SVG 1.1 (Second Edition) – 16 August 2011 Top ⋅ Contents ⋅ Previous ⋅ Next ⋅ Elements ⋅ Attributes ⋅ Properties

# 7 Coordinate Systems, Transformations and Units

## Contents

## 7.1 Introduction

For all media, the SVG canvas describes "the space where the SVG content is rendered." The canvas is infinite for each dimension of the space, but rendering occurs relative to a finite rectangular region of the canvas. This finite rectangular region is called the SVG viewport. For visual media ([CSS2], section 7.3.1) the SVG viewport is the viewing area where the user sees the SVG content.

The size of the SVG viewport (i.e., its width and height) is determined by a negotiation process (see Establishing the size of the initial viewport) between the SVG document fragment and its parent (real or implicit). Once that negotiation process is completed, the SVG user agent is provided the following information:

- a number (usually an integer) that represents the width in "pixels" of the viewport
- a number (usually an integer) that represents the height in "pixels" of the viewport
- (highly desirable but not required) a real number value that indicates the size in real world units, such as millimeters, of a "pixel" (i.e., a px unit as defined in CSS2 ([CSS2], section 4.3.2)

Using the above information, the SVG user agent determines the viewport, an initial viewport coordinate system and an initial user coordinate system such that the two coordinates systems are identical. Both coordinates systems are established such that the origin matches the origin of the viewport (for the root viewport, the viewport origin is at the top/left corner), and one unit in the initial coordinate system equals one "pixel" in the viewport. (See Initial coordinate system.) The viewport coordinate system is also called viewport space and the user coordinate system is also called user space.

Lengths in SVG can be specified as:

- (if no unit identifier is provided) values in user space — for example, "15"
- (if a unit identifier is provided) a length expressed as an absolute or relative unit measure — for example, "15mm" or "5em"

The supported length unit identifiers are: em, ex, px, pt, pc, cm, mm, in, and percentages.

A new user space (i.e., a new current coordinate system) can be established at any place within an SVG document fragment by specifying transformations in the form of transformation matrices or simple transformation operations such as rotation, skewing, scaling and translation. Establishing new user spaces via coordinate system transformations are fundamental operations to 2D graphics and represent the usual method of controlling the size, position, rotation and skew of graphic objects.

New viewports also can be established. By establishing a new viewport, you can redefine the meaning of percentages units and provide a new reference rectangle for "fitting" a graphic into a particular rectangular area. ("Fit" means that a given graphic is transformed in such a way that its bounding box in user space aligns exactly with the edges of a given viewport.)

## 7.2 The initial viewport

The SVG user agent negotiates with its parent user agent to determine the viewport into which the SVG user agent can render the document. In some circumstances, SVG content will be embedded (by reference or inline) within a containing document. This containing document might include attributes, properties and/or other parameters (explicit or implicit) which specify or provide hints about the dimensions of the viewport for the SVG content. SVG content itself optionally can provide information about the appropriate viewport region for the content via the ‘width’ and ‘height’ XML attributes on the outermost svg element. The negotiation process uses any information provided by the containing document and the SVG content itself to choose the viewport location and size.

The ‘width’ attribute on the outermost svg element establishes the viewport's width, unless the following conditions are met:

- the SVG content is a separately stored resource that is embedded by reference (such as the ‘object’ element in XHTML [XHTML]), or the SVG content is embedded inline within a containing document;
- and the referencing element or containing document is styled using CSS [CSS2] or XSL [XSL];
- and there are CSS-compatible positioning properties ([CSS2], section 9.3) specified on the referencing element (e.g., the ‘object’ element) or on the containing document's outermost svg element that are sufficient to establish the width of the viewport.

Under these conditions, the positioning properties establish the viewport's width.

Similarly, if there are positioning properties specified on the referencing element or on the outermost svg element that are sufficient to establish the height of the viewport, then these positioning properties establish the viewport's height; otherwise, the ‘height’ attribute on the outermost svg element establishes the viewport's height.

If the ‘width’ or ‘height’ attributes on the outermost svg element are in user units (i.e., no unit identifier has been provided), then the value is assumed to be equivalent to the same number of "px" units (see Units).

In the following example, an SVG graphic is embedded inline within a parent XML document which is formatted using CSS layout rules. Since CSS positioning properties are not provided on the outermost svg element, the width="100px" and height="200px" attributes determine the size of the initial viewport:

    <?xml version="1.0" standalone="yes"?>
    <parent xmlns="http://some.url">

       <!-- SVG graphic -->
       <svg xmlns='http://www.w3.org/2000/svg'
          width="100px" height="200px" version="1.1">
          <path d="M100,100 Q200,400,300,100"/>
          <!-- rest of SVG graphic would go here -->
       </svg>

    </parent>

The initial clipping path for the SVG document fragment is established according to the rules described in The initial clipping path.

## 7.3 The initial coordinate system

For the outermost svg element, the SVG user agent determines an initial viewport coordinate system and an initial user coordinate system such that the two coordinates systems are identical. The origin of both coordinate systems is at the origin of the viewport, and one unit in the initial coordinate system equals one "pixel" (i.e., a px unit as defined in CSS2 ([CSS2], section 4.3.2) in the viewport. In most cases, such as stand-alone SVG documents or SVG document fragments embedded (by reference or inline) within XML parent documents where the parent's layout is determined by CSS [CSS2] or XSL [XSL], the initial viewport coordinate system (and therefore the initial user coordinate system) has its origin at the top/left of the viewport, with the positive x-axis pointing towards the right, the positive y-axis pointing down, and text rendered with an "upright" orientation, which means glyphs are oriented such that Roman characters and full-size ideographic characters for Asian scripts have the top edge of the corresponding glyphs oriented upwards and the right edge of the corresponding glyphs oriented to the right.

If the SVG implementation is part of a user agent which supports styling XML documents using CSS2 compatible px units, then the SVG user agent should get its initial value for the size of a px unit in real world units to match the value used for other XML styling operations; otherwise, if the user agent can determine the size of a px unit from its environment, it should use that value; otherwise, it should choose an appropriate size for one px unit. In all cases, the size of a px must be in conformance with the rules described in CSS2 ([CSS2], section 4.3.2).

Example InitialCoords below shows that the initial coordinate system has the origin at the top/left with the x-axis pointing to the right and the y-axis pointing down. The initial user coordinate system has one user unit equal to the parent (implicit or explicit) user agent's "pixel".

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="300px" height="100px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example InitialCoords - SVG's initial coordinate system</desc>

      <g fill="none" stroke="black" stroke-width="3" >
        <line x1="0" y1="1.5" x2="300" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="100" />
      </g>
      <g fill="red" stroke="none" >
        <rect x="0" y="0" width="3" height="3" />
        <rect x="297" y="0" width="3" height="3" />
        <rect x="0" y="97" width="3" height="3" />
      </g>
      <g font-size="14" font-family="Verdana" >
        <text x="10" y="20">(0,0)</text>
        <text x="240" y="20">(300,0)</text>
        <text x="10" y="90">(0,100)</text>
      </g>
    </svg>

Example InitialCoords

View this example as SVG (SVG-enabled browsers only)

## 7.4 Coordinate system transformations

A new user space (i.e., a new current coordinate system) can be established by specifying transformations in the form of a ‘transform’ attribute on a container element or graphics element or a ‘viewBox’ attribute on an ‘svg’, ‘symbol’, ‘marker’, ‘pattern’ and the ‘view’ element. The ‘transform’ and ‘viewBox’ attributes transform user space coordinates and lengths on sibling attributes on the given element (see effect of the ‘transform’ attribute on sibling attributes and effect of the ‘viewBox’ attribute on sibling attributes) and all of its descendants. Transformations can be nested, in which case the effect of the transformations are cumulative.

Example OrigCoordSys below shows a document without transformations. The text string is specified in the initial coordinate system.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="150px"
         xmlns="http://www.w3.org/2000/svg" version="1.1">
      <desc>Example OrigCoordSys - Simple transformations: original picture</desc>
      <g fill="none" stroke="black" stroke-width="3" >
        <!-- Draw the axes of the original coordinate system -->
        <line x1="0" y1="1.5" x2="400" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="150" />
      </g>
      <g>
        <text x="30" y="30" font-size="20" font-family="Verdana" >
          ABC (orig coord system)
        </text>
      </g>
    </svg>

Example OrigCoordSys

View this example as SVG (SVG-enabled browsers only)

Example NewCoordSys establishes a new user coordinate system by specifying transform="translate(50,50)" on the third ‘g’ element below. The new user coordinate system has its origin at location (50,50) in the original coordinate system. The result of this transformation is that the coordinate (30,30) in the new user coordinate system gets mapped to coordinate (80,80) in the original coordinate system (i.e., the coordinates have been translated by 50 units in X and 50 units in Y).

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="150px"
         xmlns="http://www.w3.org/2000/svg" version="1.1">
      <desc>Example NewCoordSys - New user coordinate system</desc>
      <g fill="none" stroke="black" stroke-width="3" >
        <!-- Draw the axes of the original coordinate system -->
        <line x1="0" y1="1.5" x2="400" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="150" />
      </g>
      <g>
        <text x="30" y="30" font-size="20" font-family="Verdana" >
          ABC (orig coord system)
        </text>
      </g>
      <!-- Establish a new coordinate system, which is
           shifted (i.e., translated) from the initial coordinate
           system by 50 user units along each axis. -->
      <g transform="translate(50,50)">
        <g fill="none" stroke="red" stroke-width="3" >
          <!-- Draw lines of length 50 user units along
               the axes of the new coordinate system -->
          <line x1="0" y1="0" x2="50" y2="0" stroke="red" />
          <line x1="0" y1="0" x2="0" y2="50" />
        </g>
        <text x="30" y="30" font-size="20" font-family="Verdana" >
          ABC (translated coord system)
        </text>
      </g>
    </svg>

Example NewCoordSys

View this example as SVG (SVG-enabled browsers only)

Example RotateScale illustrates simple rotate and scale transformations. The example defines two new coordinate systems:

