详解 Interpolator动画插值器

Interpolator 被用来修饰动画效果，定义动画的变化率。在Android源码中对应的接口类为TimeInterpolator，通过输入均匀变化的0~1之间的值，可以得到匀速、正加速、负加速、无规则变加速等0~1之间的变化曲线。

曲线举例：
如下图所示，为Android源码中OvershootInterpolator插值器变化率曲线。
输入为均匀变化0~1.0f之间浮点值，输出为先加速超过临界值1.0f 再慢慢又回落到1.0f 连续变化的浮点值。

效果举例：

使用OvershootInterpolator动画插值器后，动画的运行效果如下所示：

上图中，旋转放大效果中，旋转动画就是使用了OvershootInterpolator动画插值器。
可以看到3D勋章 360度旋转时，旋转角度先超过了360度，然后慢慢又回到了360度位置，从而呈现一个回弹的视觉效果。

注：
了解 3D勋章具体实现，参考文章《3D勋章实现方案》：
https://xiaxl.blog.csdn.net/article/details/77048507

• Android 源码中的动画插值器
• Easing 经典动画插值器

一、Android中的插值器

Android源码中使用 TimeInterpolator 接口修饰动画效果，定义动画的变化率。
代码位于android.animation包下，只包含一个抽象方法为getInterpolation(float input)。

// 位于android.animation包下
package android.animation;
// Android源码中的 动画插值器
public interface TimeInterpolator {
	// 差值计算(输入为0~1.0f之间的浮点值，输出为连续的变化率曲线)
    float getInterpolation(float input);
}

TimeInterpolator接口类中，只有一个方法float getInterpolation(float input)，根据输入的浮点值input(0~1.0f之间)，输出为连续的变化率曲线。

Android中动画插值器的使用方式如下：

// view 位移动画
AnimatorSet localAnimatorSet = new AnimatorSet();
float[] arrayOfFloat = new float[2];
arrayOfFloat[0] = y0;
arrayOfFloat[1] = y1;
// 位移动画使用了 DecelerateInterpolator() 动画插值器
// 动画效果：先位移超过临界值，再回到临界值
ObjectAnimator localObjectAnimator = ObjectAnimator.ofFloat(view,
    "translationY", arrayOfFloat);
localObjectAnimator.setDuration(240L);
localObjectAnimator.setInterpolator(new DecelerateInterpolator());
localAnimatorSet.play(localObjectAnimator);
localAnimatorSet.start();

TimeInterpolator为接口类，其有如下接口实现类。

1.1 AccelerateDecelerateInterpolator

AccelerateDecelerateInterpolator 该插值器运动曲线 两边慢 中间快，其运动曲线如下图所示：

/**
 * An interpolator where the rate of change starts and ends slowly but
 * accelerates through the middle.
 * 两边慢 中间快
 */
public class AccelerateDecelerateInterpolator extends BaseInterpolator
        implements NativeInterpolatorFactory {
    public AccelerateDecelerateInterpolator() {
    }

    public float getInterpolation(float input) {
        return (float)(Math.cos((input + 1) * Math.PI) / 2.0f) + 0.5f;
    }
}

1.2 AccelerateInterpolator

AccelerateInterpolator 该插值器运动曲线 先慢 后快，其运动曲线如下图所示（factor值为1）：

/**
 * An interpolator where the rate of change starts out slowly and
 * and then accelerates.
 * 先慢 后快
 */
public class AccelerateInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private final float mFactor;
    private final double mDoubleFactor;

    public AccelerateInterpolator() {
        mFactor = 1.0f;
        mDoubleFactor = 2.0;
    }

    /**
     * Constructor
     *
     * @param factor Degree to which the animation should be eased. Seting
     *        factor to 1.0f produces a y=x^2 parabola. Increasing factor above
     *        1.0f  exaggerates the ease-in effect (i.e., it starts even
     *        slower and ends evens faster)
     */
    public AccelerateInterpolator(float factor) {
        mFactor = factor;
        mDoubleFactor = 2 * mFactor;
    }


    public float getInterpolation(float input) {
        if (mFactor == 1.0f) {
            return input * input;
        } else {
            return (float)Math.pow(input, mDoubleFactor);
        }
    }
}

