Geometry Interfaces Module Level 1

W3C Last Call Working Draft, 26 June 2014

This version:: http://www.w3.org/TR/2014/WD-geometry-1-20140626/
Latest version:: http://www.w3.org/TR/geometry-1/
Editor’s Draft:: http://dev.w3.org/fxtf/geometry/
Previous Versions:: http://www.w3.org/TR/2014/WD-geometry-1-20140522/
Feedback:: public-fx@w3.org with subject line “[geometry] … message topic …”(archives)
Test Suite:: http://test.csswg.org/suites/geometry-1_dev/nightly-unstable/
Editors:: Simon Pieters (Opera Software ASA); Dirk Schulze (Adobe Systems Inc.); Rik Cabanier (Adobe Systems Inc.)
Issues List:: Bugzilla (file a bug)

Abstract

This specification provides basic geometric interfaces to represent points, rectangles, quadrilaterals and transformation matrices that can be used by other modules or specifications. CSS is a language for describing the rendering of structured documents (such as HTML and XML) on screen, on paper, in speech, etc.

Status of this document

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.

Publication as a Last Call Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.

The (archived) public mailing list public-fx@w3.org (see instructions) is preferred for discussion of this specification. When sending e-mail, please put the text “geometry” in the subject, preferably like this: “[geometry] …summary of comment…”

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

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

This specification is a Last Call Working Draft. All persons are encouraged to review this document and send comments to the public-fx mailing list as described above. The deadline for comments is 7 August 2014.

1 Introduction

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

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

2 The DOMPoint interfaces

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

interface DOMPointReadOnly {
    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double z;
    readonly attribute unrestricted double w;

    DOMPoint matrixTransform(DOMMatrixReadOnly matrix);
};

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

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

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

If invoked with one argument, follow these substeps:
1. Let point be the argument.
2. Let x be the x dictionary member of point.
3. Let y be the y dictionary member of point.
4. Let z be the z dictionary member of point.
5. Let w be the w dictionary member of point.
Otherwise, let x, y, z and w be the given arguments, respectively.
Return a new DOMPoint object with the x, y, z and w attributes set to x, y, z and w, respectively.

The x attribute gives the x coordinate of the point. On getting, it must return the current value. On setting, it must set the current value to the new value.

The y attribute gives the y coordinate of the point. On getting, it must return the current value. On setting, it must set the current value to the new value.

The z attribute gives the z coordinate of the point. On getting, it must return the current value. On setting, it must set the current value to the new value.

The w attribute gives the perspective of the point. On getting, it must return the current value. On setting, it must set the current value to the new value.

The following method does not modify the current DOMPointReadOnly object and returns a new DOMPoint object.

matrixTransform(matrix)

Create a new DOMPoint point initialzed to x, y, z and w of the current point.
Post-multiply point with matrix.
Return point.

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

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

point creates a new DOMPoint object initialized to the same attribute values as point. This new DOMPoint is now scaled and the translated by matrix. This resulting transformPoint has the attribute values x: 20 and y: 18.

For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGPoint whose value is the DOMPoint interface object.

3 The DOMRect interfaces

Objects implementing the DOMRectReadOnly interface represent a rectangle. The type of box is specified by the method or attribute that returns a DOMRect or DOMRectReadOnly object.

Rectangles have the following properties:

origin: When the rectangle has a non-negative width, the rectangle`s horizontal origin is the left edge; otherwise, it is the right edge. Similarly, when the rectangle has a non-negative height, the rectangle`s vertical origin is the top edge; otherwise, it is the bottom edge.
x coordinate: The horizontal distance between the viewport`s left edge and the rectangle`s origin.
y coordinate: The vertical distance between the viewport`s top edge and the rectangle`s origin.
width: The width of the rectangle. Can be negative.
height: The height of the rectangle. Can be negative.

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

interface DOMRectReadOnly {
    readonly attribute unrestricted double x;
    readonly attribute unrestricted double y;
    readonly attribute unrestricted double width;
    readonly attribute unrestricted double height;
    readonly attribute unrestricted double top;
    readonly attribute unrestricted double right;
    readonly attribute unrestricted double bottom;
    readonly attribute unrestricted double left;
};

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

If invoked with no arguments, let x, y, width and height be zero.
Return a new DOMRect object with x coordinate set to x, y coordinate set to y, width set to width and height set to height.

