12. SMIL 3.0 Animation

This section is normative.

12.4.1 Summary of symbols used in the semantic descriptions

12.4.2 The simple animation function f(t)

Animation is defined as a time-based function of a target element (or more specifically of some attribute of the target element, the target attribute). The animation defines a mapping of time to values for the target attribute. This mapping takes into account all aspects of timing, as well as animation-specific semantics. The overall mapping is based on a simple animation function f(t) which describes the animation over the simple duration of the element. Every animation defines a simple animation function which produces a value for the target attribute for any time within the simple duration.

A target attribute is the name of a feature of a target element as defined in a host language document.

This may be (e.g.) an XML attribute contained in the element or a CSS property that applies to the element. By default, the target element of an animation will be the parent of the animation element (an animation element is typically a child of the target element). However, the target may be any element in the document, identified either by an XML ID reference or via an XLink [XLINK] locator reference.

<rect ...>
   <animate attributeName="width"  from="10px"  to="100px" 
            begin="0s" dur="10s" />
   <animate attributeName="height" from="100px" to="10px"
            begin="0s" dur="10s" />
</rect>

The base value of a target attribute a at time t is the value of a to which animation is applied at time t.

The presentation value of a target attribute a at time t is the value of a resulting from the application of animation at time t.

The presentation value reflects the effect of animation on the base value. The effect is the change to the base value of the target attribute at any given time. When an animation completes, the effect of the animation is no longer applied, and the presentation value reverts to the base value by default. The animation effect may also be extended to freeze the last value for the length of time determined by the semantics of the fill attribute.

An animation element defines a simple animation function which is evaluated as needed over time by the implementation. The resulting values are applied to the presentation value for the target attribute. Animation functions are continuous in time and may be sampled at whatever frame rate is appropriate for the rendering system. The syntactic representation of the simple animation function is independent of this model, and may be described in a variety of ways. The animation elements in this specification support syntax for a set of discrete or interpolated values, a path syntax for motion based upon SVG paths, keyframe based timing, evenly paced interpolation, and variants on these features.

The simple animation function defined by an animation element is a function of time, f(t), defined for times t, 0<=t<=d, where d is the simple duration of the element.

The simple animation function may be defined as a function which depends on factors in addition to time. This does not affect the model of animation, beyond the trivial addition of additional parameters to f(t), such as f(t,u) used in the "to" animation example immediately above.

Animations may be defined to either override or add to the base value of an attribute. In this context, the base value may be the DOM value, or the result of other animations that also target the same attribute. This more general concept of a base value is termed the underlying value. Animations that add to the underlying value are described as additive animations. Animations that override the underlying value are referred to as non-additive animations. The animation effect function of an element is the function which includes the effect of the underlying value and accounts for repeating and freezing of the element. Because the animation effect may be affected by repeating and freezing, it is defined over the active duration of the element rather than its simple duration.

Animations may be combined in ways which produce intermediate values outside of the domain of the target attribute, but where the presentation value produced is valid. The type of a target attribute is this larger set. This is detailed in The animation sandwich model.

The type of a target attribute a is the base type of which the domain of a is a subset.

The underlying value u of a target attribute a of an animation element at time t is the value of a to which the animation effect is applied at time t.

The animation effect function, F(t,u), of an animation element with active duration AD is a function mapping times t: 0<=t<AD and values u of the type of the target attribute a into values of the type of a.

The animation effect function F(t,u) is usually defined as a function of the simple animation function f(t). f(t) must be defined in such a manner that F(t,u) produces values of the correct type.

12.4.3 The animation sandwich model

When an animation is running, it does not actually change the attribute values in the DOM. The animation runtime should ideally maintain a presentation value for any target attribute, separate from the DOM, CSS, or other object model (OM) in which the target attribute is defined. The presentation value is reflected in the display form of the document. The effect of animations is to manipulate this presentation value, and not to affect the underlying DOM or CSS OM values.

The remainder of this discussion uses the generic term OM for both the XML DOM [DOM2] as well as the CSS-OM. If an implementation does not support an object model, it should ideally maintain the original value as defined by the document as well as the presentation value; for the purposes of this section, we will consider this original value to be equivalent to the value in the OM.

In some implementations of DOM, it may be difficult or impractical to maintain a presentation value as described. CSS values should always be supported as described, as the CSS-OM provides a mechanism to do so. In implementations that do not support separate presentation values for general XML DOM properties, the implementation must at least restore the original value when animations no longer have an effect.

The rest of this discussion assumes the recommended approach using a separate presentation value.

The model accounting for the OM and concurrently active or frozen animations for a given attribute is described as a "sandwich", a loose analogy to the layers of meat and cheeses in a "submarine sandwich" (a long sandwich made with many pieces of meats and cheese layered along the length of the bread). In the analogy, time is associated with the length of the sandwich, and each animation has its duration represented by the length of bread that the layer covers. On the bottom of the sandwich is the base value taken from the OM. Each active (or frozen) animation is a layer above this. The layers (i.e. the animations) are placed on the sandwich both in time along the length of the bread, as well as in order according to priority, with higher priority animations placed above (i.e. on top of) lower priority animations. At any given point in time, you can take a slice of the sandwich and see how the animation layers stack up.

Note that animations manipulate the presentation value coming out of the OM in which the attribute is defined, and pass the resulting value on to the next layer of document processing. This does not replace or override any of the normal document OM processing cascade.

Specifically, animating an attribute defined in XML will modify the presentation value before it is passed through the style sheet cascade, using the XML DOM value as its base. Animating an attribute or property defined in a style sheet language will modify the presentation value passed through the remainder of the cascade.