- one which is the result of a translation by 50 units in X and 30 units in Y, followed by a rotation of 30 degrees
- another which is the result of a translation by 200 units in X and 40 units in Y, followed by a scale transformation of 1.5.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="120px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example RotateScale - Rotate and scale transforms</desc>
      <g fill="none" stroke="black" stroke-width="3" >
        <!-- Draw the axes of the original coordinate system -->
        <line x1="0" y1="1.5" x2="400" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="120" />
      </g>
      <!-- Establish a new coordinate system whose origin is at (50,30)
           in the initial coord. system and which is rotated by 30 degrees. -->
      <g transform="translate(50,30)">
        <g transform="rotate(30)">
          <g fill="none" stroke="red" stroke-width="3" >
            <line x1="0" y1="0" x2="50" y2="0" />
            <line x1="0" y1="0" x2="0" y2="50" />
          </g>
          <text x="0" y="0" font-size="20" font-family="Verdana" fill="blue" >
            ABC (rotate)
          </text>
        </g>
      </g>
      <!-- Establish a new coordinate system whose origin is at (200,40)
           in the initial coord. system and which is scaled by 1.5. -->
      <g transform="translate(200,40)">
        <g transform="scale(1.5)">
          <g fill="none" stroke="red" stroke-width="3" >
            <line x1="0" y1="0" x2="50" y2="0" />
            <line x1="0" y1="0" x2="0" y2="50" />
          </g>
          <text x="0" y="0" font-size="20" font-family="Verdana" fill="blue" >
            ABC (scale)
          </text>
        </g>
      </g>
    </svg>

Example RotateScale

View this example as SVG (SVG-enabled browsers only)

Example Skew defines two coordinate systems which are skewed relative to the origin coordinate system.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="120px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example Skew - Show effects of skewX and skewY</desc>
      <g fill="none" stroke="black" stroke-width="3" >
        <!-- Draw the axes of the original coordinate system -->
        <line x1="0" y1="1.5" x2="400" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="120" />
      </g>
      <!-- Establish a new coordinate system whose origin is at (30,30)
           in the initial coord. system and which is skewed in X by 30 degrees. -->
      <g transform="translate(30,30)">
        <g transform="skewX(30)">
          <g fill="none" stroke="red" stroke-width="3" >
            <line x1="0" y1="0" x2="50" y2="0" />
            <line x1="0" y1="0" x2="0" y2="50" />
          </g>
          <text x="0" y="0" font-size="20" font-family="Verdana" fill="blue" >
            ABC (skewX)
          </text>
        </g>
      </g>
      <!-- Establish a new coordinate system whose origin is at (200,30)
           in the initial coord. system and which is skewed in Y by 30 degrees. -->
      <g transform="translate(200,30)">
        <g transform="skewY(30)">
          <g fill="none" stroke="red" stroke-width="3" >
            <line x1="0" y1="0" x2="50" y2="0" />
            <line x1="0" y1="0" x2="0" y2="50" />
          </g>
          <text x="0" y="0" font-size="20" font-family="Verdana" fill="blue" >
            ABC (skewY)
          </text>
        </g>
      </g>
    </svg>

Example Skew

View this example as SVG (SVG-enabled browsers only)

Mathematically, all transformations can be represented as 3x3 transformation matrices of the following form:

Since only six values are used in the above 3x3 matrix, a transformation matrix is also expressed as a vector: [a b c d e f].

Transformations map coordinates and lengths from a new coordinate system into a previous coordinate system:

Simple transformations are represented in matrix form as follows:

- Translation is equivalent to the matrix
  or [1 0 0 1 tx ty], where tx and ty are the distances to translate coordinates in X and Y, respectively.
- Scaling is equivalent to the matrix
  or [sx 0 0 sy 0 0]. One unit in the X and Y directions in the new coordinate system equals sx and sy units in the previous coordinate system, respectively.
- Rotation about the origin is equivalent to the matrix
  or [cos(a) sin(a) -sin(a) cos(a) 0 0], which has the effect of rotating the coordinate system axes by angle a.
- A skew transformation along the x-axis is equivalent to the matrix
  or [1 0 tan(a) 1 0 0], which has the effect of skewing X coordinates by angle a.
- A skew transformation along the y-axis is equivalent to the matrix
  or [1 tan(a) 0 1 0 0], which has the effect of skewing Y coordinates by angle a.

## 7.5 Nested transformations

Transformations can be nested to any level. The effect of nested transformations is to post-multiply (i.e., concatenate) the subsequent transformation matrices onto previously defined transformations:

For each given element, the accumulation of all transformations that have been defined on the given element and all of its ancestors up to and including the element that established the current viewport (usually, the ‘svg’ element which is the most immediate ancestor to the given element) is called the current transformation matrix or CTM. The CTM thus represents the mapping of current user coordinates to viewport coordinates:

Example Nested illustrates nested transformations.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="150px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example Nested - Nested transformations</desc>
      <g fill="none" stroke="black" stroke-width="3" >
        <!-- Draw the axes of the original coordinate system -->
        <line x1="0" y1="1.5" x2="400" y2="1.5" />
        <line x1="1.5" y1="0" x2="1.5" y2="150" />
      </g>
      <!-- First, a translate -->
      <g transform="translate(50,90)">
        <g fill="none" stroke="red" stroke-width="3" >
          <line x1="0" y1="0" x2="50" y2="0" />
          <line x1="0" y1="0" x2="0" y2="50" />
        </g>
        <text x="0" y="0" font-size="16" font-family="Verdana" >
          ....Translate(1)
        </text>
        <!-- Second, a rotate -->
        <g transform="rotate(-45)">
          <g fill="none" stroke="green" stroke-width="3" >
            <line x1="0" y1="0" x2="50" y2="0" />
            <line x1="0" y1="0" x2="0" y2="50" />
          </g>
          <text x="0" y="0" font-size="16" font-family="Verdana" >
            ....Rotate(2)
          </text>
          <!-- Third, another translate -->
          <g transform="translate(130,160)">
            <g fill="none" stroke="blue" stroke-width="3" >
              <line x1="0" y1="0" x2="50" y2="0" />
              <line x1="0" y1="0" x2="0" y2="50" />
            </g>
            <text x="0" y="0" font-size="16" font-family="Verdana" >
              ....Translate(3)
            </text>
          </g>
        </g>
      </g>
    </svg>

Example Nested

View this example as SVG (SVG-enabled browsers only)

In the example above, the CTM within the third nested transformation (i.e., the transform="translate(130,160)") consists of the concatenation of the three transformations, as follows:

## 7.6 The ‘transform’ attribute

The value of the ‘transform’ attribute is a <transform-list>, which is defined as a list of transform definitions, which are applied in the order provided. The individual transform definitions are separated by whitespace and/or a comma. The available types of transform definitions include:

- matrix(<a> <b> <c> <d> <e> <f>), which specifies a transformation in the form of a transformation matrix of six values. matrix(a,b,c,d,e,f) is equivalent to applying the transformation matrix [a b c d e f].
- translate(<tx> [<ty>]), which specifies a translation by tx and ty. If <ty> is not provided, it is assumed to be zero.
- scale(<sx> [<sy>]), which specifies a scale operation by sx and sy. If <sy> is not provided, it is assumed to be equal to <sx>.
- rotate(<rotate-angle> [<cx> <cy>]), which specifies a rotation by <rotate-angle> degrees about a given point.
  If optional parameters <cx> and <cy> are not supplied, the rotate is about the origin of the current user coordinate system. The operation corresponds to the matrix [cos(a) sin(a) -sin(a) cos(a) 0 0].
  If optional parameters <cx> and <cy> are supplied, the rotate is about the point (cx, cy). The operation represents the equivalent of the following specification: translate(<cx>, <cy>) rotate(<rotate-angle>) translate(-<cx>, -<cy>).
- skewX(<skew-angle>), which specifies a skew transformation along the x-axis.
- skewY(<skew-angle>), which specifies a skew transformation along the y-axis.

All numeric values are <number>s.

If a list of transforms is provided, then the net effect is as if each transform had been specified separately in the order provided. For example,

    <g transform="translate(-10,-20) scale(2) rotate(45) translate(5,10)">
      <!-- graphics elements go here -->
    </g>

is functionally equivalent to:

    <g transform="translate(-10,-20)">
      <g transform="scale(2)">
        <g transform="rotate(45)">
          <g transform="translate(5,10)">
            <!-- graphics elements go here -->
          </g>
        </g>
      </g>
    </g>

The ‘transform’ attribute is applied to an element before processing any other coordinate or length values supplied for that element. In the element

    <rect x="10" y="10" width="20" height="20" transform="scale(2)"/>

the x, y, width and height values are processed after the current coordinate system has been scaled uniformly by a factor of 2 by the ‘transform’ attribute. Attributes x, y, width and height (and any other attributes or properties) are treated as values in the new user coordinate system, not the previous user coordinate system. Thus, the above ‘rect’ element is functionally equivalent to:

    <g transform="scale(2)">
      <rect x="10" y="10" width="20" height="20"/>
    </g>

The following is the Backus-Naur Form (BNF) for values for the ‘transform’ attribute. The following notation is used:

- *: 0 or more
- +: 1 or more
- ?: 0 or 1
- (): grouping
- |: separates alternatives
- double quotes surround literals

    transform-list:
        wsp* transforms? wsp*
    transforms:
        transform
        | transform comma-wsp+ transforms
    transform:
        matrix
        | translate
        | scale
        | rotate
        | skewX
        | skewY
    matrix:
        "matrix" wsp* "(" wsp*
           number comma-wsp
           number comma-wsp
           number comma-wsp
           number comma-wsp
           number comma-wsp
           number wsp* ")"
    translate:
        "translate" wsp* "(" wsp* number ( comma-wsp number )? wsp* ")"
    scale:
        "scale" wsp* "(" wsp* number ( comma-wsp number )? wsp* ")"
    rotate:
        "rotate" wsp* "(" wsp* number ( comma-wsp number comma-wsp number )? wsp* ")"
    skewX:
        "skewX" wsp* "(" wsp* number wsp* ")"
    skewY:
        "skewY" wsp* "(" wsp* number wsp* ")"
    number:
        sign? integer-constant
        | sign? floating-point-constant
    comma-wsp:
        (wsp+ comma? wsp*) | (comma wsp*)
    comma:
        ","
    integer-constant:
        digit-sequence
    floating-point-constant:
        fractional-constant exponent?
        | digit-sequence exponent
    fractional-constant:
        digit-sequence? "." digit-sequence
        | digit-sequence "."
    exponent:
        ( "e" | "E" ) sign? digit-sequence
    sign:
        "+" | "-"
    digit-sequence:
        digit
        | digit digit-sequence
    digit:
        "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
    wsp:
        (#x20 | #x9 | #xD | #xA)

For the ‘transform’ attribute:

Animatable: yes.

See the ‘animateTransform’ element for information on animating transformations.

## 7.7 The ‘viewBox’ attribute

It is often desirable to specify that a given set of graphics stretch to fit a particular container element. The ‘viewBox’ attribute provides this capability.

