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Back ported definition for CTM and local coordinate system from SVG 1.1.
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‎css3-transforms/ChangeLog‎

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2012-06-04 dschulze@adobe.com
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Back ported definition for CTM and local coordinate system from SVG 1.1.
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More cleanup on term referencing.
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2012-06-01 dschulze@adobe.com
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More corrections on the SVG animation part.
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‎css3-transforms/Overview.html‎

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<h1>CSS Transforms</h1>
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<h2 class="no-num no-toc" id=longstatus-date>Editor's Draft 1 June 2012</h2>
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<h2 class="no-num no-toc" id=longstatus-date>Editor's Draft 5 June 2012</h2>
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<dl>
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<dt>This version:
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<dd> <a
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href="http://www.w3.org/TR/2012/ED-css3-transforms-20120601/">http://dev.w3.org/csswg/css3-transforms/</a>
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<!--http://www.w3.org/TR/2012/WD-css3-transforms-20120601/-->
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href="http://www.w3.org/TR/2012/ED-css3-transforms-20120605/">http://dev.w3.org/csswg/css3-transforms/</a>
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<!--http://www.w3.org/TR/2012/WD-css3-transforms-20120605/-->
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<dt>Latest version:
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class=property>patternTransform</code>’ or ‘<code
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class=property>gradientTransform</code>’.</p>
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<dt id=TermLocalCoordinateSystem><dfn id=local-coordinate-system>local
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coordinate system</dfn>
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<dd>
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<p> In general, a coordinate system defines locations and distances on
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the current canvas. The current local coordinate system (also user
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coordinate system) is the coordinate system that is currently active and
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which is used to define how coordinates and lengths are located and
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computed, respectively, on the current canvas.</p>
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<dt id=TermPerspectiveMatrix><dfn id=perspective-matrix>perspective
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matrix</dfn>
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<dd>
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<p> A matrix computed from the values of the ‘<a
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href="#perspective"><code class=css><code
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class=property>perspective</code></code></a>’ and ‘<a
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href="#perspective-origin"><code class=css><code
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class=property>perspective-origin</code></code></a>’ properties as
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described <a href="#perspective-matrix-computation">below</a>.</p>
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href="#perspective"><code class=property>perspective</code></a>’ and
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‘<a href="#perspective-origin"><code
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class=property>perspective-origin</code></a>’ properties as described
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<a href="#perspective-matrix-computation">below</a>.</p>
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<dt id=TermTransformationMatrix><dfn
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id=transformation-matrix>transformation matrix</dfn>
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<dd>
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<p> A matrix computed from the values of the ‘<a href="#effects"><code
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class=css><code class=property>transform</code></code></a>’ and ‘<a
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href="#transform-origin"><code class=css><code
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class=property>transform-origin</code></code></a>’ properties as
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described <a href="#transformation-matrix-computation">below</a>.</p>
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<p> A matrix that defines the mathematical mapping from one coordinate
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system into another. It is computed from the values of the ‘<a
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href="#effects"><code class=property>transform</code></a>’ and ‘<a
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href="#transform-origin"><code
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class=property>transform-origin</code></a>’ properties as described <a
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href="#transformation-matrix-computation">below</a>.</p>
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<dt id=TermCurrentTransformationMatrix><dfn
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id=current-transformation-matrix-ctm>current transformation matrix
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(CTM)</dfn>
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<dd>
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<p> A matrix that defines the mapping from the local coordinate system
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into the viewport coordinate system.</p>
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<dt id=TermAccumulated3DTransformationMatrix> <dfn
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id=accumulated-3d-transformation-matrix>accumulated 3D transformation
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href="#accumulated-3d-transformation-matrix-computation">below</a>.</p>
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<dt id=TermIdentityTransformFunction> <dfn
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id=identity-transform-function>Identity transform function</dfn>
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id=identity-transform-function>identity transform function</dfn>
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<dd>
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<p> A <a href="#transform-functions">transform function</a> that is
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<p> Specifying a value other than ‘<code class=css>none</code>’ for the
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‘<a href="#effects"><code class=css>transform</code></a>’ property
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establishes a new <em>local coordinate system</em> at the element that it
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is applied to. The mapping from where the element would have rendered into