In CSS2 and the DOM 2 CSS-OM, the terms "specified", "computed" and "actual" are used to describe the results of evaluating the syntax, the cascade and the presentation rendering. When animation is applied to CSS properties of a particular element, the base value to be animated is read using the (readonly) getComputedStyle() method on that element. The values produced by the animation are written into an override stylesheet for that element, which may be obtained using the getOverrideStyle() method. Note that it is assumed that before reading the value, the override stylesheet is cleared so that the animation works on the original document value. These new values then affect the cascade and are reflected in a new computed value (and thus, modified presentation). This means that the effect of animation overrides all style sheet rules, except for user rules with the !important property. This enables !important user style settings to have priority over animations, an important requirement for accessibility. Note that the animation may have side effects upon the document layout. See also section 6.1, "Specified, computed, and actual values," of [CSS2] and section 5.2.1, "Override and computed style sheet," of [DOM2CSS].

Within an OM, animations are prioritized according to when each begins. The animation first begun has lowest priority and the most recently begun animation has highest priority. When two animations start at the same moment in time, the activation order is resolved as follows:

• If one animation is a time dependent of another (e.g. it is specified to begin when another begins), then the time dependent is considered to activate after the syncbase element, and so has higher priority. Time dependency is further discussed in Propagating changes to times. This rule applies independent of the timing described for the syncbase element - i.e. it does not matter whether the syncbase element begins on an offset, relative to another syncbase, relative to an event-base, or via hyperlinking. In all cases, the syncbase is begun before any time dependents are begun, and so the syncbase has lower priority than the time dependent.
• If two animations share no time dependency relationship (e.g. neither is defined relative to the other, even indirectly) the element that appears first in the document has lower priority. This includes the cases in which two animation elements are defined relative to the same syncbase or event-base.

Note that if an animation is restarted, it will always move to the top of the priority list, as it becomes the most recently activated animation. That is, when an animation restarts, its layer is pulled out of the sandwich, and added back on the very top. In contrast, when an element repeats the priority is not affected (repeat behavior is not defined as restarting).

Each additive animation adds its effect to the result of all sandwich layers below. A non-additive animation simply overrides the result of all lower sandwich layers. The end result at the top of the sandwich is the presentation value that must be reflected in the document view.

Some attributes that support additive animation have a defined legal range for values (e.g. an opacity attribute may allow values between 0 and 1). In some cases, an animation function may yield out of range values. It is recommended that implementations clamp the results to the legal range as late as possible, before applying them to the presentation value. Ideally, the effect of all the animations active or frozen at a given point should be combined, before any clamping is performed. Although individual animation functions may yield out of range values, the combination of additive animations may still be legal. Clamping only the final result and not the effect of the individual animation functions provides support for these cases. Intermediate results may be clamped when necessary although this is not optimal. The host language must define the clamping semantics for each attribute that may be animated. As an example, this is defined for animateColor element.

Initially, before any animations for a given attribute are active, the presentation value will be identical to the original value specified in the document (the OM value).

When all animations for a given attribute have completed and the associated animation effects are no longer applied, the presentation value will again be equal to the OM value. Note that if any animation is defined with fill="freeze", the effect of the animation will be applied as long as the animation element remains in the frozen state, and so the presentation value will continue to reflect the animation effect. Refer also to the section "Freezing animations".

Some animations (e.g. animateMotion) will implicitly target an attribute, or possibly several attributes (e.g. the "posX" and "posY" attributes of some layout model). These animations must be combined with any other animations for each attribute that is affected. Thus, e.g. an animateMotion animation may be in more than one animation sandwich (depending upon the layout model of the host language). For animation elements that implicitly target attributes, the host language designer must specify which attributes are implicitly targeted, and the runtime must accordingly combine animations for the respective attributes.

Note that any queries (via DOM interfaces) on the target attribute will reflect the OM value, and will not reflect the effect of animations. Note also that the OM value may still be changed via the OM interfaces (e.g. using script). While it may be useful or desired to provide access to the final presentation value after all animation effects have been applied, such an interface is not provided as part of SMIL Animation. A future version may address this.

Although animation does not manipulate the OM values, the document display must reflect changes to the OM values. Host languages may support script languages that may manipulate attribute values directly in the OM. If an animation is active or frozen while a change to the OM value is made, the behavior is dependent upon whether the animation is defined to be additive or not, as follows: (see also the section Additive animation).

• If only additive animations are active or frozen (i.e. no non-additive animations are active or frozen for the given attribute) when the OM value is changed, the presentation value must reflect the changed OM value as well as the effect of the additive animations. When the animations complete and the effect of each is no longer applied, the presentation value will be equal to the changed OM value.
  
• If any non-additive animation is running when the OM value is changed, the presentation value will not reflect the changed OM value, but will only reflect the effect of the highest priority non-additive animation, and any still higher priority additive animations. When all non-additive animations complete and the effect of each is no longer applied, the presentation value will reflect the changed OM value and the effect of any additive animations that are active or frozen.

12.4.4 Animation elements as "continuous media"

Within the timing model, animation is considered to be "continuous" media. The animation elements defined in SMIL Animation do not have a natural intrinsic duration, so they are assigned an intrinsic duration of indefinite.

12.4.5 The animation effect function F(t,u)

Repeating animations

As described in the section Interval timing of the BasicInlineTiming module, repeating an element causes the element to be "played" several times in sequence. The repeated period is 0 to the simple duration of the element. Animation follows this model, where "playing" the animation means applying the simple animation function f(t) repeatedly.

The repeated animation function, fr(t), for any simple animation function f(t) is

fr(t) = f( REMAINDER( t, d ) ),

where t>=0, d is the simple duration , and REMAINDER( t, d ) is defined as (t - d*floor(t/d)).

This formulation follows the end-point exclusive model described in Interval timing. As an animation repeats, it starts at f(0), is sampled and applied up to but not including the end-point f(d). At the end of the simple duration, i.e. at the beginning of the next iteration, it starts back at f(0). f(d) may never actually be applied.