All elements that establish a new viewport (see elements that establish viewports), plus the ‘marker’, ‘pattern’ and ‘view’ elements have attribute ‘viewBox’. The value of the ‘viewBox’ attribute is a list of four numbers <min-x>, <min-y>, <width> and <height>, separated by whitespace and/or a comma, which specify a rectangle in user space which should be mapped to the bounds of the viewport established by the given element, taking into account attribute ‘preserveAspectRatio’. If specified, an additional transformation is applied to all descendants of the given element to achieve the specified effect.

A negative value for <width> or <height> is an error (see Error processing). A value of zero disables rendering of the element.

Example ViewBox illustrates the use of the ‘viewBox’ attribute on the outermost svg element to specify that the SVG content should stretch to fit bounds of the viewport.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="300px" height="200px" version="1.1"
         viewBox="0 0 1500 1000" preserveAspectRatio="none"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example ViewBox - uses the viewBox
       attribute to automatically create an initial user coordinate
       system which causes the graphic to scale to fit into the
       viewport no matter what size the viewport is.</desc>
      <!-- This rectangle goes from (0,0) to (1500,1000) in user space.
           Because of the viewBox attribute above,
           the rectangle will end up filling the entire area
           reserved for the SVG content. -->
      <rect x="0" y="0" width="1500" height="1000"
            fill="yellow" stroke="blue" stroke-width="12"  />
      <!-- A large, red triangle -->
      <path fill="red"  d="M 750,100 L 250,900 L 1250,900 z"/>
      <!-- A text string that spans most of the viewport -->
      <text x="100" y="600" font-size="200" font-family="Verdana" >
        Stretch to fit
      </text>
    </svg>

Example ViewBox
Rendered into viewport with width=300px, height=200px |  | Rendered into viewport with width=150px, height=200px
--- | --- | ---

View this example as SVG (SVG-enabled browsers only)

The effect of the ‘viewBox’ attribute is that the user agent automatically supplies the appropriate transformation matrix to map the specified rectangle in user space to the bounds of a designated region (often, the viewport). To achieve the effect of the example on the left, with viewport dimensions of 300 by 200 pixels, the user agent needs to automatically insert a transformation which scales both X and Y by 0.2. The effect is equivalent to having a viewport of size 300px by 200px and the following supplemental transformation in the document, as follows:

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="300px" height="200px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <g transform="scale(0.2)">
        <!-- Rest of document goes here -->
      </g>
    </svg>

To achieve the effect of the example on the right, with viewport dimensions of 150 by 200 pixels, the user agent needs to automatically insert a transformation which scales X by 0.1 and Y by 0.2. The effect is equivalent to having a viewport of size 150px by 200px and the following supplemental transformation in the document, as follows:

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="150px" height="200px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <g transform="scale(0.1 0.2)">
        <!-- Rest of document goes here -->
      </g>
    </svg>

(Note: in some cases the user agent will need to supply a translate transformation in addition to a scale transformation. For example, on an outermost svg element, a translate transformation will be needed if the ‘viewBox’ attributes specifies values other than zero for <min-x> or <min-y>.)

Unlike the ‘transform’ attribute (see effect of the ‘transform’ on sibling attributes), the automatic transformation that is created due to a ‘viewBox’ does not affect the ‘x’, ‘y’, ‘width’ and ‘height’ attributes (or in the case of the ‘marker’ element, the ‘markerWidth’ and ‘markerHeight’ attributes) on the element with the ‘viewBox’ attribute. Thus, in the example above which shows an ‘svg’ element which has attributes ‘width’, ‘height’ and ‘viewBox’, the ‘width’ and ‘height’ attributes represent values in the coordinate system that exists before the ‘viewBox’ transformation is applied. On the other hand, like the ‘transform’ attribute, it does establish a new coordinate system for all other attributes and for descendant elements.

For the ‘viewBox’ attribute:

Animatable: yes.

## 7.8 The ‘preserveAspectRatio’ attribute

In some cases, typically when using the ‘viewBox’ attribute, it is desirable that the graphics stretch to fit non-uniformly to take up the entire viewport. In other cases, it is desirable that uniform scaling be used for the purposes of preserving the aspect ratio of the graphics.

Attribute preserveAspectRatio="[defer] <align> [<meetOrSlice>]", which is available for all elements that establish a new viewport (see elements that establish viewports), plus the ‘image’, ‘marker’, ‘pattern’ and ‘view’ elements, indicates whether or not to force uniform scaling.

For elements that establish a new viewport (see elements that establish viewports), plus the ‘marker’, ‘pattern’ and ‘view’ elements, ‘preserveAspectRatio’ only applies when a value has been provided for ‘viewBox’ on the same element. For these elements, if attribute ‘viewBox’ is not provided, then ‘preserveAspectRatio’ is ignored.

For ‘image’ elements, ‘preserveAspectRatio’ indicates how referenced images should be fitted with respect to the reference rectangle and whether the aspect ratio of the referenced image should be preserved with respect to the current user coordinate system.

If the value of ‘preserveAspectRatio’ on an ‘image’ element starts with 'defer' then the value of the ‘preserveAspectRatio’ attribute on the referenced content if present should be used. If the referenced content lacks a value for ‘preserveAspectRatio’ then the ‘preserveAspectRatio’ attribute should be processed as normal (ignoring 'defer'). For ‘preserveAspectRatio’ on all other elements the 'defer' portion of the attribute is ignored.

The <align> parameter indicates whether to force uniform scaling and, if so, the alignment method to use in case the aspect ratio of the ‘viewBox’ doesn't match the aspect ratio of the viewport. The <align> parameter must be one of the following strings:

- none - Do not force uniform scaling. Scale the graphic content of the given element non-uniformly if necessary such that the element's bounding box exactly matches the viewport rectangle.
  (Note: if <align> is none, then the optional <meetOrSlice> value is ignored.)
- xMinYMin - Force uniform scaling.
  Align the <min-x> of the element's ‘viewBox’ with the smallest X value of the viewport.
  Align the <min-y> of the element's ‘viewBox’ with the smallest Y value of the viewport.
- xMidYMin - Force uniform scaling.
  Align the midpoint X value of the element's ‘viewBox’ with the midpoint X value of the viewport.
  Align the <min-y> of the element's ‘viewBox’ with the smallest Y value of the viewport.
- xMaxYMin - Force uniform scaling.
  Align the <min-x>+<width> of the element's ‘viewBox’ with the maximum X value of the viewport.
  Align the <min-y> of the element's ‘viewBox’ with the smallest Y value of the viewport.
- xMinYMid - Force uniform scaling.
  Align the <min-x> of the element's ‘viewBox’ with the smallest X value of the viewport.
  Align the midpoint Y value of the element's ‘viewBox’ with the midpoint Y value of the viewport.
- xMidYMid (the default) - Force uniform scaling.
  Align the midpoint X value of the element's ‘viewBox’ with the midpoint X value of the viewport.
  Align the midpoint Y value of the element's ‘viewBox’ with the midpoint Y value of the viewport.
- xMaxYMid - Force uniform scaling.
  Align the <min-x>+<width> of the element's ‘viewBox’ with the maximum X value of the viewport.
  Align the midpoint Y value of the element's ‘viewBox’ with the midpoint Y value of the viewport.
- xMinYMax - Force uniform scaling.
  Align the <min-x> of the element's ‘viewBox’ with the smallest X value of the viewport.
  Align the <min-y>+<height> of the element's ‘viewBox’ with the maximum Y value of the viewport.
- xMidYMax - Force uniform scaling.
  Align the midpoint X value of the element's ‘viewBox’ with the midpoint X value of the viewport.
  Align the <min-y>+<height> of the element's ‘viewBox’ with the maximum Y value of the viewport.
- xMaxYMax - Force uniform scaling.
  Align the <min-x>+<width> of the element's ‘viewBox’ with the maximum X value of the viewport.
  Align the <min-y>+<height> of the element's ‘viewBox’ with the maximum Y value of the viewport.

The <meetOrSlice> parameter is optional and, if provided, is separated from the <align> value by one or more spaces and then must be one of the following strings:

- meet (the default) - Scale the graphic such that:
  - aspect ratio is preserved
  - the entire ‘viewBox’ is visible within the viewport
  - the ‘viewBox’ is scaled up as much as possible, while still meeting the other criteria
  In this case, if the aspect ratio of the graphic does not match the viewport, some of the viewport will extend beyond the bounds of the ‘viewBox’ (i.e., the area into which the ‘viewBox’ will draw will be smaller than the viewport).
- slice - Scale the graphic such that:
  - aspect ratio is preserved
  - the entire viewport is covered by the ‘viewBox’
  - the ‘viewBox’ is scaled down as much as possible, while still meeting the other criteria
  In this case, if the aspect ratio of the ‘viewBox’ does not match the viewport, some of the ‘viewBox’ will extend beyond the bounds of the viewport (i.e., the area into which the ‘viewBox’ will draw is larger than the viewport).

Example PreserveAspectRatio illustrates the various options on ‘preserveAspectRatio’. To save space, XML entities have been defined for the three repeated graphic objects, the rectangle with the smile inside and the outlines of the two rectangles which have the same dimensions as the target viewports. The example creates several new viewports by including ‘svg’ sub-elements embedded inside the outermost svg element (see Establishing a new viewport).