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that local coordinate system is given by the element's <a
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href="#TermTransformationMatrix"><i>transformation matrix</i></a>.
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Transformations are cumulative. That is, elements establish their local
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coordinate system within the coordinate system of their parent. From the
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perspective of the user, an element effectively accumulates all the ‘<a
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establishes a new <a class=term href="#local-coordinate-system">local
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coordinate system</a> at the element that it is applied to. The mapping
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from where the element would have rendered into that local coordinate
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system is given by the element's <a class=term
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href="#transformation-matrix">transformation matrix</a>. Transformations
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are cumulative. That is, elements establish their local coordinate system
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within the coordinate system of their parent. From the perspective of the
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user, an element effectively accumulates all the ‘<a
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href="#effects"><code class=property>transform</code></a>’ properties of
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its ancestors as well as any local transform applied to it. The
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accumulation of these transforms defines a <em>current transformation
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matrix (CTM)</em> for the element.
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accumulation of these transforms defines a <a class=term
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href="#current-transformation-matrix-ctm">current transformation matrix
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(CTM)</a> for the element.
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<p> The coordinate space behaves as described in the <a
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href="http://www.w3.org/TR/SVG/coords.html#EstablishingANewUserSpace">coordinate
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system transformations</a> section of the SVG 1.1 specification. This is a
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coordinate system with two axes: the X axis increases horizontally to the
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right; the Y axis increases vertically downwards. Three-dimensional
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transform functions extent this coordinate space into three dimensions,
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adding a Z axis perpendicular to the plane of the screen, that increases
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towards the viewer.
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<p id=transformation-matrix-computation> The <a
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href="#TermTransformationMatrix"><i>transformation matrix</i></a> is
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computed from the ‘<a href="#effects"><code
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class=property>transform</code></a>’ and ‘<a
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href="#transform-origin"><code
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system transformations</a> section of <a href="#SVG11"
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rel=biblioentry>[SVG11]<!--{{SVG11}}--></a>. This is a coordinate system
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with two axes: the X axis increases horizontally to the right; the Y axis
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increases vertically downwards. Three-dimensional transform functions
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extent this coordinate space into three dimensions, adding a Z axis
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perpendicular to the plane of the screen, that increases towards the
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viewer.
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<p class=issue> The coordinate space should be defined in this spec.
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<p id=transformation-matrix-computation> The <a class=term
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href="#transformation-matrix">transformation matrix</a> is computed from
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the ‘<a href="#effects"><code class=property>transform</code></a>’ and
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‘<a href="#transform-origin"><code
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class=property>transform-origin</code></a>’ properties as follows:
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<ol>
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transform functions, applied from the outside in. The resulting transform
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is the matrix multiplication of the list of transforms.
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<p> If a transform function causes the CTM of an object to be
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non-invertible, the object and it's content does not get displayed.
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<p> If a transform function causes the <a class=term
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href="#current-transformation-matrix-ctm">current transformation matrix
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(CTM)</a> of an object to be non-invertible, the object and it's content
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does not get displayed.
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<div class=example>
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<p> The object in the following example gets scaled by 0.</p>
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<li>bounding box, <a href="#bounding-box"
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title="bounding box"><strong>4.</strong></a>
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<li>Identity transform function, <a href="#identity-transform-function"
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title="Identity transform function"><strong>4.</strong></a>
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<li>current transformation matrix (CTM), <a
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href="#current-transformation-matrix-ctm"
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title="current transformation matrix (CTM)"><strong>4.</strong></a>
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<li>identity transform function, <a href="#identity-transform-function"
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title="identity transform function"><strong>4.</strong></a>
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<li>local coordinate system, <a href="#local-coordinate-system"
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title="local coordinate system"><strong>4.</strong></a>
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<li>perspective, <a href="#perspective"
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title=perspective><strong>10.</strong></a>