Examples

Controlling behavior of repeating animation - Cumulative animation

Every animation element must be defined as either cumulative or non-cumulative. An animation element may be defined as cumulative only if addition is defined for the target attribute.

First we define some intermediate functions. The first iteration f0(t) is unaffected by accumulate, and so is the same as the original simple animation function definition. Each subsequent iteration adds to the result of the previous iterations:

f0(t) = f(t)

If the animation is non-cumulative, then:

fi(t) = f(t - (i*d)) for any integer i > 0.

If the animation is cumulative, then:

fi(t) = (f(d) * i) + f(t - (i*d)) for any integer i > 0.

The cumulative animation function, fc(t), for any simple animation function f(t) is then:

fc(t) = fi(t), where i = floor(t/d).

<img ...>
   <animateMotion path="m 0 0 c 30 50 70 50 100 0 z" dur="5s"
      accumulate="sum" repeatCount="4" />
</img>

<rect width="20px"...>
   <animate attributeName="width" dur="5s"
      values="0; 15; 10" additive="sum"
      accumulate="sum" repeatCount="10" />
</rect>

Freezing animations

<img top="3" ...>
   <animate begin="5s" dur="10s" attributeName="top" by="100"/>
</img>

<img top="3" ...>
   <animate begin= "5s" dur="10s" attributeName="top" by="100"
          fill="freeze" />
</img>

<img top="3" ...>
   <animate begin= "5s" dur="10s" attributeName="top" by="100"
          repeatCount="2.5" fill="freeze" />
</img>

<animate from="10" to="20" end="10s" fill="freeze" .../> 

For an element with active duration AD and intermediate active duration IAD, we define the repeat duration rd as:

rd = min(AD,IAD).

The frozen animation function is then given by:

ff(t) = fc(t) for all times t: 0<=t<rd;

ff(t) = ff(rd) for all times t: rd<=t<=AD where ff(rd) is defined below.

This is the value before the element is frozen.

When the element is frozen, t is effectively equal to AD, which according to the above definition is equivalent to saying t is effectively equal to rd.

In the following equations we define ff(rd).

If rd is not an integer multiple of the simple duration d, then ff(rd) = fi(rd), where i = floor(rd/d).

This is equivalent to fc(rd), except that fc(t) is not formally defined for t=rd. In this case, the equations remain consistent, and so the equivalent of fc(rd) is used for the frozen value ff(rd).

If rd is an integer multiple of d, i.e. rd = d*i for some positive integer i, and the animation is non-cumulative,
ff(rd) = f(d).

If rd is an integer multiple of d, i.e. rd = d*i for some positive integer i, and the animation is cumulative,

ff(rd) = f(d) * i.

Note that f(d) is a shorthand for the "last value defined for the animation function" (e.g., the to value or the last value in the values list).

Also note that if the fill behavior of the animation element is "remove", the animation effect is removed at the end of the repeat duration and the definition of fc(rd) is not used. The remainder of the active duration (if any) is only relevant for synchronization purposes.

Additive animation

<rect width="20px" ...>
   <animate attributeName="width" from="0px" to="10px" dur="10s"
      additive="sum"/>
</rect>

<img ...>
   <animateMotion from="0,0" to="100,0" dur="10s" />
   <animateMotion values="0,0; 0,5; 0,0" dur="1s"
                  repeatDur="10s" additive="sum"/>
</img>

Every animation element must be defined as either additive or non-additive. An element may be defined as additive only if addition is defined for the type of the target attribute.

The animation effect function F(t,u) combines all previously defined functions into one for a single animation element.

If the animation is additive, F(t,u) = u + ff(t).

If the animation is non-additive, F(t,u) = ff(t).

<img ...>
   <animateMotion begin="0" dur="5s" path="[some path]"
           additive="sum" fill="freeze" />
   <animateMotion begin="5s" dur="5s" path="[some path]"
           additive="sum" fill="freeze" />
   <animateMotion begin="10s" dur="5s" path="[some path]"
           additive="sum" fill="freeze" />
</img>

<img ...>
   <animateMotion dur="10s" repeatDur="indefinite"
           path="[some nice path]" />
   <mouseFollow begin="mouseover" dur="5s"
           additive="replace" fill="remove" />
</img>

<img ...>
   <animate dur="10s" repeatDur="indefinite"
            attributeName="top" from="20" by="10"
            additive="replace" accumulate="sum" />
</img>

<img top="10" ... >
  <animate dur="10s" repeatDur="indefinite"

           attributename="top" from="20" by="10"

           additive="sum" accumulate="sum" />
</img>

12.4.6 Restarting animations

12.4.7 Animation function value details

This section is normative.

12.6.1 Specifying the animation target

The animation target is defined as a specific attribute of a particular element. The means of specifying the target attribute and the target element are detailed in this section.

The target attribute

The target attribute to be animated is specified with attributeName. The value of this attribute is a string that specifies the name of the target attribute, as defined in the host language.

The attributes of an element that may be animated are often defined by different languages, and/or in different namespaces. For example, in many XML applications, the position of an element (which is a typical target attribute) is defined as a CSS property rather than as XML attributes. In some cases, the same attribute name is associated with attributes or properties in more than one language, or namespace. To allow the author to disambiguate the name mapping, an additional attribute attributeType is provided that specifies the intended namespace.

The attributeType attribute is optional. By default, the animation runtime will resolve the names according to the following rule: If there is a name conflict and attributeType is not specified, the list of CSS properties supported by the host language is matched first (if CSS is supported in the host language); if no CSS match is made (or CSS does not apply) the per-element-type partition namespace for the target element will be matched.