    <?xml version="1.0" encoding="UTF-8"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"
    [ <!ENTITY Smile "
    <rect x='.5' y='.5' width='29' height='39' fill='black' stroke='red'/>
    <g transform='translate(0, 5)'>
    <circle cx='15' cy='15' r='10' fill='yellow'/>
    <circle cx='12' cy='12' r='1.5' fill='black'/>
    <circle cx='17' cy='12' r='1.5' fill='black'/>
    <path d='M 10 19 A 8 8 0 0 0 20 19' stroke='black' stroke-width='2'/>
    </g>
    ">
    <!ENTITY Viewport1 "<rect x='.5' y='.5' width='49' height='29'
    fill='none' stroke='blue'/>">
    <!ENTITY Viewport2 "<rect x='.5' y='.5' width='29' height='59'
    fill='none' stroke='blue'/>">
    ]>

    <svg width="450px" height="300px" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>Example PreserveAspectRatio - illustrates preserveAspectRatio attribute</desc>
      <rect x="1" y="1" width="448" height="298"
            fill="none" stroke="blue"/>
      <g font-size="9">
        <text x="10" y="30">SVG to fit</text>
        <g transform="translate(20,40)">&Smile;</g>
        <text x="10" y="110">Viewport 1</text>
        <g transform="translate(10,120)">&Viewport1;</g>
        <text x="10" y="180">Viewport 2</text>
        <g transform="translate(20,190)">&Viewport2;</g>

        <g id="meet-group-1" transform="translate(100, 60)">
          <text x="0" y="-30">--------------- meet ---------------</text>
          <g><text y="-10">xMin*</text>&Viewport1;
            <svg preserveAspectRatio="xMinYMin meet" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
          <g transform="translate(70,0)"><text y="-10">xMid*</text>&Viewport1;
            <svg preserveAspectRatio="xMidYMid meet" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
          <g transform="translate(0,70)"><text y="-10">xMax*</text>&Viewport1;
            <svg preserveAspectRatio="xMaxYMax meet" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
        </g>

        <g id="meet-group-2" transform="translate(250, 60)">
          <text x="0" y="-30">---------- meet ----------</text>
          <g><text y="-10">*YMin</text>&Viewport2;
            <svg preserveAspectRatio="xMinYMin meet" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
          <g transform="translate(50, 0)"><text y="-10">*YMid</text>&Viewport2;
            <svg preserveAspectRatio="xMidYMid meet" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
          <g transform="translate(100, 0)"><text y="-10">*YMax</text>&Viewport2;
            <svg preserveAspectRatio="xMaxYMax meet" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
        </g>

        <g id="slice-group-1" transform="translate(100, 220)">
          <text x="0" y="-30">---------- slice ----------</text>
          <g><text y="-10">xMin*</text>&Viewport2;
            <svg preserveAspectRatio="xMinYMin slice" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
          <g transform="translate(50,0)"><text y="-10">xMid*</text>&Viewport2;
            <svg preserveAspectRatio="xMidYMid slice" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
          <g transform="translate(100,0)"><text y="-10">xMax*</text>&Viewport2;
            <svg preserveAspectRatio="xMaxYMax slice" viewBox="0 0 30 40"
                 width="30" height="60">&Smile;</svg></g>
        </g>

        <g id="slice-group-2" transform="translate(250, 220)">
          <text x="0" y="-30">--------------- slice ---------------</text>
          <g><text y="-10">*YMin</text>&Viewport1;
            <svg preserveAspectRatio="xMinYMin slice" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
          <g transform="translate(70,0)"><text y="-10">*YMid</text>&Viewport1;
            <svg preserveAspectRatio="xMidYMid slice" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
          <g transform="translate(140,0)"><text y="-10">*YMax</text>&Viewport1;
            <svg preserveAspectRatio="xMaxYMax slice" viewBox="0 0 30 40"
                 width="50" height="30">&Smile;</svg></g>
        </g>
      </g>
    </svg>

Example PreserveAspectRatio

View this example as SVG (SVG-enabled browsers only)

For the ‘preserveAspectRatio’ attribute:

Animatable: yes.

## 7.9 Establishing a new viewport

At any point in an SVG drawing, you can establish a new viewport into which all contained graphics is drawn by including an ‘svg’ element inside SVG content. By establishing a new viewport, you also implicitly establish a new viewport coordinate system, a new user coordinate system, and, potentially, a new clipping path (see the definition of the ‘overflow’ property). Additionally, there is a new meaning for percentage units defined to be relative to the current viewport since a new viewport has been established (see Units).

The bounds of the new viewport are defined by the ‘x’, ‘y’, ‘width’ and ‘height’ attributes on the element establishing the new viewport, such as an ‘svg’ element. Both the new viewport coordinate system and the new user coordinate system have their origins at (‘x’, ‘y’), where ‘x’ and ‘y’ represent the value of the corresponding attributes on the element establishing the viewport. The orientation of the new viewport coordinate system and the new user coordinate system correspond to the orientation of the current user coordinate system for the element establishing the viewport. A single unit in the new viewport coordinate system and the new user coordinate system are the same size as a single unit in the current user coordinate system for the element establishing the viewport.

Here is an example:

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="4in" height="3in" version="1.1"
         xmlns="http://www.w3.org/2000/svg">
      <desc>This SVG drawing embeds another one,
        thus establishing a new viewport
      </desc>
      <!-- The following statement establishing a new viewport
           and renders SVG drawing B into that viewport -->
      <svg x="25%" y="25%" width="50%" height="50%">
         <!-- drawing B goes here -->
      </svg>
    </svg>

For an extensive example of creating new viewports, see Example PreserveAspectRatio.

The following elements establish new viewports:

- The ‘svg’ element
- A ‘symbol’ element define new viewports whenever they are instanced by a ‘use’ element.
- An ‘image’ element that references an SVG file will result in the establishment of a temporary new viewport since the referenced resource by definition will have an ‘svg’ element.
- A ‘foreignObject’ element creates a new viewport for rendering the content that is within the element.

Whether a new viewport also establishes a new additional clipping path is determined by the value of the ‘overflow’ property on the element that establishes the new viewport. If a clipping path is created to correspond to the new viewport, the clipping path's geometry is determined by the value of the ‘clip’ property. Also, see Clip to viewport vs. clip to ‘viewBox’.

## 7.10 Units

All coordinates and lengths in SVG can be specified with or without a unit identifier.

When a coordinate or length value is a number without a unit identifier (e.g., "25"), then the given coordinate or length is assumed to be in user units (i.e., a value in the current user coordinate system). For example:

    <text font-size="50">Text size is 50 user units</text>

Alternatively, a coordinate or length value can be expressed as a number followed by a unit identifier (e.g., "25cm" or "15em"). (Note that CSS defined properties used in a CSS style sheet or the ‘style’ attribute require units for non-zero lengths, see SVG's styling properties.) The list of unit identifiers in SVG matches the list of unit identifiers in CSS: em, ex, px, pt, pc, cm, mm and in. The <length> type can also have a percentage unit identifier. The following describes how the various unit identifiers are processed:

- As in CSS, the em and ex unit identifiers are relative to the current font's font-size and x-height, respectively.

- One px unit is defined to be equal to one user unit. Thus, a length of "5px" is the same as a length of "5".

  Note that at initialization, a user unit in the the initial coordinate system is equivalenced to the parent environment's notion of a px unit. Thus, in the the initial coordinate system, because the user coordinate system aligns exactly with the parent's coordinate system, and because often the parent's coordinate system aligns with the device pixel grid, "5px" might actually map to 5 devices pixels. However, if there are any coordinate system transformation due to the use of ‘transform’ or ‘viewBox’ attributes, because "5px" maps to 5 user units and because the coordinate system transformations have resulted in a revised user coordinate system, "5px" likely will not map to 5 device pixels. As a result, in most circumstances, "px" units will not map to the device pixel grid.

- The other absolute unit identifiers from CSS (i.e., pt, pc, cm, mm, in) are all defined as an appropriate multiple of one px unit (which, according to the previous item, is defined to be equal to one user unit), based on what the SVG user agent determines is the size of a px unit (possibly passed from the parent processor or environment at initialization time). For example, suppose that the user agent can determine from its environment that "1px" corresponds to "0.2822222mm" (i.e., 90dpi). Then, for all processing of SVG content:

  - "1pt" equals "1.25px" (and therefore 1.25 user units)
  - "1pc" equals "15px" (and therefore 15 user units)
  - "1mm" would be "3.543307px" (3.543307 user units)
  - "1cm" equals "35.43307px" (and therefore 35.43307 user units)
  - "1in" equals "90px" (and therefore 90 user units)

Note that use of px units or any other absolute unit identifiers can cause inconsistent visual results on different viewing environments since the size of "1px" may map to a different number of user units on different systems; thus, absolute units identifiers are only recommended for the ‘width’ and the ‘height’ on and situations where the content contains no transformations and it is desirable to specify values relative to the device pixel grid or to a particular real world unit size.

For percentage values that are defined to be relative to the size of viewport:

- For any x-coordinate value or width value expressed as a percentage of the viewport, the value to use is the specified percentage of the actual-width in user units for the nearest containing viewport, where actual-width is the width dimension of the viewport element within the user coordinate system for the viewport element.
- For any y-coordinate value or height value expressed as a percentage of the viewport, the value to use is the specified percentage of the actual-height in user units for the nearest containing viewport, where actual-height is the height dimension of the viewport element within the user coordinate system for the viewport element.
- For any other length value expressed as a percentage of the viewport, the percentage is calculated as the specified percentage of `sqrt((actual-width)**2 + (actual-height)**2))/sqrt(2)`.

Example Units below illustrates some of the processing rules for different types of units.

    <?xml version="1.0" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
      "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
    <svg width="400px" height="200px" viewBox="0 0 4000 2000"
         xmlns="http://www.w3.org/2000/svg" version="1.1">
      <title>Example Units</title>
      <desc>Illustrates various units options</desc>

      <!-- Frame the picture -->
      <rect x="5" y="5" width="3990" height="1990"
            fill="none" stroke="blue" stroke-width="10"/>

      <g fill="blue" stroke="red" font-family="Verdana" font-size="150">
        <!-- Absolute unit specifiers -->
        <g transform="translate(400,0)">
          <text x="-50" y="300" fill="black" stroke="none">Abs. units:</text>
          <rect x="0" y="400" width="4in" height="2in" stroke-width=".4in"/>
          <rect x="0" y="750" width="384" height="192" stroke-width="38.4"/>
          <g transform="scale(2)">
            <rect x="0" y="600" width="4in" height="2in" stroke-width=".4in"/>
          </g>
        </g>

        <!-- Relative unit specifiers -->
        <g transform="translate(1600,0)">
          <text x="-50" y="300" fill="black" stroke="none">Rel. units:</text>
          <rect x="0" y="400" width="2.5em" height="1.25em" stroke-width=".25em"/>
          <rect x="0" y="750" width="375" height="187.5" stroke-width="37.5"/>
          <g transform="scale(2)">
            <rect x="0" y="600" width="2.5em" height="1.25em" stroke-width=".25em"/>
          </g>
        </g>

        <!-- Percentages -->
        <g transform="translate(2800,0)">
          <text x="-50" y="300" fill="black" stroke="none">Percentages:</text>
          <rect x="0" y="400" width="10%" height="10%" stroke-width="1%"/>
          <rect x="0" y="750" width="400" height="200" stroke-width="31.62"/>
          <g transform="scale(2)">
            <rect x="0" y="600" width="10%" height="10%" stroke-width="1%"/>
          </g>
        </g>
      </g>
    </svg>

Example Units

View this example as SVG (SVG-enabled browsers only)

The three rectangles on the left demonstrate the use of one of the absolute unit identifiers, the "in" unit (inch). The reference image above was generated on a 96dpi system (i.e., 1 inch = 96 pixels). Therefore, the topmost rectangle, which is specified in inches, is exactly the same size as the middle rectangle, which is specified in user units such that there are 96 user units for each corresponding inch in the topmost rectangle. (Note: on systems with different screen resolutions, the top and middle rectangles will likely be rendered at different sizes.) The bottom rectangle of the group illustrates what happens when values specified in inches are scaled.

