps.
- a and m11 are both present and SameValueZero(a, m11) is false.
- b and m12 are both present and SameValueZero(b, m12) is false.
- c and m21 are both present and SameValueZero(c, m21) is false.
- d and m22 are both present and SameValueZero(d, m22) is false.
- e and m41 are both present and SameValueZero(e, m41) is false.
- f and m42 are both present and SameValueZero(f, m42) is false.
If m11 is not present then set it to the value of member a, or value 1 if a is also not present.
If m12 is not present then set it to the value of member b, or value 0 if b is also not present.
If m21 is not present then set it to the value of member c, or value 0 if c is also not present.
If m22 is not present then set it to the value of member d, or value 1 if d is also not present.
If m41 is not present then set it to the value of member e, or value 0 if e is also not present.
If m42 is not present then set it to the value of member f, or value 0 if f is also not present.

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

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

Validate and fixup (2D) dict.
If is2D is true 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, then throw a TypeError exception and abort these steps.
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.
If is2D is still not present, set it to true.

6.2. 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.

If transformList is the empty string, set it to the string "matrix(1, 0, 0, 1, 0, 0)".
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]
If parsedValue is none, set parsedValue to a <transform-list> containing a single identity matrix.
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.
Transform all <transform-function>s to 4x4 abstract matrices by following the “Mathematical Description of Transform Functions”. [CSS3-TRANSFORMS]
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.
Return matrix and 2dTransform.

6.3. 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:

Let matrix be a new instance of type.
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.
Set m13 element, m14 element, m23 element, m24 element, m31 element, m32 element, m34 element, and m43 element to 0.
Set m33 element and m44 element to 1.
Set is 2D to true.
Return matrix

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

Let matrix be a new instance of type.
Set m11 element to m44 element to the values of init in column-major order.
Set is 2D to false.
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

If current global object is not a Window object, then throw a TypeError exception.
Parse init into an abstract matrix, and let matrix and 2dTransform be the result. If the result is failure, then throw a "SyntaxError" DOMException.
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 2D dictionary other or to create a DOMMatrix from a 2D dictionary other, follow these steps:

Validate and fixup (2D) other.
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.

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

Validate and fixup other.
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.

6.4. 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:

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

Note: 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.