If a target attribute is defined in an XML Namespace other than the per-element-type partition namespace for the target element, the author must specify the namespace of the target attribute using the associated namespace prefix as defined in the scope of the animation element. The prefix is prepended to the value for attributeName.

For more information on XML namespaces, see [XML-NS].

The target element

An animation element may define the target element of the animation either explicitly or implicitly. An explicit definition uses an attribute to specify the target element. The syntax for this is described below.

If no explicit target is specified, the implicit target element is the parent element of the animation element in the document tree. It is expected that the common case will be that an animation element is declared as a child of the element to be animated. In this case, no explicit target need be specified.

If an explicit target element reference cannot be resolved (e.g. if no such element can be found), the animation has no effect. In addition, if the target element (either implicit or explicit) does not support the specified target attribute, the animation has no effect. See also Handling syntax errors.

The following two attributes may be used to identify the target element explicitly:

When integrating animation elements into the host language, the language designer should avoid including both of these attributes. If however, the host language designer chooses to include both attributes in the host language, then when both are specified for a given animation element the XLink href attribute takes precedence over the targetElement attribute.

<animate targetElement="foo" attributeName="bar" .../> 

<foo xmlns:xlink="http://www.w3.org/1999/xlink">
   ...
   <animate xlink:href="#foo" attributeName="bar" .../>
   ...
</foo>

When using an XLink href attribute on an animation element, the following additional XLink attributes must be defined in the host language. These may be defined in a DTD, or the host language may require these in the document syntax to support generic XLink processors. For more information, refer to [XLINK].

The following XLink attributes are required by the XLink specification. The values are fixed, and so may be specified as such in a DTD. All other XLink attributes are optional, and do not affect SMIL Animation semantics.

Additional details on the target element specification as relates to the host document and language are described in Required definitions and constraints on animation targets.

12.6.2 Specifying the simple animation function f(t)

Every animation function defines the value of the attribute at a particular moment in time. The time range for which the animation function is defined is the simple duration. The animation function does not produce defined results for times outside the range of 0 to the simple duration.

An animation is described either as a list of values, or in a simplified form that describes the from, to and by values. The from/to/by form is defined in Simple animation functions defined by from, to and by.

The animation will apply the values in order over the course of the animation. For discrete and linear animations, values in the values attribute are equally spaced through the animation duration. For paced animations, the values are spaced so that a uniform rate of change is obtained.

<rect ...>
   <animate attributeName="width" values="40;100;40" dur="10s"/>
</rect>

The simple animation function defined by the values and calcMode attributes can be formally specified:

Let i = floor((t*n)/d), d be the simple duration of the animation element, n be the number of entries in the values attribute, value[i] be the ith entry (counting from 0), di be the duration of the the ith time period, and ti be the time at which the the ith time period begins.

• For discrete animation, with no keyTimes attribute, the duration is divided into n equal time periods, one per value. With a keyTimes attribute, the time periods are specified by the keyTimes values. The animation function takes on the values in order, one value for each time period:

  f(t) = value[i]

• For linear animation with no keyTimes attribute, the duration is divided into n-1 equal periods, and di = d/(n-1) for any value of i. The animation function is a linear interpolation between the values at the associated times:

  f(t) = value[i] + (value[i+1]-value[i]) * (t-ti)/di.

  With a keyTimes attribute, the time periods are specified by the keyTimes values and so di is the duration of the ith period as defined by the keyTimes values:

  di = (keyTimes[i+1] - keyTimes[i]) * d

• For paced animations, the duration is divided into periods of lengths such that the rate of change of the attribute remains constant. If the distance between two values is dist(v1,v2), the total distance traversed D(i) up to and including value[i] is

  D(0) = 0, and

  D(i) = dist(value[0],value[1]) + dist(value[1],value[2]) +...+ dist(value[i-1],value[i]), for integers i with 0<i<=n.

  The animation function takes on the values in the values attribute at times determined by these distances:

  ti = (D(i)/D(n)) * d, for integers i with 0<=i<=n.

  di = ti+1 - ti = ((D(i+1) - D(i)) / D(n)) * d = (dist(value[i],value[i+1]) / D(n)) * d

  f(t) = value[i] + (value[i+1]-value[i]) * (t-ti)/ di

  where i is the largest non-negative integer such that ti<=t.

Note that a linear or paced animation will be a smoothly closed loop if the first value is repeated as the last. The keyTimes attribute is described in the SplineAnimation section.

Interpolation modes illustrated

This section is informative.

The three figures 5a, 5b and 5c below show how the same basic animation will change a value over time, given different interpolation modes. All examples are based upon the following example, but with different values for calcMode:

<animate dur="30s" values="0; 6; 5; 11; 10; 16" calcMode="[as specified]" />

Figure 5 - Discrete, linear and paced animation

	Figure 5a: Default discrete animation. calcMode="discrete" There are 6 segments of equal duration: 1 segment per value.
	Figure 5b: Default linear animation. calcMode="linear" There are 5 segments of equal duration: n-1 segments for n values.
	Figure 5c: Default paced animation. calcMode="paced" There are 5 segments of varying duration: n-1 segments for n values, computed to yield a constant rate of change in the value.

Examples of calcMode

<animate attributeName="foo" dur="8s" 
     values="bar; fun; far; boo" />

<animate attributeName="x" dur="10s" values="0; 10; 100" 
     calcMode="linear"/>

<animate attributeName="x" dur="10s" values="0; 10; 100" 
     calcMode="paced"/>

12.6.3 Specifying the animation effect function F(t,u)

12.6.4 Simple animation functions specified by from, to and by

An animation is described either as a list of values, as described earlier, or in a simplified form that uses from, to and by values.