The three rectangles in the middle demonstrate the use of one of the relative unit identifiers, the "em" unit. Because the ‘font-size’ property has been set to 150 on the outermost ‘g’ element, each "em" unit is equal to 150 user units. The topmost rectangle, which is specified in "em" units, is exactly the same size as the middle rectangle, which is specified in user units such that there are 150 user units for each corresponding "em" unit in the topmost rectangle. The bottom rectangle of the group illustrates what happens when values specified in "em" units are scaled.

The three rectangles on the right demonstrate the use of percentages. Note that the width and height of the viewport in the user coordinate system for the viewport element (in this case, the outermost svg element) are 4000 and 2000, respectively, because processing the ‘viewBox’ attribute results in a transformed user coordinate system. The topmost rectangle, which is specified in percentage units, is exactly the same size as the middle rectangle, which is specified in equivalent user units. In particular, note that the ‘stroke-width’ property in the middle rectangle is set to 1% of the `sqrt((actual-width)**2 + (actual-height)**2)) / sqrt(2)`, which in this case is .01*sqrt(4000*4000+2000*2000)/sqrt(2), or 31.62. The bottom rectangle of the group illustrates what happens when values specified in percentage units are scaled.

## 7.11 Object bounding box units

The following elements offer the option of expressing coordinate values and lengths as fractions (and, in some cases, percentages) of the bounding box, by setting a specified attribute to 'objectBoundingBox' on the given element:

Element | Attribute | Effect
--- | --- | ---
‘linearGradient’ | ‘gradientUnits’ | Indicates that the attributes which specify the gradient vector (‘x1’, ‘y1’, ‘x2’, ‘y2’) represent fractions or percentages of the bounding box of the element to which the gradient is applied.
‘radialGradient’ | ‘gradientUnits’ | Indicates that the attributes which specify the center (‘cx’, ‘cy’), the radius (‘r’) and focus (‘fx’, ‘fy’) represent fractions or percentages of the bounding box of the element to which the gradient is applied.
‘pattern’ | ‘patternUnits’ | Indicates that the attributes which define how to tile the pattern (‘x’, ‘y’, ‘width’, ‘height’) are established using the bounding box of the element to which the pattern is applied.
‘pattern’ | ‘patternContentUnits’ | Indicates that the user coordinate system for the contents of the pattern is established using the bounding box of the element to which the pattern is applied.
‘clipPath’ | ‘clipPathUnits’ | Indicates that the user coordinate system for the contents of the ‘clipPath’ element is established using the bounding box of the element to which the clipping path is applied.
‘mask’ | ‘maskUnits’ | Indicates that the attributes which define the masking region (‘x’, ‘y’, ‘width’, ‘height’) is established using the bounding box of the element to which the mask is applied.
‘mask’ | ‘maskContentUnits’ | Indicates that the user coordinate system for the contents of the ‘mask’ element are established using the bounding box of the element to which the mask is applied.
‘filter’ | ‘filterUnits’ | Indicates that the attributes which define the filter effects region (‘x’, ‘y’, ‘width’, ‘height’) represent fractions or percentages of the bounding box of the element to which the filter is applied.
‘filter’ | ‘primitiveUnits’ | Indicates that the various length values within the filter primitives represent fractions or percentages of the bounding box of the element to which the filter is applied.

In the discussion that follows, the term applicable element is the element to which the given effect applies. For gradients and patterns, the applicable element is the graphics element which has its ‘fill’ or ‘stroke’ property referencing the given gradient or pattern. (See Inheritance of Painting Properties. For special rules concerning text elements, see the discussion of object bounding box units and text elements.) For clipping paths, masks and filters, the applicable element can be either a container element or a graphics element.

When keyword objectBoundingBox is used, then the effect is as if a supplemental transformation matrix were inserted into the list of nested transformation matrices to create a new user coordinate system.

First, the (minx,miny) and (maxx,maxy) coordinates are determined for the applicable element and all of its descendants. The values minx, miny, maxx and maxy are determined by computing the maximum extent of the shape of the element in X and Y with respect to the user coordinate system for the applicable element. The bounding box is the tightest fitting rectangle aligned with the axes of the applicable element's user coordinate system that entirely encloses the applicable element and its descendants. The bounding box is computed exclusive of any values for clipping, masking, filter effects, opacity and stroke-width. For curved shapes, the bounding box encloses all portions of the shape, not just end points. For ‘text’ elements, for the purposes of the bounding box calculation, each glyph is treated as a separate graphics element. The calculations assume that all glyphs occupy the full glyph cell. For example, for horizontal text, the calculations assume that each glyph extends vertically to the full ascent and descent values for the font.

Then, coordinate (0,0) in the new user coordinate system is mapped to the (minx,miny) corner of the tight bounding box within the user coordinate system of the applicable element and coordinate (1,1) in the new user coordinate system is mapped to the (maxx,maxy) corner of the tight bounding box of the applicable element. In most situations, the following transformation matrix produces the correct effect:

    [ (maxx-minx) 0 0 (maxy-miny) minx miny ]

When percentages are used with attributes that define the gradient vector, the pattern tile, the filter region or the masking region, a percentage represents the same value as the corresponding decimal value (e.g., 50% means the same as 0.5). If percentages are used within the content of a ‘pattern’, ‘clipPath’, ‘mask’ or ‘filter’ element, these values are treated according to the processing rules for percentages as defined in Units.

Any numeric value can be specified for values expressed as a fraction or percentage of object bounding box units. In particular, fractions less are zero or greater than one and percentages less than 0% or greater than 100% can be specified.

Keyword objectBoundingBox should not be used when the geometry of the applicable element has no width or no height, such as the case of a horizontal or vertical line, even when the line has actual thickness when viewed due to having a non-zero stroke width since stroke width is ignored for bounding box calculations. When the geometry of the applicable element has no width or height and objectBoundingBox is specified, then the given effect (e.g., a gradient or a filter) will be ignored.

## 7.12 Intrinsic sizing properties of the viewport of SVG content

SVG needs to specify how to calculate some intrinsic sizing properties to enable inclusion within other languages. The intrinsic width and height of the viewport of SVG content must be determined from the ‘width’ and ‘height’ attributes. If either of these are not specified, a value of '100%' must be assumed. Note: the ‘width’ and ‘height’ attributes are not the same as the CSS width and height properties. Specifically, percentage values do not provide an intrinsic width or height, and do not indicate a percentage of the containing block. Rather, once the viewport is established, they indicate the portion of the viewport that is actually covered by image data.

The intrinsic aspect ratio of the viewport of SVG content is necessary for example, when including SVG from an ‘object’ element in HTML styled with CSS. It is possible (indeed, common) for an SVG graphic to have an intrinsic aspect ratio but not to have an intrinsic width or height. The intrinsic aspect ratio must be calculated based upon the following rules:

- The aspect ratio is calculated by dividing a width by a height.

- If the ‘width’ and ‘height’ of the rootmost ‘svg’ element are both specified with unit identifiers (in, mm, cm, pt, pc, px, em, ex) or in user units, then the aspect ratio is calculated from the ‘width’ and ‘height’ attributes after resolving both values to user units.

- If either/both of the ‘width’ and ‘height’ of the rootmost ‘svg’ element are in percentage units (or omitted), the aspect ratio is calculated from the width and height values of the ‘viewBox’ specified for the current SVG document fragment. If the ‘viewBox’ is not correctly specified, or set to 'none', the intrinsic aspect ratio cannot be calculated and is considered unspecified.

Examples:

Example: Intrinsic Aspect Ratio 1

    <svg xmlns="http://www.w3.org/2000/svg" version="1.2" baseProfile="tiny"
         width="10cm" height="5cm">
      ...
    </svg>

In this example the intrinsic aspect ratio of the viewport is 2:1. The intrinsic width is 10cm and the intrinsic height is 5cm.

Example: Intrinsic Aspect Ratio 2

    <svg xmlns="http://www.w3.org/2000/svg" version="1.2" baseProfile="tiny"
         width="100%" height="50%" viewBox="0 0 200 200">
      ...
    </svg>

In this example the intrinsic aspect ratio of the rootmost viewport is 1:1. An aspect ratio calculation in this case allows embedding in an object within a containing block that is only constrained in one direction.

Example: Intrinsic Aspect Ratio 3

    <svg xmlns="http://www.w3.org/2000/svg" version="1.2" baseProfile="tiny"
         width="10cm" viewBox="0 0 200 200">
      ...
    </svg>

In this case the intrinsic aspect ratio is 1:1.

Example: Intrinsic Aspect Ratio 4

    <svg xmlns="http://www.w3.org/2000/svg" version="1.2" baseProfile="tiny"
         width="75%" height="10cm" viewBox="0 0 200 200">
      ...
    </svg>

In this example, the intrinsic aspect ratio is 1:1.

## 7.13 Geographic coordinate systems

In order to allow interoperability between SVG content generators and user agents dealing with maps encoded in SVG, the use of a common metadata definition for describing the coordinate system used to generate SVG documents is encouraged.

Such metadata must be added under the ‘metadata’ element of the topmost ‘svg’ element describing the map, consisting of an RDF description of the Coordinate Reference System definition used to generate the SVG map [RDF-PRIMER]. Note that the presence of this metadata does not affect the rendering of the SVG in any way; it merely provides added semantic value for applications that make use of combined maps.

The definition must be conformant to the XML grammar described in GML 3.2.1, an OpenGIS Standard for encoding common CRS data types in XML [GML]. In order to correctly map the 2-dimensional data used by SVG, the CRS must be of subtype ProjectedCRS or Geographic2dCRS. The first axis of the described CRS maps the SVG x-axis and the second axis maps the SVG y-axis.

The main purpose of such metadata is to indicate to the user agent that two or more SVG documents can be overlayed or merged into a single document. Obviously, if two maps reference the same Coordinate Reference System definition and have the same SVG ‘transform’ attribute value then they can be overlayed without reprojecting the data. If the maps reference different Coordinate Reference Systems and/or have different SVG ‘transform’ attribute values, then a specialized cartographic user agent may choose to transform the coordinate data to overlay the data. However, typical SVG user agents are not required to perform these types of transformations, or even recognize the metadata. It is described in this specification so that the connection between geographic coordinate systems and the SVG coordinate system is clear.