‎css3-transforms/Transforms.src.html‎

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</p>
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</dd>
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<dt id="TermLocalCoordinateSystem"><dfn>local coordinate system</dfn></dt>
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<dd>
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<p>
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In general, a coordinate system defines locations and distances on the current
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canvas. The current local coordinate system (also user coordinate system) is the
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coordinate system that is currently active and which is used to define how
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coordinates and lengths are located and computed, respectively, on the current
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canvas.
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</p>
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</dd>
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<dt id="TermPerspectiveMatrix"><dfn>perspective matrix</dfn></dt>
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<dd>
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<p>
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A matrix computed from the values of the '<code class="property">perspective</code>' and '<code class="property">perspective-origin</code>' properties as described <a href="#perspective-matrix-computation">below</a>.
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A matrix computed from the values of the 'perspective' and 'perspective-origin' properties as described <a href="#perspective-matrix-computation">below</a>.
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</p>
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</dd>
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<dt id="TermTransformationMatrix"><dfn>transformation matrix</dfn></dt>
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<dd>
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<p>
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A matrix computed from the values of the '<code class="property">transform</code>' and '<code class="property">transform-origin</code>' properties as described <a href="#transformation-matrix-computation">below</a>.
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A matrix that defines the mathematical mapping from one coordinate system into another. It is computed from the values of the 'transform' and 'transform-origin' properties as described <a href="#transformation-matrix-computation">below</a>.
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</p>
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</dd>
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<dt id="TermCurrentTransformationMatrix"><dfn>current transformation matrix (CTM)</dfn></dt>
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<dd>
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<p>
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A matrix that defines the mapping from the local coordinate system into the viewport coordinate system.
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</p>
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</dd>
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</dd>
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<dt id="TermIdentityTransformFunction">
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<dfn>Identity transform function</dfn>
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<dfn>identity transform function</dfn>
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</dt>
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<dd>
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<p>
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<h2 id="transform-rendering">The Transform Rendering Model</h2>
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<!-- This section is normative -->
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<p>
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Specifying a value other than ''none'' for the ''transform'' property establishes a new
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<em>local coordinate system</em> at the element that it is applied to. The mapping from
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where the element would have rendered into that local coordinate system is given by the
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element's <a href="#TermTransformationMatrix"><i>transformation matrix</i></a>.
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Transformations are cumulative. That is, elements establish their local coordinate
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system within the coordinate system of their parent. From the perspective of the user,
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an element effectively accumulates all the 'transform' properties of its ancestors as
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well as any local transform applied to it. The accumulation of these transforms defines
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a <em>current transformation matrix (CTM)</em> for the element.
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Specifying a value other than ''none'' for the ''transform'' property establishes a
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new <span class="term">local coordinate system</span> at the element that it is
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applied to. The mapping from where the element would have rendered into that local
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coordinate system is given by the element's <span class="term">transformation
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matrix</span>. Transformations are cumulative. That is, elements establish their local
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coordinate system within the coordinate system of their parent. From the perspective
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of the user, an element effectively accumulates all the 'transform' properties of its
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ancestors as well as any local transform applied to it. The accumulation of these
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transforms defines a <span class="term">current transformation matrix (CTM)</span> for
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the element.
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</p>
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<p>
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The coordinate space behaves as described in the <a
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href="http://www.w3.org/TR/SVG/coords.html#EstablishingANewUserSpace">coordinate
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system transformations</a> section of the SVG 1.1 specification. This is a
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system transformations</a> section of [[SVG11]]. This is a
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coordinate system with two axes: the X axis increases horizontally to the right; the
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Y axis increases vertically downwards. Three-dimensional transform functions extent
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this coordinate space into three dimensions, adding a Z axis perpendicular to the
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plane of the screen, that increases towards the viewer.
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</p>
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<p class="issue">
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The coordinate space should be defined in this spec.
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</p>
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<p id="transformation-matrix-computation">
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The <a href="#TermTransformationMatrix"><i>transformation matrix</i></a> is computed
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The <span class="term">transformation matrix</span> is computed
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from the 'transform' and 'transform-origin' properties as follows:
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<ol>
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<li>Start with the identity matrix.</li>
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</p>
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<p>
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If a transform function causes the CTM of an object to be non-invertible, the object
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and it's content does not get displayed.
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If a transform function causes the <span class="term">current transformation matrix
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(CTM)</span> of an object to be non-invertible, the object and it's content does not
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get displayed.
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</p>
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<div class="example">

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