The simpler from/to/by syntax provides for several variants. To use one of these variants, one of by or to must be specified; a from may be specified. The by and to attributes must not both be specified; if both are specified, only the to attribute will be used (the by will be ignored). The combinations of attributes yield the following classes of animation.

from-to animation

Specifying a from value and a to value defines a simple animation. The animation function is defined to start with the from value, and to finish with the to value.

Normative: A from-to animation with a from value vf and a to value vt is equivalent to the same animation with a values list with 2 values, vf and vt.

from-by animation

Specifying a from value and a by value defines a simple animation in which the animation function is defined to start with the from value, and to change this over the course of the simple duration by a delta specified with the by attribute. This may only be used with attributes that support addition (e.g. most numeric attributes).

Normative: A from-by animation with a from value vf and a by value vb is equivalent to the same animation with a values list with 2 values, vf and (vf+vb).

by animation

Specifying only a by value defines a simple animation in which the animation function is defined to offset the underlying value for the attribute, using a delta that varies over the course of the simple duration, starting from a delta of 0 and ending with the delta specified with the by attribute. This may only be used with attributes that support additive animation.

Normative: A by animation with a by value vb is equivalent to the same animation with a values list with 2 values, the neutral element for addition for the domain of the target attribute (denoted 0) and vb, and additive="sum". Any other specification of the additive attribute in a by animation is ignored.

to animation

This describes an animation in which the animation function is defined to start with the underlying value for the attribute, and finish with the value specified with the to attribute. Using this form, an author may describe an animation that will start with any current value for the attribute, and will end up at the desired to value.

A normative definition of a to animation is given below in To animation.

<rect ...>
   <animate attributeName="width" from="50" to="100" dur="10s"/>
</rect>

<rect ...>
   <animate attributeName="width" from="50" by="25" dur="10s"/>
</rect>

<rect width="40"...>
   <animate attributeName="width" by="30" dur="10s"/>
</rect>

<rect width="20px"...>
   <animate attributeName="width" dur="5s" from="10px" to="20px"
      accumulate="sum" repeatCount="10" />
</rect>

<rect width="20px"...>
   <animate attributeName="width" dur="5s" from="10px" to="20px"
      accumulate="sum" additive="sum" repeatCount="10" />
</rect>

To animation

<rect width="40"...>
   <animate attributeName="width" to="100" dur="10s"/>
</rect>

<rect color="red"...>
   <animate attributeName="color" to="blue" dur="10s" calcMode="discrete"/>
</rect>

The simple animation function f(t,u) for a discrete to animation with to value vt is a constant function which ignores the underlying value:

f(t,u) = vt

Otherwise, the simple animation function f(t,u) for a to animation with to value vt is a linear interpolation between the underlying value, u, and the to value:

f(t,u) = (u * (d-t)/d) + (vt * t/d), for t: 0<=t<=d where d is the simple duration.

If no other (lower priority) animations are active or frozen, this defines simple interpolation. However if another animation is manipulating the underlying value, the to animation will initially add to the effect of the lower priority animation, and increasingly dominate it as it nears the end of the simple duration, eventually overriding it completely. The value for f(t,u) at the end of the simple duration is just the to value.

Repeating to animations is the same as repeating other animations:

Normative

The repeated animation function, fr(t,u), has the standard definition:

fr(t,u) = f( REMAINDER(t,d), u ).

Because to animation is defined in terms of absolute values of the target attribute, cumulative animation is not defined:

The cumulative animation function, fc(t), for a to animation is

fc(t,u) =fr(t,u).

A frozen to animation takes on the value at the time it is frozen, masking further changes in the underlying value. This matches the dominance of the to value at the end of the simple duration. Even if other, lower priority animations are active while a to animation is frozen, the value does not change.

The frozen animation function, ff(t), for a to animation is

ff(t,u) = fc(t,u), if the animation is not frozen at time t, and

ff(t,u) = vf, if the animation is frozen at time t, where vf is the value of ff(t,u) at the moment the animation was frozen.

<rect width="40"...>
   <animate attributeName="width" to="100" dur="10s" repeatCount="2.5" fill="freeze"/>
</rect>

To animation defines its own kind of additive semantics, so the additive attribute is ignored.

The animation effect function, F(t,u) for a to animation is

F(t,u) = ff(t,u).

Multiple to animations will also combine according to these semantics. As the animation progresses, the higher-priority animation will have greater and greater effect, and the end result will be to set the attribute to the final value of the higher-priority to animation.

 <foo x="0" ...>
    <animate xml:id="A1" attributeName="x" 
        by="-10" dur="10s" fill="freeze" />
    <animate xml:id="A2" attributeName="x" 
        to="10"  dur="10s" fill="freeze" />
 </foo>

This section is normative.

The SMIL BasicAnimation module defines four elements, animate, set, animateMotion and animateColor.

12.7.1 The animate element

The animate element introduces a generic attribute animation that requires little or no semantic understanding of the attribute being animated. It can animate numeric scalars as well as numeric vectors. It can also animate a single non-numeric attribute through a discrete set of values. The animate element is an empty element; it does not have child elements.

This element supports from/to/by and values descriptions for the animation function, as well as all of the calculation modes. It supports all the described timing attributes. These are all described in respective sections above.

Numerous examples are provided above, as are normative definitions of the semantics of all attributes supported by animate.

12.7.2 The set element

The set element provides a simple means of just setting the value of an attribute for a specified duration. As with all animation elements, this only manipulates the presentation value, and when the animation completes, the effect is no longer applied. That is, set does not permanently set the value of the attribute.

The set element supports all attribute types, including those that cannot reasonably be interpolated and that more sensibly support semantics of simply setting a value (e.g. strings and Boolean values). The set element is non-additive. The additive and accumulate attributes are not allowed, and will be ignored if specified.