## 7.14 The ‘svg:transform’ attribute

Attribute definition:

svg:transform = "<transform>" | "none"
  <transform>

    Specifies the affine transformation that has been applied to the map data. The syntax is identical to that described in The ‘transform’ attribute section.

  none

    Specifies that no supplemental affine transformation has been applied to the map data. Using this value has the same meaning as specifying the identity matrix, which in turn is just the same as not specifying the ‘svg:transform’ the attribute at all.

  Animatable: no.

This attribute describes an optional additional affine transformation that may have been applied during this mapping. This attribute may be added to the OpenGIS ‘CoordinateReferenceSystem’ element. Note that, unlike the ‘transform’ attribute, it does not indicate that a transformation is to be applied to the data within the file. Instead, it simply describes the transformation that was already applied to the data when being encoded in SVG.

There are three typical uses for the ‘svg:transform’ global attribute. These are described below and used in the examples.

- Most ProjectedCRS have the north direction represented by positive values of the second axis and conversely SVG has a y-down coordinate system. That's why, in order to follow the usual way to represent a map with the north at its top, it is recommended for that kind of ProjectedCRS to use the ‘svg:transform’ global attribute with a 'scale(1, -1)' value as in the third example below.

- Most Geographic2dCRS have the latitude as their first axis rather than the longitude, which means that the south-north axis would be represented by the x-axis in SVG instead of the usual y-axis. That's why, in order to follow the usual way to represent a map with the north at its top, it is recommended for that kind of Geographic2dCRS to use the ‘svg:transform’ global attribute with a 'rotate(-90)' value as in the first example (while also adding the 'scale(1, -1)' as for ProjectedCRS).

- In addition, when converting for profiles which place restrictions on precision of real number values, it may be useful to add an additional scaling factor to retain good precision for a specific area. When generating an SVG document from WGS84 geographic coordinates (EPGS 4326), we recommend the use of an additional 100 times scaling factor corresponding to an ‘svg:transform’ global attribute with a 'rotate(-90) scale(100)' value (shown in the second example). Different scaling values may be required depending on the particular CRS.

Below is a simple example of the coordinate metadata, which describes the coordinate system used by the document via a URI.

    <?xml version="1.0"?>
    <svg xmlns="http://www.w3.org/2000/svg" version="1.1"
         width="100" height="100" viewBox="0 0 1000 1000">

      <desc>An example that references coordinate data.</desc>

      <metadata>
        <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
                 xmlns:crs="http://www.ogc.org/crs"
                 xmlns:svg="http://www.w3.org/2000/svg">
          <rdf:Description rdf:about="">
            <!-- The Coordinate Reference System is described
                 through a URI. -->
            <crs:CoordinateReferenceSystem
                svg:transform="rotate(-90)"
                rdf:resource="http://www.example.org/srs/epsg.xml#4326"/>
          </rdf:Description>
        </rdf:RDF>
      </metadata>

      <!-- The actual map content -->
    </svg>

The second example uses a well-known identifier to describe the coordinate system. Note that the coordinates used in the document have had the supplied transform applied.

    <?xml version="1.0"?>
    <svg xmlns="http://www.w3.org/2000/svg" version="1.1"
         width="100" height="100" viewBox="0 0 1000 1000">

      <desc>Example using a well known coordinate system.</desc>

      <metadata>
        <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
                 xmlns:crs="http://www.ogc.org/crs"
                 xmlns:svg="http://www.w3.org/2000/svg">
          <rdf:Description rdf:about="">
            <!-- In case of a well-known Coordinate Reference System
                 an 'Identifier' is enough to describe the CRS -->
            <crs:CoordinateReferenceSystem svg:transform="rotate(-90) scale(100, 100)">
              <crs:Identifier>
                <crs:code>4326</crs:code>
                <crs:codeSpace>EPSG</crs:codeSpace>
                <crs:edition>5.2</crs:edition>
              </crs:Identifier>
            </crs:CoordinateReferenceSystem>
          </rdf:Description>
        </rdf:RDF>
      </metadata>

      <!-- The actual map content -->
    </svg>

The third example defines the coordinate system completely within the SVG document.

    <?xml version="1.0"?>
    <svg xmlns="http://www.w3.org/2000/svg" version="1.1"
         width="100" height="100" viewBox="0 0 1000 1000">

      <desc>Coordinate metadata defined within the SVG document</desc>

      <metadata>
        <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
                 xmlns:crs="http://www.ogc.org/crs"
                 xmlns:svg="http://www.w3.org/2000/svg">
          <rdf:Description rdf:about="">
            <!-- For other CRS it should be entirely defined -->
            <crs:CoordinateReferenceSystem svg:transform="scale(1,-1)">
              <crs:NameSet>
                <crs:name>Mercator projection of WGS84</crs:name>
              </crs:NameSet>
              <crs:ProjectedCRS>
                <!-- The actual definition of the CRS -->
                <crs:CartesianCoordinateSystem>
                  <crs:dimension>2</crs:dimension>
                  <crs:CoordinateAxis>
                    <crs:axisDirection>north</crs:axisDirection>
                    <crs:AngularUnit>
                      <crs:Identifier>
                        <crs:code>9108</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                    </crs:AngularUnit>
                  </crs:CoordinateAxis>
                  <crs:CoordinateAxis>
                    <crs:axisDirection>east</crs:axisDirection>
                    <crs:AngularUnit>
                      <crs:Identifier>
                        <crs:code>9108</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                    </crs:AngularUnit>
                  </crs:CoordinateAxis>
                </crs:CartesianCoordinateSystem>
                <crs:CoordinateReferenceSystem>
                  <!-- the reference system of that projected system is
                             WGS84 which is EPSG 4326 in EPSG codeSpace -->
                  <crs:NameSet>
                    <crs:name>WGS 84</crs:name>
                  </crs:NameSet>
                  <crs:Identifier>
                    <crs:code>4326</crs:code>
                    <crs:codeSpace>EPSG</crs:codeSpace>
                    <crs:edition>5.2</crs:edition>
                  </crs:Identifier>
                </crs:CoordinateReferenceSystem>
                <crs:CoordinateTransformationDefinition>
                  <crs:sourceDimensions>2</crs:sourceDimensions>
                  <crs:targetDimensions>2</crs:targetDimensions>
                  <crs:ParameterizedTransformation>
                    <crs:TransformationMethod>
                      <!-- the projection is a Mercator projection which is
                            EPSG 9805 in EPSG codeSpace -->
                      <crs:NameSet>
                        <crs:name>Mercator</crs:name>
                      </crs:NameSet>
                      <crs:Identifier>
                        <crs:code>9805</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                      <crs:description>Mercator (2SP)</crs:description>
                    </crs:TransformationMethod>
                    <crs:Parameter>
                      <crs:NameSet>
                        <crs:name>Latitude of 1st standart parallel</crs:name>
                      </crs:NameSet>
                      <crs:Identifier>
                        <crs:code>8823</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                      <crs:value>0</crs:value>
                    </crs:Parameter>
                    <crs:Parameter>
                      <crs:NameSet>
                        <crs:name>Longitude of natural origin</crs:name>
                      </crs:NameSet>
                      <crs:Identifier>
                        <crs:code>8802</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                      <crs:value>0</crs:value>
                    </crs:Parameter>
                    <crs:Parameter>
                      <crs:NameSet>
                        <crs:name>False Easting</crs:name>
                      </crs:NameSet>
                      <crs:Identifier>
                        <crs:code>8806</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                      <crs:value>0</crs:value>
                    </crs:Parameter>
                    <crs:Parameter>
                      <crs:NameSet>
                        <crs:name>False Northing</crs:name>
                      </crs:NameSet>
                      <crs:Identifier>
                        <crs:code>8807</crs:code>
                        <crs:codeSpace>EPSG</crs:codeSpace>
                        <crs:edition>5.2</crs:edition>
                      </crs:Identifier>
                      <crs:value>0</crs:value>
                    </crs:Parameter>
                  </crs:ParameterizedTransformation>
                </crs:CoordinateTransformationDefinition>
              </crs:ProjectedCRS>
            </crs:CoordinateReferenceSystem>
          </rdf:Description>
        </rdf:RDF>
      </metadata>

      <!-- the actual map content -->
    </svg>

## 7.15 DOM interfaces

### 7.15.1 Interface SVGPoint

Many of the SVG DOM interfaces refer to objects of class SVGPoint. An SVGPoint is an (x, y) coordinate pair. When used in matrix operations, an SVGPoint is treated as a vector of the form:

    [x]
    [y]
    [1]

If an SVGRect object is designated as read only, then attempting to assign to one of its attributes will result in an exception being thrown.

    interface SVGPoint {

      attribute float x setraises(DOMException);
      attribute float y setraises(DOMException);

      SVGPoint matrixTransform(in SVGMatrix matrix);
    };

Attributes:
  x (float)
    The x coordinate.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised if the SVGPoint object is read only, or corresponds to a DOM attribute that is read only.
  y (float)
    The y coordinate.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised if the SVGPoint object is read only, or corresponds to a DOM attribute that is read only.
Operations:
  SVGPoint matrixTransform(in SVGMatrix matrix)

    Applies a 2x3 matrix transformation on this SVGPoint object and returns a new, transformed SVGPoint object:

        newpoint = matrix * thispoint

    Parameters
      1. SVGMatrix matrix
         The matrix which is to be applied to this SVGPoint object.
    Returns
      A new SVGPoint object.

### 7.15.2 Interface SVGPointList

This interface defines a list of SVGPoint objects.