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

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

The width attribute, on getting, must return the width. The width attribute, on setting, must set the width to the new value.

The height attribute, on getting, must return the height. The height attribute, on setting, must set the height to the new value.

The top attribute, on getting, must return min(y coordinate, y coordinate + height).

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

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

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

For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGRect whose value is the DOMRect interface object.

4 The DOMRectList Interface

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 throw an IndexSizeError exception when index is greater than the number of DOMRect objects associated with the object. Otherwise, the DOMRect object at index must be returned.

5 The DOMQuad interface

Objects implementing the DOMQuad interface represents a quadrilateral.

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

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

If invoked with one argument, follow these substeps:
1. Let rect be the argument.
2. Let x, y, width and height be the value of rect`s x, y, width and height attributes, respectively.
3. Let point 1 be a new DOMPoint object with x set to x, y set to y, z set to zero and w set to one.
4. Let point 2 be a new DOMPoint object with x set to x + width, y set to y, z set to zero and w set to one.
5. Let point 3 be a new DOMPoint object with x set to x + width, y set to y + height, z set to zero and w set to one.
6. Let point 4 be a new DOMPoint object with x set to x, y set to y + height, z set to zero and w set to one.
Otherwise, follow these substeps:
1. Let p1, p2, p3 and p4 be the given arguments, in the same order.
2. Let point 1 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p1.
3. Let point 2 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p2.
4. Let point 3 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p3.
5. Let point 4 be a new DOMPoint object with its attributes set to the values of the namesake dictionary members in p4.
Return a new DOMQuad with p1 set to point 1, p2 set to point 2, p3 set to point 3 and p4 set to point 4, and let the associated bounding rectangle be bounds.
Note that it is possible to pass DOMPoint/DOMPointReadOnly arguments as well. The passed arguments will be transformed to the correct object type internally following the WebIDL rules [WEBIDL].

The p1 attribute must return a DOMPoint that represents p1 of the quadrilateral. The author can modify the returned DOMPoint object, which has direct affect on the quadrilateral.

The p2 attribute must return a DOMPoint that represents p2 of the quadrilateral. The author can modify the returned DOMPoint object, which has direct affect on the quadrilateral.

The p3 attribute must return a DOMPoint that represents p3 of the quadrilateral. The author can modify the returned DOMPoint object, which has direct affect on the quadrilateral.

The p4 attribute must return a DOMPoint that represents p4 of the quadrilateral. The author can modify the returned DOMPoint object, which has direct affect on the quadrilateral.

The bounds attribute must return the associated bounding rectangle.

DOMQuad objects have an associated bounding rectangle set to a DOMRectReadOnly object when created. The associated bounding rectangle is live; whenever the objects in p1, p2, p3 or p4 are changed, the associated bounding rectangle must update its attributes as appropriate to describe the new smallest bounding box of the four points.

The associated bounding rectangle is computed as follows:

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

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

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

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

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

This is an example of an irregular quadrilateral:

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

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

6 The DOMMatrix interfaces

The DOMMatrix and DOMMatrixReadOnly interfaces represent a mathematical matrix with the purpose of describing transformations in a graphical context. The following sections describe the details of the interface.

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

For legacy reasons, if the user agent supports SVG, Window objects must have a writable, configurable, non-enumerable property named SVGMatrix whose value is the DOMMatrix interface object. [SVG11]

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

A 4x4 matrix representing a DOMMatrix with items m11 to m44.

In the following sections, terms have the following meaning:

post-multiply: Term A post-multiplied by term B is equal to A · B.
pre-multiply: Term A pre-multiplied by term B is equal to B · A.
multiply: Multiply term A by term B is equal to A · B.

interface DOMMatrixReadOnly {
    // These attributes are simple aliases for certain elements of the 4x4 matrix
    readonly attribute unrestricted double a;
    readonly attribute unrestricted double b;
    readonly attribute unrestricted double c;
    readonly attribute unrestricted double d;
    readonly attribute unrestricted double e;
    readonly attribute unrestricted double f;

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

    readonly attribute boolean is2D;
    readonly attribute boolean isIdentity;

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

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

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

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

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

    DOMMatrix setMatrixValue(DOMString transformList);
};

For historical reasons, Window objects must also have a writable, configurable, non-enumerable property named SVGMatrix whose value is the DOMMatrix interface object.