The set element supports all the timing attributes to specify the simple and active durations. However, the repeatCount and repeatDur attributes will just affect the active duration of the set, extending the effect of the set (since it is not really meaningful to "repeat" a static operation). Note that using fill="freeze" with set will have the same effect as defining the timing so that the active duration is indefinite.

The set element supports a more restricted set of attributes than the animate element. Only one value is specified, and neither interpolation control nor additive or cumulative animation is supported:

The simple animation function defined by a set element is

f(t) = v

where v is the value of the to attribute.

The set element is non-cumulative and non-additive.

Examples

<rect ...>
   <set attributeName="stroke-width" to="5px" 
            begin="5s" dur="10s" fill="remove" />
</rect>

<text>This will highlight if you mouse over it...
   <set attributeName="class" to="highlight" 
            begin="mouseover" end="mouseout" />
</text> 

12.7.3 The animateMotion element

The animateMotion element will move an element along a path. The element abstracts the notion of motion and position across a variety of layout mechanisms - the host language defines the layout model and must specify the precise semantics of position and motion. The path may be described in either of two ways:

• Specifying an x,y pair for each of the from/to/by attributes. These will define a straight line motion path.
• Specifying a semicolon separated list of x,y pairs for the values attribute. This will define a motion path of straight line segments, or points (if calcMode is set to discrete). This will override any from/to/by attribute values.

All values must be x, y value pairs. Each x and y value may specify any units supported for element positioning by the host language. The host language defines the default units. In addition, the host language defines the reference point for positioning an element. This is the point within the element that is aligned to the position described by the motion animation. The reference point defaults in some languages to the upper left corner of the element bounding box; in other languages the reference point may be implicit, or may be specified for an element.

The syntax for the x, y value pairs is:

Coordinate-pair ::= "(" Coordinate Comma-wsp Coordinate ")"
Coordinate      ::= Num
Num             ::= Number

Coordinate values are separated by at least one white space character or a comma. Additional white space around the separator is allowed. The values of Coordinate must be defined as some sort of number in the host language.

The attributeName and attributeType attributes are not used with animateMotion, as the manipulated position attribute(s) are defined by the host language. If the position is exposed as an attribute or attributes that may also be animated (e.g. as "top" and "left", or "posX" and "posY"), implementations must combine animateMotion animations with other animations that manipulate individual position attributes. See also The animation sandwich model.

If none of the from, to, by and values attributes are specified, the animation will have no effect.

The default calculation mode (calcMode) for animateMotion is paced. This will produce constant velocity motion along the specified path. Note that while animateMotion elements may be additive, the addition of two or more paced (constant velocity) animations may not result in a combined motion animation with constant velocity.

12.7.4 The animateColor element

The animateColor element specifies an animation of a color attribute. The host language must specify those attributes that describe color values and may support color animation.

All values must represent [sRGB] color values. Legal value syntax for attribute values is defined by the host language.

Interpolation is defined on a per-color-channel basis.

The values in the from/to/by and values attributes may specify negative and out of gamut values for colors. The function defined by an individual animateColor may yield negative or out of gamut values. The implementation must correct the resulting presentation value, to be legal for the destination (display) colorspace. However, as described in The animation sandwich model, the implementation should only correct the final combined result of all animations for a given attribute, and should not correct the effect of individual animations.

Values are corrected by "clamping" the values to the correct range. Values less than the minimum allowed value are clamped to the minimum value (commonly 0, but not necessarily so for some color profiles). Values greater than the defined maximum are clamped to the maximum value (defined by the host language) .

This section is normative.

12.8.1 BasicAnimation integration requirements

This section describes what a language designer must actually do to specify the integration of SMIL Animation into a host language. This includes basic definitions and constraints upon animation.

In addition to the requirements listed in this section, those listed in Common animation integration requirements must be satisfied.

Required definitions and constraints on animation targets

Specifying the target element

The host language designer must choose whether to support the targetElement attribute or the XLink attributes for specifying the target element. Note that if the XLink syntax is used, the host language designer must decide how to denote the XLink namespace for the associated attributes. The namespace may be fixed in a DTD, or the language designer may require colonized attribute names (qnames) to denote the XLink namespace for the attributes. The required XLink attributes have fixed values, and so may also be specified in a DTD, or may be required on the animation elements. Host language designers may require that the optional XLink attributes be specified. These decisions are left to the host language designer - the syntax details for XLink attributes do not affect the semantics of SMIL Animation.

In general, target elements may be any element in the document. Host language designers must specify any exceptions to this. Host language designers are discouraged from allowing animation elements to target elements outside of the document in which the animation element is defined. The XLink syntax for the target element could allow this, but the SMIL timing and animation semantics of this are not defined in this version of SMIL Animation.

Target attribute issues

The definitions in this module may be used to animate any attribute of any element in a host document. However, it is expected that host language designers integrating SMIL Animation may choose to constrain which elements and attributes may support animation. For example, a host language may choose not to support animation of the language attribute of a script element. A host language which included a specification for DOM functionality might limit animation to the attributes which may legally be modified through the DOM.

Any attribute of any element not specifically excluded from animation by the host language may be animated, as long as the underlying data type (as defined by the host language for the attribute) supports discrete values (for discrete animation) and/or addition (for interpolated, additive and cumulative animation).

All constraints upon animation must be described in the host language specification or in an appropriate schema, as the DTD alone cannot reasonably express this.

The host language must define which language abstract values should be handled for animated attributes. For example, a host language that incorporates CSS may require that CSS length values be supported. This is further detailed in Animation function value details.

The host language must specify the interpretation of relative values. For example, if a value is specified as a percentage of the size of a container, the host language must specify whether this value will be dynamically interpreted as the container size is animated.

The host language must specify the semantics of clamping values for attributes. The language must specify any defined ranges for values, and how out of range values will be handled.