SVGPointList has the same attributes and methods as other SVGxxxList interfaces. Implementers may consider using a single base class to implement the various SVGxxxList interfaces.

    interface SVGPointList {

      readonly attribute unsigned long numberOfItems;

      void clear() raises(DOMException);
      SVGPoint initialize(in SVGPoint newItem) raises(DOMException);
      SVGPoint getItem(in unsigned long index) raises(DOMException);
      SVGPoint insertItemBefore(in SVGPoint newItem, in unsigned long index) raises(DOMException);
      SVGPoint replaceItem(in SVGPoint newItem, in unsigned long index) raises(DOMException);
      SVGPoint removeItem(in unsigned long index) raises(DOMException);
      SVGPoint appendItem(in SVGPoint newItem) raises(DOMException);
    };

Attributes:
  numberOfItems (readonly unsigned long)
    The number of items in the list.
Operations:
  void clear()
    Clears all existing current items from the list, with the result being an empty list.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.
  SVGPoint initialize(in SVGPoint newItem)
    Clears all existing current items from the list and re-initializes the list to hold the single item specified by the parameter. If the inserted item is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy.
    Parameters
      1. SVGPoint newItem
         The item which should become the only member of the list.
    Returns
      The item being inserted into the list.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.
  SVGPoint getItem(in unsigned long index)
    Returns the specified item from the list. The returned item is the item itself and not a copy. Any changes made to the item are immediately reflected in the list.
    Parameters
      1. unsigned long index
         The index of the item from the list which is to be returned. The first item is number 0.
    Returns
      The selected item.
    Exceptions
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGPoint insertItemBefore(in SVGPoint newItem, in unsigned long index)
    Inserts a new item into the list at the specified position. The first item is number 0. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy. If the item is already in this list, note that the index of the item to insert before is before the removal of the item.
    Parameters
      1. SVGPoint newItem
         The item which is to be inserted into the list.
      2. unsigned long index
         The index of the item before which the new item is to be inserted. The first item is number 0. If the index is equal to 0, then the new item is inserted at the front of the list. If the index is greater than or equal to numberOfItems, then the new item is appended to the end of the list.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.
  SVGPoint replaceItem(in SVGPoint newItem, in unsigned long index)
    Replaces an existing item in the list with a new item. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy. If the item is already in this list, note that the index of the item to replace is before the removal of the item.
    Parameters
      1. SVGPoint newItem
         The item which is to be inserted into the list.
      2. unsigned long index
         The index of the item which is to be replaced. The first item is number 0.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGPoint removeItem(in unsigned long index)
    Removes an existing item from the list.
    Parameters
      1. unsigned long index
         The index of the item which is to be removed. The first item is number 0.
    Returns
      The removed item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGPoint appendItem(in SVGPoint newItem)
    Inserts a new item at the end of the list. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy.
    Parameters
      1. SVGPoint newItem
         The item which is to be inserted. The first item is number 0.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list cannot be modified.

### 7.15.3 Interface SVGMatrix

Many of SVG's graphics operations utilize 2x3 matrices of the form:

    [a c e]
    [b d f]

which, when expanded into a 3x3 matrix for the purposes of matrix arithmetic, become:

    [a c e]
    [b d f]
    [0 0 1]

    interface SVGMatrix {

      attribute float a setraises(DOMException);
      attribute float b setraises(DOMException);
      attribute float c setraises(DOMException);
      attribute float d setraises(DOMException);
      attribute float e setraises(DOMException);
      attribute float f setraises(DOMException);

      SVGMatrix multiply(in SVGMatrix secondMatrix);
      SVGMatrix inverse() raises(SVGException);
      SVGMatrix translate(in float x, in float y);
      SVGMatrix scale(in float scaleFactor);
      SVGMatrix scaleNonUniform(in float scaleFactorX, in float scaleFactorY);
      SVGMatrix rotate(in float angle);
      SVGMatrix rotateFromVector(in float x, in float y) raises(SVGException);
      SVGMatrix flipX();
      SVGMatrix flipY();
      SVGMatrix skewX(in float angle);
      SVGMatrix skewY(in float angle);
    };

Attributes:
  a (float)
    The a component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  b (float)
    The b component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  c (float)
    The c component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  d (float)
    The d component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  e (float)
    The e component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  f (float)
    The f component of the matrix.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
Operations:
  SVGMatrix multiply(in SVGMatrix secondMatrix)
    Performs matrix multiplication. This matrix is post-multiplied by another matrix, returning the resulting new matrix.
    Parameters
      1. SVGMatrix secondMatrix
         The matrix which is post-multiplied to this matrix.
    Returns
      The resulting matrix.
  SVGMatrix inverse()
    Returns the inverse matrix.
    Returns
      The inverse matrix.
    Exceptions
      SVGException, code SVG_MATRIX_NOT_INVERTABLE
        Raised if this matrix is not invertable.
  SVGMatrix translate(in float x, in float y)
    Post-multiplies a translation transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float x
         The distance to translate along the x-axis.
      2. float y
         The distance to translate along the y-axis.
    Returns
      The resulting matrix.
  SVGMatrix scale(in float scaleFactor)
    Post-multiplies a uniform scale transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float scaleFactor
         Scale factor in both X and Y.
    Returns
      The resulting matrix.
  SVGMatrix scaleNonUniform(in float scaleFactorX, in float scaleFactorY)
    Post-multiplies a non-uniform scale transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float scaleFactorX
         Scale factor in X.
      2. float scaleFactorY
         Scale factor in Y.
    Returns
      The resulting matrix.
  SVGMatrix rotate(in float angle)
    Post-multiplies a rotation transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float angle
         Rotation angle.
    Returns
      The resulting matrix.
  SVGMatrix rotateFromVector(in float x, in float y)
    Post-multiplies a rotation transformation on the current matrix and returns the resulting matrix. The rotation angle is determined by taking (+/-) atan(y/x). The direction of the vector (x, y) determines whether the positive or negative angle value is used.
    Parameters
      1. float x
         The X coordinate of the vector (x,y). Must not be zero.
      2. float y
         The Y coordinate of the vector (x,y). Must not be zero.
    Returns
      The resulting matrix.
    Exceptions
      SVGException, code SVG_INVALID_VALUE_ERR
        Raised if one of the parameters has an invalid value.
  SVGMatrix flipX()
    Post-multiplies the transformation [-1 0 0 1 0 0] and returns the resulting matrix.
    Returns
      The resulting matrix.
  SVGMatrix flipY()
    Post-multiplies the transformation [1 0 0 -1 0 0] and returns the resulting matrix.
    Returns
      The resulting matrix.
  SVGMatrix skewX(in float angle)
    Post-multiplies a skewX transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float angle
         Skew angle.
    Returns
      The resulting matrix.
  SVGMatrix skewY(in float angle)
    Post-multiplies a skewY transformation on the current matrix and returns the resulting matrix.
    Parameters
      1. float angle
         Skew angle.
    Returns
      The resulting matrix.

### 7.15.4 Interface SVGTransform

SVGTransform is the interface for one of the component transformations within an SVGTransformList; thus, an SVGTransform object corresponds to a single component (e.g., 'scale(…)' or 'matrix(…)') within a ‘transform’ attribute specification.

    interface SVGTransform {

      // Transform Types
      const unsigned short SVG_TRANSFORM_UNKNOWN = 0;
      const unsigned short SVG_TRANSFORM_MATRIX = 1;
      const unsigned short SVG_TRANSFORM_TRANSLATE = 2;
      const unsigned short SVG_TRANSFORM_SCALE = 3;
      const unsigned short SVG_TRANSFORM_ROTATE = 4;
      const unsigned short SVG_TRANSFORM_SKEWX = 5;
      const unsigned short SVG_TRANSFORM_SKEWY = 6;

      readonly attribute unsigned short type;
      readonly attribute SVGMatrix matrix;
      readonly attribute float angle;

      void setMatrix(in SVGMatrix matrix) raises(DOMException);
      void setTranslate(in float tx, in float ty) raises(DOMException);
      void setScale(in float sx, in float sy) raises(DOMException);
      void setRotate(in float angle, in float cx, in float cy) raises(DOMException);
      void setSkewX(in float angle) raises(DOMException);
      void setSkewY(in float angle) raises(DOMException);
    };

Constants in group “Transform Types”:
  SVG_TRANSFORM_UNKNOWN (unsigned short)
    The unit type is not one of predefined types. It is invalid to attempt to define a new value of this type or to attempt to switch an existing value to this type.
  SVG_TRANSFORM_MATRIX (unsigned short)
    A 'matrix(…)' transformation.
  SVG_TRANSFORM_TRANSLATE (unsigned short)
    A 'translate(…)' transformation.
  SVG_TRANSFORM_SCALE (unsigned short)
    A 'scale(…)' transformation.
  SVG_TRANSFORM_ROTATE (unsigned short)
    A 'rotate(…)' transformation.
  SVG_TRANSFORM_SKEWX (unsigned short)
    A 'skewX(…)' transformation.
  SVG_TRANSFORM_SKEWY (unsigned short)
    A 'skewY(…)' transformation.
Attributes:
  type (readonly unsigned short)
    The type of the value as specified by one of the SVG_TRANSFORM_* constants defined on this interface.
  matrix (readonly SVGMatrix)

    The matrix that represents this transformation. The matrix object is live, meaning that any changes made to the SVGTransform object are immediately reflected in the matrix object and vice versa. In case the matrix object is changed directly (i.e., without using the methods on the SVGTransform interface itself) then the type of the SVGTransform changes to SVG_TRANSFORM_MATRIX.

    - For SVG_TRANSFORM_MATRIX, the matrix contains the a, b, c, d, e, f values supplied by the user.
    - For SVG_TRANSFORM_TRANSLATE, e and f represent the translation amounts (a=1, b=0, c=0 and d=1).
    - For SVG_TRANSFORM_SCALE, a and d represent the scale amounts (b=0, c=0, e=0 and f=0).
    - For SVG_TRANSFORM_SKEWX and SVG_TRANSFORM_SKEWY, a, b, c and d represent the matrix which will result in the given skew (e=0 and f=0).
    - For SVG_TRANSFORM_ROTATE, a, b, c, d, e and f together represent the matrix which will result in the given rotation. When the rotation is around the center point (0, 0), e and f will be zero.
  angle (readonly float)

    A convenience attribute for SVG_TRANSFORM_ROTATE, SVG_TRANSFORM_SKEWX and SVG_TRANSFORM_SKEWY. It holds the angle that was specified.

    For SVG_TRANSFORM_MATRIX, SVG_TRANSFORM_TRANSLATE and SVG_TRANSFORM_SCALE, angle will be zero.

Operations:
  void setMatrix(in SVGMatrix matrix)

    Sets the transform type to SVG_TRANSFORM_MATRIX, with parameter matrix defining the new transformation. The values from the parameter matrix are copied, the matrix parameter does not replace SVGTransform::matrix.

