Problem to achieve curved animation [duplicate]

Below is fully functioning code that will animate along a curved path defined by three points. A Point is just a class holding an x value and a y value (though you could easily extend it for more dimensions).

All the m variables are taken from TranslateAnimation and used in in a similar manner, so you should be able to compare it to the TranslateAnimation code relatively eaSILY if something doesn’t make sense.

The calls to resolveSize in initialize mean that you can specify the start, end, and radius of the arc using any of the Animation types (ABSOLUTE, RELATIVE_TO_SELF, RELATIVE_TO_PARENT) just as you would for a normal TranslateAnimation.

calcBezier calculates the quadratic bezier curve taken directly from Wikipedia. The Bezier curve is supposed to allow for smooth scaling and is common in graphics (and also used in Android’s Path class).

The actual movement happens in applyTransformation. interpolatedTime gives a value between 0 and 1, which increases nonlinearly depending on the interpolator provided. dx and dy are the actual x and y points along the curve for the given time.

The only limitation of this class is that the largest change in y always occurs at the center of the curve (see the calculation for middleX in initialize). However it would be easy to modify, for example, to give a particular point along the curve at which the high point should occur if you want a non-symmetric curve.

Looking at the android code for TranslateAnimation was particularly helpful. See: http://grepcode.com/file/repository.grepcode.com/java/ext/com.google.android/android/2.3.5_r1/android/view/animation/TranslateAnimation.java#TranslateAnimation

public class ArcTranslate extends Animation {

private Point start;
private Point end;
private Point middle;
private final float mFromXValue;
private final float mToXValue;
private final float mYValue;
private final int mFromXType;
private final int mToXType;
private final int mYType;

/**
 * A translation along an arc defined by three points and a Bezier Curve
 *
 * @param duration - the time in ms it will take for the translation to complete
 * @param fromXType - One of Animation.ABSOLUTE, Animation.RELATIVE_TO_SELF, or Animation.RELATIVE_TO_PARENT.
 * @param fromXValue - Change in X coordinate to apply at the start of the animation
 * @param toXType - One of Animation.ABSOLUTE, Animation.RELATIVE_TO_SELF, or Animation.RELATIVE_TO_PARENT.
 * @param toXValue - Change in X coordinate to apply at the end of the animation
 * @param yType - One of Animation.ABSOLUTE, Animation.RELATIVE_TO_SELF, or Animation.RELATIVE_TO_PARENT.
 * @param yValue - Change in Y coordinate to apply at the middle of the animation (the radius of the arc)
 */
public ArcTranslate(long duration, int fromXType, float fromXValue,
        int toXType, float toXValue, int yType, float yValue){
    setDuration(duration);

     mFromXValue = fromXValue;
     mToXValue = toXValue;
     mYValue = yValue;

     mFromXType = fromXType;
     mToXType = toXType;
     mYType = yType;

}

/** Calculate the position on a quadratic bezier curve given three points
 *  and the percentage of time passed.
 * from http://en.wikipedia.org/wiki/B%C3%A9zier_curve
 * @param interpolatedTime - the fraction of the duration that has passed where 0<=time<=1
 * @param p0 - a single dimension of the starting point
 * @param p1 - a single dimension of the middle point
 * @param p2 - a single dimension of the ending point
 */
private long calcBezier(float interpolatedTime, float p0, float p1, float p2){
    return Math.round((Math.pow((1 - interpolatedTime), 2) * p0)
           + (2 * (1 - interpolatedTime) * interpolatedTime * p1)
           + (Math.pow(interpolatedTime, 2) * p2));
}

@Override
protected void applyTransformation(float interpolatedTime, Transformation t) {
    float dx = calcBezier(interpolatedTime, start.x, middle.x, end.x);
    float dy = calcBezier(interpolatedTime, start.y, middle.y, end.y);

    t.getMatrix().setTranslate(dx, dy);
}

@Override
public void initialize(int width, int height, int parentWidth, int parentHeight) {
    super.initialize(width, height, parentWidth, parentHeight);
    float startX = resolveSize(mFromXType, mFromXValue, width, parentWidth);
    float endX = resolveSize(mToXType, mToXValue, width, parentWidth);
    float middleY = resolveSize(mYType, mYValue, width, parentWidth);
    float middleX = startX + ((endX-startX)/2);
    start = new Point(startX, 0);
    end = new Point(endX, 0);
    middle = new Point(middleX, middleY);
}
}