The host language must specify the formats supported for numeric attribute values. This includes both integer values and floating point values. As a reasonable minimum, host language designers are encouraged to support the format described in section 4.3.1, "Integers and real numbers," of [CSS2].

Integrating animateMotion functionality

The host language specification must define which elements may be the target of animateMotion. In addition, the host language specification must describe the positioning model for elements, and must describe the model for animateMotion in this context (i.e. the semantics of the default value for the origin attribute must be defined). If there are different ways to describe position, additional attribute values for the origin attribute should be defined to allow authors control over the positioning model.

12.8.2 Document type definition (DTD) for the BasicAnimation module

This section is normative.

12.9.1 SMIL 3.0 SplineAnimation Module Attributes

Spline animation function calculation mode

The SplineAnimation module extends the discrete, linear and paced calculation modes of the BasicAnimation module, providing additional control over interpolation and timing:

• The calcMode attribute is extended to support splines.
• A path attribute is added to the animateMotion element, allowing authors to define a motion path using a subset of the SVG [SVG] path syntax, and providing smooth path motion.
• The keyTimes attribute provides additional control over the timing of the animation function, associating a time with each value in the values list (or the points in a path description for the animateMotion element).
• The keySplines attribute provides a means of controlling the pacing of interpolation between the values in the values list.

This semantic (the duration is divided into n-1 equal periods) applies as well when the keySplines attribute is specified, but keyTimes is not. The times associated to the keySplines values are determined as described above.

The syntax for the control point sets in keySplines lists is:

Control-pt-set ::= ( Fpval Comma-wsp Fpval Comma-wsp Fpval Comma-wsp Fpval )

Using:

Fpval          ::= Floating point number
Comma-wsp      ::= S? (S|",") S?
S              ::= (#x20 | #x9 | #xD | #xA)+ /* from [XML11] */

Control point values are separated by at least one white space character or a comma. Additional white space around the separator is allowed. The allowed syntax for floating point numbers must be defined in the host language.

If the argument values for keyTimes or keySplines are not legal (including too few or too many values for either attribute), the animation will have no effect (see also Handling syntax errors).

In the calcMode, keyTimes and keySplines attribute values, leading and trailing white space and white space before and after semicolon separators will be ignored.

This section is informative.

Examples of advanced uses of calcMode

Discrete animation may be used with keyTimes, as in the following example:

<animateColor attributeName="color" dur="10s" calcMode="discrete"
     values="green; yellow; red" keyTimes="0.0; 0.5; 0.8" />

The value of the "color" attribute will be set to green for 5 seconds, and then to yellow for 3 seconds, and then will remain red for the last 2 seconds.

When using discrete animation with a keyTimes value of 1, the result may be somewhat surprising. Consider the following example:

<par dur="30">
  <animate calcMode="discrete" repeatCount="2" dur="10" fill="freeze"
    accumulate="[as specified]" keyTimes="0.0; 0.5; 1.0" values="0; 1; 2" .../>
</par>

This example is tricky because of the end-point-exclusive nature of the SMIL time model. At first flush, the final value is never reached since the final time is never reached, but the definitions above make that the value is used anyway. The table gives the value for selected times for the possible values of the accumulate attribute:

time	accumulate
	none	sum
t=0	0	0
t=5	1	1
t=10	0	2
t=15	1	3
t=20	2	4
t=25	2	4

The following example illustrates the use of keyTimes:

<animate attributeName="x" dur="10s" values="0; 50; 100" 
     keyTimes="0; .8; 1" calcMode="linear"/>

The keyTimes values cause the "x" attribute to have a value of "0" at the start of the animation, "50" after 8 seconds (at 80% into the simple duration) and "100" at the end of the animation. The value will change more slowly in the first half of the animation, and more quickly in the second half.

Interpolation with keySplines

For some attributes, the pace of change may not be easily discernibly by viewers. However for animations like motion, the ability to make the speed of the motion change gradually, and not in abrupt steps, can be important. The keySplines attribute provides this control.

Extending the above example to use keySplines:

<animate attributeName="x" dur="10s" values="0; 50; 100" 
     keyTimes="0; .8; 1" calcMode="spline" 
     keySplines=".5 0 .5 1; 0 0 1 1" />

The keyTimes still cause the "x" attribute to have a value of "0" at the start of the animation, "50" after 8 seconds and "100" at the end of the animation. However, the keySplines values define a curve for pacing the interpolation between values. In the example above, the spline causes an ease-in and ease-out effect between time 0 and 8 seconds (i.e. between keyTimes 0 and .8, and values "0" and "50"), but a strict linear interpolation between 8 seconds and the end (i.e. between keyTimes .8 and 1, and values "50" and "100"). Figure 7 shows the curves that these keySplines values define.

Figure 7 - Illustration of keySplines effect

	keySplines="0 0 1 1" (the default)		keySplines=".5 0 .5 1"
	keySplines="0 .75 .25 1"		keySplines="1 0 .25 .25"

Each diagram in Figure 7 illustrates the effect of keySplines settings for a single interval (i.e. between the associated pairs of values in the keyTimes and values lists.). The horizontal axis can be thought of as the input value for the unit progress of interpolation within the interval - i.e. the pace with which interpolation proceeds along the given interval. The vertical axis is the resulting value for the unit progress, yielded by the keySplines function. Another way of describing this is that the horizontal axis is the input unit time for the interval, and the vertical axis is the output unit time. See also the section Timing and real-world clock times.