1.3 AnticipateInterpolator

AnticipateInterpolator 该插值器运动曲线 先向后超过临界值，再快速向前，像一个回荡的秋千，因此被称为回荡秋千插值器曲线图如下：

/**
 * An interpolator where the change starts backward then flings forward.
 * 先向后 再向前
 */
public class AnticipateInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private final float mTension;

    public AnticipateInterpolator() {
        mTension = 2.0f;
    }

    /**
     * @param tension Amount of anticipation. When tension equals 0.0f, there is
     *                no anticipation and the interpolator becomes a simple
     *                acceleration interpolator.
     */
    public AnticipateInterpolator(float tension) {
        mTension = tension;
    }

    public float getInterpolation(float t) {
        // a(t) = t * t * ((tension + 1) * t - tension)
        return t * t * ((mTension + 1) * t - mTension);
    }
}

1.4 AnticipateOvershootInterpolator

AnticipateOvershootInterpolator 该插值器运动曲线 先向后运动 超过临界值，再快速向前运动到达临界值，其运动曲线如下图所示：

/**
 * An interpolator where the change starts backward then flings forward and overshoots
 * the target value and finally goes back to the final value.
 * 先向后运动 超过临界值，再快速向前运动超过临界值，最后慢慢回到临界值
 */
public class AnticipateOvershootInterpolator extends BaseInterpolator
        implements NativeInterpolatorFactory {
    private final float mTension;

    public AnticipateOvershootInterpolator() {
        mTension = 2.0f * 1.5f;
    }

    /**
     * @param tension Amount of anticipation/overshoot. When tension equals 0.0f,
     *                there is no anticipation/overshoot and the interpolator becomes
     *                a simple acceleration/deceleration interpolator.
     */
    public AnticipateOvershootInterpolator(float tension) {
        mTension = tension * 1.5f;
    }

    /**
     * @param tension Amount of anticipation/overshoot. When tension equals 0.0f,
     *                there is no anticipation/overshoot and the interpolator becomes
     *                a simple acceleration/deceleration interpolator.
     * @param extraTension Amount by which to multiply the tension. For instance,
     *                     to get the same overshoot as an OvershootInterpolator with
     *                     a tension of 2.0f, you would use an extraTension of 1.5f.
     */
    public AnticipateOvershootInterpolator(float tension, float extraTension) {
        mTension = tension * extraTension;
    }

    private static float a(float t, float s) {
        return t * t * ((s + 1) * t - s);
    }

    private static float o(float t, float s) {
        return t * t * ((s + 1) * t + s);
    }

    public float getInterpolation(float t) {
        // a(t, s) = t * t * ((s + 1) * t - s)
        // o(t, s) = t * t * ((s + 1) * t + s)
        // f(t) = 0.5 * a(t * 2, tension * extraTension), when t < 0.5
        // f(t) = 0.5 * (o(t * 2 - 2, tension * extraTension) + 2), when t <= 1.0
        if (t < 0.5f) return 0.5f * a(t * 2.0f, mTension);
        else return 0.5f * (o(t * 2.0f - 2.0f, mTension) + 2.0f);
    }
}

1.5 BounceInterpolator

BounceInterpolator 该插值器运动曲线 快速运动到临界值后，进行几次回跳，类似一个从高空坠落篮球的运动曲线，其运动曲线如下图所示：

/**
 * An interpolator where the change bounces at the end.
 * 快速运动到临界值后，进行几次回跳，类似一个从高空坠落篮球的运动曲线。
 */
public class BounceInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    public BounceInterpolator() {
    }

    private static float bounce(float t) {
        return t * t * 8.0f;
    }

    public float getInterpolation(float t) {
        // _b(t) = t * t * 8
        // bs(t) = _b(t) for t < 0.3535
        // bs(t) = _b(t - 0.54719) + 0.7 for t < 0.7408
        // bs(t) = _b(t - 0.8526) + 0.9 for t < 0.9644
        // bs(t) = _b(t - 1.0435) + 0.95 for t <= 1.0
        // b(t) = bs(t * 1.1226)
        t *= 1.1226f;
        if (t < 0.3535f) return bounce(t);
        else if (t < 0.7408f) return bounce(t - 0.54719f) + 0.7f;
        else if (t < 0.9644f) return bounce(t - 0.8526f) + 0.9f;
        else return bounce(t - 1.0435f) + 0.95f;
    }
}

