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CHAPTER 10 ANIMATION
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The Bezier curve modeling the car in Figure 10-13 used the control points (0.9,0.25) (0.1,0.75). The code in this chapter with the name SplineDemo includes a plot of the Bezier curve, along with our famous rectangle moving in a straight line (on top of a line that marks the full path of the rectangle). Figure 10-14 shows the curve and the rectangle in its starting position. You can divide this Bezier curve into two regions: the first curvy segment (from x = 0 to x = 0.5) and the second curvy segment (from x = 0.5 to x = 1). The first segment starts out with a subtle curve that corresponds to a slowly increasing rate of movement (it s not quite straight along a diagonal, so the rate is not constant). After the bend, the curve is quite steep up to the center point, corresponding to a fast rate of change. The second curvy segment is the mirror opposite of this: the movement continues quickly and suddenly starts slowing down before coming to a complete stop (when the final value of the property is reached).
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Figure 10-14. Rectangle animated using spline interpolation, and the curve plotted If you want to figure out the curve that describes the animation you desire, you have several options. There are tools online that can assist, since Bezier curves are a popular approach to modeling animation. You can experiment using the code in this chapter by plugging in control points using sliders to preview the animation curve. You can also take out the trusty pen and paper and draw a curve that you think will work, roughly determine the control points, and then experiment. (The derivative for Bezier curves to show the rate of change, while interesting, is left as an exercise for the reader.)
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Animation Easing
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When it comes to using keyframe animations and attempting to define an interpolation function to model the effect you desire, you might spend a while getting it just right (unless you know the formula to use ahead of time). Silverlight 3 introduced a stock set of easing functions that control the change of property values over the duration of the animation. Two of these easing functions are bouncing and springing effects, and you can also define your own custom easing function with the use of the IEasingFunction interface. The full set of easing functions that come with Silverlight are shown in Table 10-4.
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CHAPTER 10 ANIMATION
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Table 10-4. Stock Animation-Easing Functions
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Easing Function
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The property value is first backed up a little before animating to its end. For example, a property value animating from 10 to 90 might go from 10 to 5 first and then from 5 to 90. This function has one double property, Amplitude, which controls the animation. The property bounces before stopping at its final value. The number of bounces is specified by the integer property Bounces. Uses a circular function to control the animation. Uses the function f(t) = t^3. Property oscillates back and forth as if on a spring, slowing down until it comes to rest. Uses an exponential function. Uses an arbitrary power (specified by the double Power property). This is a general form of the cubic, quadratic, quartic, and quintic easing functions. Uses the function f(t) = t^2. Uses the function f(t) = t^4. Uses the function f(t) = t^5. Uses a sine formula.
BounceEase
CircleEase CubicEase ElasticEase
ExponentialEase PowerEase
QuadraticEase QuarticEase QuinticEase SineEase
The easing functions that come with Silverlight inherit from the base class EasingFunctionBase. This base class provides an additional property, EasingMode, which makes it easy to invert the easing function or to run it inverted for half the time and then normal for the other half. The EasingMode enums are as follows: EaseOut: This mode of interpolation follows 100 percent interpolation minus the output of the formula associated with the easing function. EaseIn: This mode of interpolation follows the mathematical formula associated with the easing function. EaseInOut: This mode of interpolation uses EaseIn for the first half of the animation and EaseOut for the second half.
Using an easing function in XAML starts with an Easing keyframe corresponding to the type you want to animate, such as EasingDoubleKeyFrame and EasingColorKeyFrame. Then the easing function is
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