Geometry Interfaces Module Level 1

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:

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 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:

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

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

2. Return the result of invoking transform a point with a matrix, given the current point and matrixObject. The current point does not get modified.

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

2.1. Transforming a point with a matrix

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

1. Let x be point’s x coordinate.

2. Let y be point’s y coordinate.

3. Let z be point’s z coordinate.

4. Let w be point’s w perspective.

5. Let pointVector be a new column vector with the elements being x, y, z, and w, respectively.

   $\left[\begin{array}{c}x\\ y\\ z\\ w\end{array}\right]$

6. Set pointVector to pointVector pre-multiplied by matrix.

7. Let transformedPoint be a new DOMPoint object.

8. Set transformedPoint’s x coordinate to pointVector’s first element.

9. Set transformedPoint’s y coordinate to pointVector’s second element.

10. Set transformedPoint’s z coordinate to pointVector’s third element.

11. Set transformedPoint’s w perspective to pointVector’s fourth element.

12. 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:

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.

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:

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.

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:

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

1. Let bounds be a DOMRect object.

2. 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.

3. 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.

4. 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.

5. 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.

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.

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

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

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

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.

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:

1. 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.

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.

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:

1. Validate and fixup (2D) dict.

2. 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.

3. 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.

4. 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.

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.

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:

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 2D dictionary other or to create a DOMMatrix from a 2D dictionary other, follow these steps:

1. Validate and fixup (2D) other.

2. 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:

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.

6.4. DOMMatrix attributes

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

The following attributes provide status information about DOMMatrixReadOnly.

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.

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.

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

2. Let result be the resulting matrix initialized to the values of the current matrix.

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

4. Return result.

The current matrix is not modified.

scaleNonUniform(scaleX, scaleY)

Note: Supported for legacy reasons to be compatible with SVGMatrix as defined in SVG 1.1 [SVG11]. Authors are encouraged to use scale() instead.

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, 1, 0, 0, 0.

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. Return the result of invoking transform a point with a matrix, given pointObject and the current matrix. The passed argument does not get modified.

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.

   Note: 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.

   Note: 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.

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

5. Return string.

Tests

• DOMMatrix-stringifier.html (live test) (source)

var matrix = new DOMMatrix();
matrix.scaleSelf(2);
matrix.translateSelf(20,20);
console.assert(matrix.toString() ===
                "matrix(2, 0, 0, 2, 40, 40)");

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)");

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

6.6. 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.

var matrix = new DOMMatrix();
matrix.translateSelf(20, 20);
matrix.scaleSelf(2);
matrix.translateSelf(-20, -20);

var matrix = new DOMMatrix();
matrix.translateSelf(20, 20).scaleSelf(2).translateSelf(-20, -20);

Note: 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, 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.

Tests

• DOMMatrix-invert-invertible.html (live test) (source)
• DOMMatrix-invert-non-invertible.html (live test) (source)
• DOMMatrix-invert-preserves-2d.html (live test) (source)
• DOMMatrix-invertSelf.html (live test) (source)

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.

Tests

• DOMMatrix-css-string.worker.js (live test) (source)

7. 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.

   Note: 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.

8. Security Considerations

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

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.

9. Privacy Considerations

10. 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.

10.1. 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]

10.2. SVG

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

10.3. 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.

Document conventions

The NaN-safe minimum of a non-empty list of unrestricted double values is NaN if any member of the list is NaN, or the minimum of the list otherwise.

Analogously, the NaN-safe maximum of a non-empty list of unrestricted double values is NaN if any member of the list is NaN, or the maximum of the list otherwise.

Changes since last publication

This section is non-normative.

The following changes were made since the 4 December 2018 Candidate Recommendation.

• Clarified that column vectors are pre-multiplied by matrices #294, #359

• Defined minimum and maximum as preferring NaN #222

• Used new WebIDL constructor definition

• Added default dictionary value

• Added [NewObject] to matrixTransform, to align with prose description

• Removed redundant originZ check #350

• Added explicit [Exposed] to DOMRectList

• Added Web Platform Tests coverage

The following changes were made since the 25 November 2014 Candidate Recommendation.

• Changed the interfaces to generally use specific static operations for construction instead of using overloaded constructors, and made the interfaces more consistent. However, DOMMatrix still uses an overloaded constructor for compatibility with WebKitCSSMatrix.

• Introduced the DOMMatrixInit dictionary.

• Added JSON serializers for the interfaces.

• Changed DOMMatrixReadOnly and DOMMatrix to be compatible with WebKitCSSMatrix:

  • Changed rotate() and rotateSelf() arguments from (angle, originX, originY) to (rotX, rotY, rotZ).

  • Changed the scale() and scaleSelf() methods to be more like the previous scaleNonUniform()/scaleNonUniformSelf() methods, and dropped the scaleNonUniformSelf() method. Keep support for scaleNonUniform() for legacy reasons.

  • Made all arguments optional for DOMMatrix/DOMMatrixReadOnly methods, except for setMatrixValue().

  • Added no-argument constructor.

  • Defined WebKitCSSMatrix to be a legacy window alias for DOMMatrix.

• In workers, DOMMatrix and DOMMatrixReadOnly do not support parsing or stringifying with CSS syntax.

• Defined structured serialization of the interfaces.

• The live bounds attribute on DOMQuad was replaced with a non-live getBounds() method. The "associated bounding rectangle" concept was also removed.

• Changed the string parser for DOMMatrix and DOMMatrixReadOnly to use CSS rules instead of SVG rules.

• The stringifier for DOMMatrix and DOMMatrixReadOnly now throws if there are non-finite values, and otherwise uses the ToString algorithm. [ECMA-262]

• Made comparisons treat 0 and -0 as equal throughout.

• Added § 9 Privacy Considerations and § 10 Historical sections.

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

• Exposed DOMPointReadOnly, DOMPoint, DOMRectReadOnly, DOMRect, DOMQuad, DOMMatrixReadOnly and DOMMatrix to Window and Worker. Defined cloning of the interface.

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.

• Renamed mutable transformation methods *By to *Self. (E.g. translateBy() got renamed to translateSelf().)

• Renamed invert() to invertSelf().

• Added setMatrixValue() which takes a transformation list as DOMString.

• is2D and isIdentity are read-only attributes now.

• DOMMatrixReadOnly gets flagged to track 3D transformation and attribute settings for is2D.

• invertSelf() and inverse() do not throw exceptions anymore.

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, Simon Fraser, and Timothy Loh for their careful reviews, comments, and corrections.