1.6 CycleInterpolator

CycleInterpolator 该插值器运动曲线 正弦变化曲线，其运动曲线如下图所示：

/**
 * Repeats the animation for a specified number of cycles. The
 * rate of change follows a sinusoidal pattern.
 * sin正弦变化曲线
 */
@HasNativeInterpolator
public class CycleInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private float mCycles;
    
    public CycleInterpolator(float cycles) {
        mCycles = cycles;
    }

    public float getInterpolation(float input) {
        return (float)(Math.sin(2 * mCycles * Math.PI * input));
    }
}

1.7 DecelerateInterpolator

DecelerateInterpolator 该插值器运动曲线 减速插值器变化曲线，其算法为AccelerateInterpolator的完全倒置，同样有DecelerateInterpolator(float factor)构造函数来指定mFactor运动曲线如下图所示（factor值为1）：

/**
 * An interpolator where the rate of change starts out quickly and
 * and then decelerates.
 * 减速插值器变化曲线，其算法为AccelerateInterpolator的完全倒置。
 */
public class DecelerateInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private float mFactor = 1.0f;
    
    public DecelerateInterpolator() {
    }

    /**
     * Constructor
     *
     * @param factor Degree to which the animation should be eased. Setting factor to 1.0f produces
     *        an upside-down y=x^2 parabola. Increasing factor above 1.0f exaggerates the
     *        ease-out effect (i.e., it starts even faster and ends evens slower).
     */
    public DecelerateInterpolator(float factor) {
        mFactor = factor;
    }

    public float getInterpolation(float input) {
        float result;
        if (mFactor == 1.0f) {
            result = (float)(1.0f - (1.0f - input) * (1.0f - input));
        } else {
            result = (float)(1.0f - Math.pow((1.0f - input), 2 * mFactor));
        }
        return result;
    }
}

1.8 LinearInterpolator

LinearInterpolator 该插值器运动曲线 为0~1之间匀速变化的一条直线，其运动曲线如下图所示：

/**
 * An interpolator where the rate of change starts out quickly and
 * and then decelerates.
 * 为0~1之间匀速变化的一条直线。
 */
/**
 * An interpolator where the rate of change is constant
 */
public class LinearInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {

    public LinearInterpolator() {
    }

    public float getInterpolation(float input) {
        return input;
    }
}

1.9 OvershootInterpolator

OvershootInterpolator 该插值器运动曲线 先加速超过临界值1.0f 再慢慢又回落到1.0f，有一个回弹的效果。

可使用OvershootInterpolator(float tension)构造函数设置mTension弹力值，mTension值越大，超出目标值的时间点越靠前，超出目标值的回弹距离越大，回弹越明显。

其运动曲线如下图所示：

/**
 * An interpolator where the change flings forward and overshoots the last value
 * then comes back.
 * 先超过临界值 再慢慢回到临界值
 */
public class OvershootInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private final float mTension;

    public OvershootInterpolator() {
        mTension = 2.0f;
    }

    /**
     * @param tension Amount of overshoot. When tension equals 0.0f, there is
     *                no overshoot and the interpolator becomes a simple
     *                deceleration interpolator.
     */
    public OvershootInterpolator(float tension) {
        mTension = tension;
    }

    public float getInterpolation(float t) {
        // _o(t) = t * t * ((tension + 1) * t + tension)
        // o(t) = _o(t - 1) + 1
        t -= 1.0f;
        return t * t * ((mTension + 1) * t + mTension) + 1.0f;
    }
}

1.10 PathInterpolator

PathInterpolator 可以称之为万能插值器，可以通过PathInterpolator构造一个Path路径 或 通过传入点来构造一个贝塞尔曲线（通过这个贝塞尔曲线，我们可以构造任意的变化曲线）。

//创建一个任意Path的插值器
PathInterpolator(Path path)
//创建一个二阶贝塞尔曲线的插值器
PathInterpolator(float controlX, float controlY)
//创建一个三阶贝塞尔曲线的插值器
PathInterpolator(float controlX1, float controlY1, float controlX2, float controlY2)