6.1 DOMMatrix constructors

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

If invoked with no arguments:
1. set the m12, m13, m14, m21, m23, m24, m31, m32, m34, m41, m42, m43 attributes to 0 and the m11, m22, m33, m44 attributes to 1.
2. Set is2D to true.
If invoked with a DOMString argument transformList:
1. Parse transformList by following the syntax description in “Syntax of the SVG ‘transform’ attribute” [CSS3-TRANSFORMS] to a <transform-list>. If parsing is not successful or any <transform-function> has <length> values without absolute length units, throw an SyntaxError exception.
2. Set is2D to false if the <transform-list> consists of any 3D Transform functions. Otherwise set is2D to true.
3. Transform all <transform-function>s to 4x4 matrices by following the “Mathematical Description of Transform Functions” [CSS3-TRANSFORMS].
4. Post-multiply all matrices from left to right to a combined 4x4 matrix.
5. Set the m11 to m44 attributes to the element values of the 4x4 matrix in column-major order.
If invoked with a DOMMatrixReadOnly argument other:
1. Set m11 to m44 attributes to the corresponding attribute values of other.
2. Set is2D to the corresponding flag of other.
If invoked with a Float32Array argument array32:
- If array32 has 6 elements set a, b, c, d, e, f to the element values of array32 in element order starting with the first element. Furthermore, set m31, m32, m13, m23, m43, m14, m24, m34 to 0 and m33, m44 to 1. Set is2D to true.
- If array32 has 16 elements set m11 to m44 to the element values of array32 in column-major order. Set is2D to false.
- Otherwise throw an IndexSizeError exception.
If invoked with a Float64Array argument array64:
- If array64 has 6 elements set a, b, c, d, e, f to the element values of array64 in element order starting with the first element. Furthermore, set m31, m32, m13, m23, m43, m14, m24, m34 to 0 and m33, m44 to 1. Set is2D to true.
- If array64 has 16 elements set m11 to m44 to the element values of array64 in column-major order. Set is2D to false.
- Otherwise throw an IndexSizeError exception.
If invoked with a sequence<unrestricted double> argument numberSequence:
- If numberSequence has 6 elements set a, b, c, d, e, f to the element values of numberSequence in element order starting with the first element. Furthermore, set m31, m32, m13, m23, m43, m14, m24, m34 to 0 and m33, m44 to 1. Set is2D to true.
- If numberSequence has 16 elements set m11 to m44 to the element values of numberSequence in column-major order. Set is2D to false.
- Otherwise throw an IndexSizeError exception.

6.2 DOMMatrix attributes

The following attributes m11 to m44 correspond to the 16 items of the matrix interfaces. If the attributes m31, m32, m13, m23, m43, m14, m24, m34 are set to something else than 0 or m33, m44 are set to something else than 1 set is2D to false.

m11: The value of the element in column 1, row 1 of the matrix.
m12: The value of the element in column 1, row 2 of the matrix.
m13: The value of the element in column 1, row 3 of the matrix.
m14: The value of the element in column 1, row 4 of the matrix.
m21: The value of the element in column 2, row 1 of the matrix.
m22: The value of the element in column 2, row 2 of the matrix.
m23: The value of the element in column 2, row 3 of the matrix.
m24: The value of the element in column 2, row 4 of the matrix.
m31: The value of the element in column 3, row 1 of the matrix.
m32: The value of the element in column 3, row 2 of the matrix.
m33: The value of the element in column 3, row 3 of the matrix.
m34: The value of the element in column 3, row 4 of the matrix.
m41: The value of the element in column 4, row 1 of the matrix.
m42: The value of the element in column 4, row 2 of the matrix.
m43: The value of the element in column 4, row 3 of the matrix.
m44: The value of the element in column 4, row 4 of the matrix.

The following attributes a to b correspond to the 2D components of the matrix interfaces.

a: Corresponds to the attribute m11.
b: Corresponds to the attribute m12.
c: Corresponds to the attribute m21.
d: Corresponds to the attribute m22.
e: Corresponds to the attribute m41.
f: Corresponds to the attribute m42.

The following attribute provide status information about DOMMatrixReadOnly.

is2D

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

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

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

Returns the value of is2D.

isIdentity

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