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14 January 2003

7 Coordinate Systems, Transformations and Units

7.1 Introduction
7.2 The initial viewport
7.3 The initial coordinate system
7.4 Coordinate system transformations
7.5 Nested transformations
7.6 The 'transform' attribute
7.7 The 'viewBox' attribute
7.8 The 'preserveAspectRatio' attribute
7.9 Establishing a new viewport
7.10 Units
7.11 Object bounding box units
7.12 Geographic

Coordinate Systems

coordinate systems
7.13

Viewport Attribute Module

The 'svg:transform' attribute
7.14 DOM interfaces

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-VISUAL], 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 CSS 2 ([CSS2 lengths], 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-POSN] ], 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 [ CSS2-POSN] specified on the referencing element or on the outermost 'svg' 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 CSS 2 ([CSS2 lengths], 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-CSS 2 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 CSS 2 ([CSS2 lengths], 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"

version="1.1"

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"

version="1.1"

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:
3-by-3 transformation matrix

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:
3-by-3 transformation matrix

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:
3-by-3 matrix concatenation

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:
current transformation matrix: CTM

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:
Matrix concatenation

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>cx, <cy> 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 real <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', 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 Coordinate Systems, Transformations and Units

Contents

7.1 Introduction

7.2 The initial viewport

7.3 The initial coordinate system

7.4 Coordinate system transformations

7.5 Nested transformations

7.6 The 'transform' attribute

7.7 The 'viewBox' attribute

7.8 The 'preserveAspectRatio' attribute

7.9 Establishing a new viewport