贝塞尔曲线的构建，可以使用如下辅助工具 cubic-bezier：
https://cubic-bezier.com/

/**
 * An interpolator that can traverse a Path that extends from <code>Point</code>
 * <code>(0, 0)</code> to <code>(1, 1)</code>. The x coordinate along the <code>Path</code>
 * is the input value and the output is the y coordinate of the line at that point.
 * This means that the Path must conform to a function <code>y = f(x)</code>.
 *
 * <p>The <code>Path</code> must not have gaps in the x direction and must not
 * loop back on itself such that there can be two points sharing the same x coordinate.
 * It is alright to have a disjoint line in the vertical direction:</p>
 * <p><blockquote><pre>
 *     Path path = new Path();
 *     path.lineTo(0.25f, 0.25f);
 *     path.moveTo(0.25f, 0.5f);
 *     path.lineTo(1f, 1f);
 * </pre></blockquote></p>
 * 构造一个普通Path路径或者贝塞尔曲线的插值器
 */
public class PathInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {

    // This governs how accurate the approximation of the Path is.
    private static final float PRECISION = 0.002f;

    private float[] mX; // x coordinates in the line

    private float[] mY; // y coordinates in the line

    /**
     * Create an interpolator for an arbitrary <code>Path</code>. The <code>Path</code>
     * must begin at <code>(0, 0)</code> and end at <code>(1, 1)</code>.
     *
     * @param path The <code>Path</code> to use to make the line representing the interpolator.
     */
    public PathInterpolator(Path path) {
        initPath(path);
    }

    public PathInterpolator(float controlX, float controlY) {
        initQuad(controlX, controlY);
    }

    /**
     * Create an interpolator for a cubic Bezier curve.  The end points
     * <code>(0, 0)</code> and <code>(1, 1)</code> are assumed.
     *
     * @param controlX1 The x coordinate of the first control point of the cubic Bezier.
     * @param controlY1 The y coordinate of the first control point of the cubic Bezier.
     * @param controlX2 The x coordinate of the second control point of the cubic Bezier.
     * @param controlY2 The y coordinate of the second control point of the cubic Bezier.
     */
    public PathInterpolator(float controlX1, float controlY1, float controlX2, float controlY2) {
        initCubic(controlX1, controlY1, controlX2, controlY2);
    }

    private void initQuad(float controlX, float controlY) {
        Path path = new Path();
        path.moveTo(0, 0);
        path.quadTo(controlX, controlY, 1f, 1f);
        initPath(path);
    }

    private void initCubic(float x1, float y1, float x2, float y2) {
        Path path = new Path();
        path.moveTo(0, 0);
        path.cubicTo(x1, y1, x2, y2, 1f, 1f);
        initPath(path);
    }

    private void initPath(Path path) {
        float[] pointComponents = path.approximate(PRECISION);

        int numPoints = pointComponents.length / 3;
        if (pointComponents[1] != 0 || pointComponents[2] != 0
                || pointComponents[pointComponents.length - 2] != 1
                || pointComponents[pointComponents.length - 1] != 1) {
            throw new IllegalArgumentException("The Path must start at (0,0) and end at (1,1)");
        }

        mX = new float[numPoints];
        mY = new float[numPoints];
        float prevX = 0;
        float prevFraction = 0;
        int componentIndex = 0;
        for (int i = 0; i < numPoints; i++) {
            float fraction = pointComponents[componentIndex++];
            float x = pointComponents[componentIndex++];
            float y = pointComponents[componentIndex++];
            if (fraction == prevFraction && x != prevX) {
                throw new IllegalArgumentException(
                        "The Path cannot have discontinuity in the X axis.");
            }
            if (x < prevX) {
                throw new IllegalArgumentException("The Path cannot loop back on itself.");
            }
            mX[i] = x;
            mY[i] = y;
            prevX = x;
            prevFraction = fraction;
        }
    }