    Parameters
      1. SVGMatrix matrix
         The new matrix for the transformation.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  void setTranslate(in float tx, in float ty)
    Sets the transform type to SVG_TRANSFORM_TRANSLATE, with parameters tx and ty defining the translation amounts.
    Parameters
      1. float tx
         The translation amount in X.
      2. float ty
         The translation amount in Y.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  void setScale(in float sx, in float sy)
    Sets the transform type to SVG_TRANSFORM_SCALE, with parameters sx and sy defining the scale amounts.
    Parameters
      1. float sx
         The scale amount in X.
      2. float sy
         The scale amount in Y.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  void setRotate(in float angle, in float cx, in float cy)
    Sets the transform type to SVG_TRANSFORM_ROTATE, with parameter angle defining the rotation angle and parameters cx and cy defining the optional center of rotation.
    Parameters
      1. float angle
         The rotation angle.
      2. float cx
         The x coordinate of center of rotation.
      3. float cy
         The y coordinate of center of rotation.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  void setSkewX(in float angle)
    Sets the transform type to SVG_TRANSFORM_SKEWX, with parameter angle defining the amount of skew.
    Parameters
      1. float angle
         The skew angle.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.
  void setSkewY(in float angle)
    Sets the transform type to SVG_TRANSFORM_SKEWY, with parameter angle defining the amount of skew.
    Parameters
      1. float angle
         The skew angle.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised on an attempt to change the value of a read only attribute.

### 7.15.5 Interface SVGTransformList

This interface defines a list of SVGTransform objects.

The SVGTransformList and SVGTransform interfaces correspond to the various attributes which specify a set of transformations, such as the ‘transform’ attribute which is available for many of SVG's elements.

SVGTransformList has the same attributes and methods as other SVGxxxList interfaces. Implementers may consider using a single base class to implement the various SVGxxxList interfaces.

An SVGTransformList object can be designated as read only, which means that attempts to modify the object will result in an exception being thrown, as described below.

    interface SVGTransformList {

      readonly attribute unsigned long numberOfItems;

      void clear() raises(DOMException);
      SVGTransform initialize(in SVGTransform newItem) raises(DOMException);
      SVGTransform getItem(in unsigned long index) raises(DOMException);
      SVGTransform insertItemBefore(in SVGTransform newItem, in unsigned long index) raises(DOMException);
      SVGTransform replaceItem(in SVGTransform newItem, in unsigned long index) raises(DOMException);
      SVGTransform removeItem(in unsigned long index) raises(DOMException);
      SVGTransform appendItem(in SVGTransform newItem) raises(DOMException);
      SVGTransform createSVGTransformFromMatrix(in SVGMatrix matrix);
      SVGTransform consolidate() raises(DOMException);
    };

Attributes:
  numberOfItems (readonly unsigned long)
    The number of items in the list.
Operations:
  void clear()
    Clears all existing current items from the list, with the result being an empty list.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
  SVGTransform initialize(in SVGTransform newItem)
    Clears all existing current items from the list and re-initializes the list to hold the single item specified by the parameter. If the inserted item is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy.
    Parameters
      1. SVGTransform newItem
         The item which should become the only member of the list.
    Returns
      The item being inserted into the list.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
  SVGTransform getItem(in unsigned long index)
    Returns the specified item from the list. The returned item is the item itself and not a copy. Any changes made to the item are immediately reflected in the list.
    Parameters
      1. unsigned long index
         The index of the item from the list which is to be returned. The first item is number 0.
    Returns
      The selected item.
    Exceptions
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGTransform insertItemBefore(in SVGTransform newItem, in unsigned long index)
    Inserts a new item into the list at the specified position. The first item is number 0. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy. If the item is already in this list, note that the index of the item to insert before is before the removal of the item.
    Parameters
      1. SVGTransform newItem
         The item which is to be inserted into the list.
      2. unsigned long index
         The index of the item before which the new item is to be inserted. The first item is number 0. If the index is equal to 0, then the new item is inserted at the front of the list. If the index is greater than or equal to numberOfItems, then the new item is appended to the end of the list.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
  SVGTransform replaceItem(in SVGTransform newItem, in unsigned long index)
    Replaces an existing item in the list with a new item. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy. If the item is already in this list, note that the index of the item to replace is before the removal of the item.
    Parameters
      1. SVGTransform newItem
         The item which is to be inserted into the list.
      2. unsigned long index
         The index of the item which is to be replaced. The first item is number 0.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGTransform removeItem(in unsigned long index)
    Removes an existing item from the list.
    Parameters
      1. unsigned long index
         The index of the item which is to be removed. The first item is number 0.
    Returns
      The removed item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
      DOMException, code INDEX_SIZE_ERR
        Raised if the index number is greater than or equal to numberOfItems.
  SVGTransform appendItem(in SVGTransform newItem)
    Inserts a new item at the end of the list. If newItem is already in a list, it is removed from its previous list before it is inserted into this list. The inserted item is the item itself and not a copy.
    Parameters
      1. SVGTransform newItem
         The item which is to be inserted. The first item is number 0.
    Returns
      The inserted item.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.
  SVGTransform createSVGTransformFromMatrix(in SVGMatrix matrix)

    Creates an SVGTransform object which is initialized to transform of type SVG_TRANSFORM_MATRIX and whose values are the given matrix. The values from the parameter matrix are copied, the matrix parameter is not adopted as SVGTransform::matrix.

    Parameters
      1. SVGMatrix matrix
         The matrix which defines the transformation.
    Returns
      The returned SVGTransform object.
  SVGTransform consolidate()
    Consolidates the list of separate SVGTransform objects by multiplying the equivalent transformation matrices together to result in a list consisting of a single SVGTransform object of type SVG_TRANSFORM_MATRIX. The consolidation operation creates new SVGTransform object as the first and only item in the list. The returned item is the item itself and not a copy. Any changes made to the item are immediately reflected in the list.
    Returns
      The resulting SVGTransform object which becomes single item in the list. If the list was empty, then a value of null is returned.
    Exceptions
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the list corresponds to a read only attribute or when the object itself is read only.

### 7.15.6 Interface SVGAnimatedTransformList

Used for the various attributes which specify a set of transformations, such as the ‘transform’ attribute which is available for many of SVG's elements, and which can be animated.

    interface SVGAnimatedTransformList {
      readonly attribute SVGTransformList baseVal;
      readonly attribute SVGTransformList animVal;
    };

Attributes:
  baseVal (readonly SVGTransformList)
    The base value of the given attribute before applying any animations.
  animVal (readonly SVGTransformList)
    A read only SVGTransformList representing the current animated value of the given attribute. If the given attribute is not currently being animated, then the SVGTransformList will have the same contents as baseVal. The object referenced by animVal will always be distinct from the one referenced by baseVal, even when the attribute is not animated.

### 7.15.7 Interface SVGPreserveAspectRatio

The SVGPreserveAspectRatio interface corresponds to the ‘preserveAspectRatio’ attribute, which is available for some of SVG's elements.

An SVGPreserveAspectRatio object can be designated as read only, which means that attempts to modify the object will result in an exception being thrown, as described below.

    interface SVGPreserveAspectRatio {

      // Alignment Types
      const unsigned short SVG_PRESERVEASPECTRATIO_UNKNOWN = 0;
      const unsigned short SVG_PRESERVEASPECTRATIO_NONE = 1;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMINYMIN = 2;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMIDYMIN = 3;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMAXYMIN = 4;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMINYMID = 5;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMIDYMID = 6;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMAXYMID = 7;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMINYMAX = 8;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMIDYMAX = 9;
      const unsigned short SVG_PRESERVEASPECTRATIO_XMAXYMAX = 10;

      // Meet-or-slice Types
      const unsigned short SVG_MEETORSLICE_UNKNOWN = 0;
      const unsigned short SVG_MEETORSLICE_MEET = 1;
      const unsigned short SVG_MEETORSLICE_SLICE = 2;

      attribute unsigned short align setraises(DOMException);
      attribute unsigned short meetOrSlice setraises(DOMException);
    };

Constants in group “Alignment Types”:
  SVG_PRESERVEASPECTRATIO_UNKNOWN (unsigned short)
    The enumeration was set to a value that is not one of predefined types. It is invalid to attempt to define a new value of this type or to attempt to switch an existing value to this type.
  SVG_PRESERVEASPECTRATIO_NONE (unsigned short)
    Corresponds to value 'none' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMINYMIN (unsigned short)
    Corresponds to value 'xMinYMin' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMIDYMIN (unsigned short)
    Corresponds to value 'xMidYMin' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMAXYMIN (unsigned short)
    Corresponds to value 'xMaxYMin' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMINYMID (unsigned short)
    Corresponds to value 'XMinYMid' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMIDYMID (unsigned short)
    Corresponds to value 'xMidYMid' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMAXYMID (unsigned short)
    Corresponds to value 'xMaxYMid' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMINYMAX (unsigned short)
    Corresponds to value 'xMinYMax' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMIDYMAX (unsigned short)
    Corresponds to value 'xMidYMax' for attribute ‘preserveAspectRatio’.
  SVG_PRESERVEASPECTRATIO_XMAXYMAX (unsigned short)
    Corresponds to value 'xMaxYMax' for attribute ‘preserveAspectRatio’.
Constants in group “Meet-or-slice Types”:
  SVG_MEETORSLICE_UNKNOWN (unsigned short)
    The enumeration was set to a value that is not one of predefined types. It is invalid to attempt to define a new value of this type or to attempt to switch an existing value to this type.
  SVG_MEETORSLICE_MEET (unsigned short)
    Corresponds to value 'meet' for attribute ‘preserveAspectRatio’.
  SVG_MEETORSLICE_SLICE (unsigned short)
    Corresponds to value 'slice' for attribute ‘preserveAspectRatio’.
Attributes:
  align (unsigned short)
    The type of the alignment value as specified by one of the SVG_PRESERVEASPECTRATIO_* constants defined on this interface.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the object corresponds to a read only attribute or when the object itself is read only.
  meetOrSlice (unsigned short)
    The type of the meet-or-slice value as specified by one of the SVG_MEETORSLICE_* constants defined on this interface.
    Exceptions on setting
      DOMException, code NO_MODIFICATION_ALLOWED_ERR
        Raised when the object corresponds to a read only attribute or when the object itself is read only.

### 7.15.8 Interface SVGAnimatedPreserveAspectRatio

Used for attributes of type SVGPreserveAspectRatio which can be animated.

    interface SVGAnimatedPreserveAspectRatio {
      readonly attribute SVGPreserveAspectRatio baseVal;
      readonly attribute SVGPreserveAspectRatio animVal;
    };

Attributes:
  baseVal (readonly SVGPreserveAspectRatio)
    The base value of the given attribute before applying any animations.
  animVal (readonly SVGPreserveAspectRatio)
    A read only SVGPreserveAspectRatio representing the current animated value of the given attribute. If the given attribute is not currently being animated, then the SVGPreserveAspectRatio will have the same contents as baseVal. The object referenced by animVal will always be distinct from the one referenced by baseVal, even when the attribute is not animated.

SVG 1.1 (Second Edition) – 16 August 2011 Top ⋅ Contents ⋅ Previous ⋅ Next ⋅ Elements ⋅ Attributes ⋅ Properties