To illustrate the calculations, consider the simple example:

<animate dur="4s" values="10; 20" keyTimes="0; 1"
     calcMode="spline" keySplines={as in table} />

Using the keySplines values for each of the four cases above, the approximate interpolated values as the animation proceeds are:

keySplines values	Initial value	After 1s	After 2s	After 3s	Final value
0 0 1 1	10.0	12.5	15.0	17.5	20.0
.5 0 .5 1	10.0	11.0	15.0	19.0	20.0
0 .75 .25 1	10.0	18.0	19.3	19.8	20.0
1 0 .25 .25	10.0	10.1	10.6	16.9	20.0

For a formal definition of Bezier spline calculation, see [COMP-GRAPHICS], pages 488-491.

The keyTimes and keySplines attributes may also be used with the from/to/by shorthand forms for specifying values, as in the following example:

<animate attributeName="foo" from="10" to="20" 
     dur="10s" keyTimes="0.0; 1.0"
     calcMode="spline" keySplines=".5 0 .5 1" />

The value will change from 10 to 20, using an "ease-in/ease-out" curve specified by the keySplines values. The keyTimes values cause the value of 20 to be reached at 10 seconds.

The following example describes a somewhat unusual usage, a from-to animation with discrete animation. The stroke-linecap attribute of SVG elements takes a string, and so implies a calcMode of discrete. The animation will set the stroke-linecap attribute to round for 5 seconds (half the simple duration) and then set the stroke-linecap to square for 5 seconds.

<rect stroke-linecap="butt"...>
   <animate attributeName="stroke-linecap" 
      from="round" to="square" dur="10s"/>
</rect>

12.9.2 SMIL 3.0 SplineAnimation Module Elements

12.9.3 The spline animate element

The SplineAnimation module extends the animate element defined by the BasicAnimation module, adding the following attributes and values.

Examples are provided above, as are normative definitions of the semantics of all attributes supported by animate.

12.9.4 The spline animateMotion element

The SplineAnimation module extends the animateMotion element defined by the BasicAnimation module, adding the following attributes and values.

Examples are provided above, as are normative definitions of the semantics of all attributes supported by animate.

For complete velocity control, calcMode may be set to spline and the author may specify a velocity control spline with keyTimes and keySplines.

12.9.5 The spline animateColor element

The SplineAnimation module extends the animateColor element defined by the BasicAnimation module, adding the following attributes and values.

This section is normative.

12.10.1 SplineAnimation integration requirements

To specify the integration of the SMIL 3.0 SplineAnimation module into a host language, the language designer must integrate SMIL 3.0 BasicAnimation into the language, satisfying all the requirements listed in BasicAnimation integration requirements.

In addition to integrating BasicAnimation, the requirements listed in Common animation integration requirements must be satisfied for the SplineAnimation module.

12.10.2 Document type definition (DTD) for the SplineAnimation module

This section is normative.

12.11.1 Integration requirements

The host language profile must integrate the SMIL 3.0 BasicInlineTiming module into the host language, satisfying all requirements of that module. In addition, all modules of the SMIL 3.0 Timing and Synchronization modules and of the SMIL 3.0 Time Manipulation modules which are integrated into the host language must be available on BasicAnimation elements.

In particular, the fill attribute is supported on animation elements only if the host language integrates the SMIL 3.0 BasicTimeContainers module in addition to the BasicInlineTiming module.

If the Eventbase-element term is missing, the event-base element is defined to be the target element of the animation.

The host language profile may add additional attributes to Animation elements. Attributes added to any Animation element must be added to all Animation elements. In particular, this module does not define an XML ID attribute. It is expected that the host language profile will add an XML ID attribute to the Animation elements.

Extending Animation

Language designers integrating SMIL Animation are encouraged to define new animation elements where such additions will be of convenience to authors. The new elements must be based on SMIL Animation and SMIL Timing and Synchronization, and must stay within the framework provided by SMIL Timing and Synchronization and SMIL Animation.

Language designers are also encouraged to define support for additive and cumulative animation for non-numeric data types where addition can sensibly be defined.

Constraints on manipulating animation elements

Language designers integrating SMIL Animation are encouraged to disallow manipulation of attributes of the animation elements after the document has begun. This includes both the attributes specifying targets and values, as well as the timing attributes. In particular, the id attribute (of type ID) on all animation elements must not be mutable (i.e. should be read-only). Requiring animation runtimes to track changes to id values introduces considerable complexity, for what is at best a questionable feature.

It is recommended that language specifications disallow manipulation of animation element attributes through DOM interfaces after the document has begun. It is also recommended that language specifications disallow the use of animation elements to target other animation elements.

Note in particular that if the attributeName attribute can be changed (either by animation or script), problems may arise if the target attribute has a namespace qualified name. Current DOM specifications do not include a mechanism to handle this binding.

Dynamically changing the attribute values of animation elements introduces semantic complications to the model that are not yet sufficiently resolved. This constraint may be lifted in a future version of SMIL Animation.

Handling syntax errors

The specific error handling mechanisms for each attribute are described with the individual syntax descriptions. Some of these specifications describe the behavior of an animation with syntax errors as "having no effect". This means that the animation will continue to behave normally with respect to timing, but will not manipulate any presentation value, and so will have no visible impact upon the presentation.

In particular, this means that if other animation elements are defined to begin or end relative to an animation that "has no effect", the other animation elements will begin and end as though there were no syntax errors. The presentation runtime may indicate an error, but need not halt presentation or animation of the document.

Some host languages and/or runtimes may choose to impose stricter error handling (see also Error handling semantics for a discussion of host language issues with error handling). Authoring environments may also choose to be more intrusive when errors are detected.

Error handling semantics

The host language designer may impose stricter constraints upon the error handling semantics. That is, in the case of syntax errors, the host language may specify additional or stricter mechanisms to be used to indicate an error. An example would be to stop all processing of the document, or to halt all animation.

Host language designers may not relax the error handling specifications, or the error handling response (as described in Handling syntax errors). For example, host language designers may not define error recovery semantics for missing or erroneous values in the values or keyTimes attribute values.