    /**
     * Using the line in the Path in this interpolator that can be described as
     * <code>y = f(x)</code>, finds the y coordinate of the line given <code>t</code>
     * as the x coordinate. Values less than 0 will always return 0 and values greater
     * than 1 will always return 1.
     *
     * @param t Treated as the x coordinate along the line.
     * @return The y coordinate of the Path along the line where x = <code>t</code>.
     * @see Interpolator#getInterpolation(float)
     */
    @Override
    public float getInterpolation(float t) {
        if (t <= 0) {
            return 0;
        } else if (t >= 1) {
            return 1;
        }
        // Do a binary search for the correct x to interpolate between.
        int startIndex = 0;
        int endIndex = mX.length - 1;

        while (endIndex - startIndex > 1) {
            int midIndex = (startIndex + endIndex) / 2;
            if (t < mX[midIndex]) {
                endIndex = midIndex;
            } else {
                startIndex = midIndex;
            }
        }

        float xRange = mX[endIndex] - mX[startIndex];
        if (xRange == 0) {
            return mY[startIndex];
        }

        float tInRange = t - mX[startIndex];
        float fraction = tInRange / xRange;

        float startY = mY[startIndex];
        float endY = mY[endIndex];
        return startY + (fraction * (endY - startY));
    }
}

1.11 OvershootInterpolator

OvershootInterpolator 该插值器运动曲线 先加速超过临界值1.0f 再慢慢又回落到1.0f，有一个回弹的效果。

可使用OvershootInterpolator(float tension)构造函数设置mTension弹力值，mTension值越大，超出目标值的时间点越靠前，超出目标值的回弹距离越大，回弹越明显。

其运动曲线如下图所示：

/**
 * An interpolator where the change flings forward and overshoots the last value
 * then comes back.
 * 先超过临界值 再慢慢回到临界值
 */
public class OvershootInterpolator extends BaseInterpolator implements NativeInterpolatorFactory {
    private final float mTension;

    public OvershootInterpolator() {
        mTension = 2.0f;
    }

    /**
     * @param tension Amount of overshoot. When tension equals 0.0f, there is
     *                no overshoot and the interpolator becomes a simple
     *                deceleration interpolator.
     */
    public OvershootInterpolator(float tension) {
        mTension = tension;
    }

    public float getInterpolation(float t) {
        // _o(t) = t * t * ((tension + 1) * t + tension)
        // o(t) = _o(t - 1) + 1
        t -= 1.0f;
        return t * t * ((mTension + 1) * t + mTension) + 1.0f;
    }
}

注：
使用PathInterpolator插值器会消耗更多的内存，不同于其他简单插值器，一般的插值器都是在算法上来生成插值，而PathInterpolator是在初始化时依赖Path算法生成一系列插值点存储，源码显示是以0.02为step在0到1范围内取点，生成500个x样本和500个y样本共计1000个float数据，相比其他插值器消耗了相当1000倍的内存，虽然对目前手机性能来说微不足道，但在动画这种要求高性能的操作时建议谨慎使用，不要频繁初始化，尽量复用同参数的插值器，以提高性能。

二、Easing 插值器

Easing算法是业界著名的一组插值器算法，涵盖了各种速率的曲线算法。
其涵盖的曲线算法如下图所示：

注：
easings 官方网址：
https://easings.net/

easeInOutBounce

举例一个动画插值器 easeInOutBounce。Easing官方对于每一个动画插值器，均给出了完整的算法实现和动画运动曲线，开发者可以根据自己的需要自行选择对应的插值器算法，构造自己的动画插值器。

function easeInOutBounce(x: number): number {
return x < 0.5
  ? (1 - easeOutBounce(1 - 2 * x)) / 2
  : (1 + easeOutBounce(2 * x - 1)) / 2;
}

三、调试插值器

调试动画插值器，可以使用如下小工具：

wolframalpha 调试动画插值器：
https://www.wolframalpha.com/input/?i=x%5E%282*3%29%280%3Cx%3C%3D1%29

参考

wolframalpha调试工具：
https://www.wolframalpha.com/input/?i=x%5E%282*3%29%280%3Cx%3C%3D1%29

cubic-bezier辅助工具：
https://cubic-bezier.com/

easings 插值器：
https://easings.net/

3D勋章实现方案：
https://xiaxl.blog.csdn.net/article/details/77048507

= THE END =