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/*
 * Copyright (C) 2014 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package android.transition;

import android.content.Context;
import android.content.res.TypedArray;
import android.graphics.Path;
import android.util.AttributeSet;

import com.android.internal.R;


A PathMotion that generates a curved path along an arc on an imaginary circle containing
the two points. If the horizontal distance between the points is less than the vertical
distance, then the circle's center point will be horizontally aligned with the end point. If the
vertical distance is less than the horizontal distance then the circle's center point
will be vertically aligned with the end point.

 When the two points are near horizontal or vertical, the curve of the motion will be small as the center of the circle will be far from both points. To force curvature of the path, setMinimumHorizontalAngle(float) and setMinimumVerticalAngle(float) may be used to set the minimum angle of the arc between two points. 


This may be used in XML as an element inside a transition.



<changeBounds>
  <arcMotion android:minimumHorizontalAngle="15"
             android:minimumVerticalAngle="0"
             android:maximumAngle="90"/>
</changeBounds> 


/**
 * A PathMotion that generates a curved path along an arc on an imaginary circle containing
 * the two points. If the horizontal distance between the points is less than the vertical
 * distance, then the circle's center point will be horizontally aligned with the end point. If the
 * vertical distance is less than the horizontal distance then the circle's center point
 * will be vertically aligned with the end point.
 * <p>
 * When the two points are near horizontal or vertical, the curve of the motion will be
 * small as the center of the circle will be far from both points. To force curvature of
 * the path, {@link #setMinimumHorizontalAngle(float)} and
 * {@link #setMinimumVerticalAngle(float)} may be used to set the minimum angle of the
 * arc between two points.
 * </p>
 * <p>This may be used in XML as an element inside a transition.</p>
 * <pre>{@code
 * <changeBounds>
 *   <arcMotion android:minimumHorizontalAngle="15"
 *              android:minimumVerticalAngle="0"
 *              android:maximumAngle="90"/>
 * </changeBounds>}
 * </pre>
 */
public class ArcMotion extends PathMotion {

    private static final float DEFAULT_MIN_ANGLE_DEGREES = 0;
    private static final float DEFAULT_MAX_ANGLE_DEGREES = 70;
    private static final float DEFAULT_MAX_TANGENT = (float)
            Math.tan(Math.toRadians(DEFAULT_MAX_ANGLE_DEGREES/2));

    private float mMinimumHorizontalAngle = 0;
    private float mMinimumVerticalAngle = 0;
    private float mMaximumAngle = DEFAULT_MAX_ANGLE_DEGREES;
    private float mMinimumHorizontalTangent = 0;
    private float mMinimumVerticalTangent = 0;
    private float mMaximumTangent = DEFAULT_MAX_TANGENT;

    public ArcMotion() {}

    public ArcMotion(Context context, AttributeSet attrs) {
        super(context, attrs);
        TypedArray a = context.obtainStyledAttributes(attrs, R.styleable.ArcMotion);
        float minimumVerticalAngle = a.getFloat(R.styleable.ArcMotion_minimumVerticalAngle,
                DEFAULT_MIN_ANGLE_DEGREES);
        setMinimumVerticalAngle(minimumVerticalAngle);
        float minimumHorizontalAngle = a.getFloat(R.styleable.ArcMotion_minimumHorizontalAngle,
                DEFAULT_MIN_ANGLE_DEGREES);
        setMinimumHorizontalAngle(minimumHorizontalAngle);
        float maximumAngle = a.getFloat(R.styleable.ArcMotion_maximumAngle,
                DEFAULT_MAX_ANGLE_DEGREES);
        setMaximumAngle(maximumAngle);
        a.recycle();
    }

    
Sets the minimum arc along the circle between two points aligned near horizontally.
When start and end points are close to horizontal, the calculated center point of the
circle will be far from both points, giving a near straight path between the points.
By setting a minimum angle, this forces the center point to be closer and give an
exaggerated curve to the path.

The default value is 0.


Params:
  • angleInDegrees – The minimum angle of the arc on a circle describing the Path
                      between two nearly horizontally-separated points.
@attrref android.R.styleable#ArcMotion_minimumHorizontalAngle
/**
     * Sets the minimum arc along the circle between two points aligned near horizontally.
     * When start and end points are close to horizontal, the calculated center point of the
     * circle will be far from both points, giving a near straight path between the points.
     * By setting a minimum angle, this forces the center point to be closer and give an
     * exaggerated curve to the path.
     * <p>The default value is 0.</p>
     *
     * @param angleInDegrees The minimum angle of the arc on a circle describing the Path
     *                       between two nearly horizontally-separated points.
     * @attr ref android.R.styleable#ArcMotion_minimumHorizontalAngle
     */
    public void setMinimumHorizontalAngle(float angleInDegrees) {
        mMinimumHorizontalAngle = angleInDegrees;
        mMinimumHorizontalTangent = toTangent(angleInDegrees);
    }

    
Returns the minimum arc along the circle between two points aligned near horizontally.
When start and end points are close to horizontal, the calculated center point of the
circle will be far from both points, giving a near straight path between the points.
By setting a minimum angle, this forces the center point to be closer and give an
exaggerated curve to the path.

The default value is 0.


Returns: The minimum arc along the circle between two points aligned near horizontally.
@attrref android.R.styleable#ArcMotion_minimumHorizontalAngle
/**
     * Returns the minimum arc along the circle between two points aligned near horizontally.
     * When start and end points are close to horizontal, the calculated center point of the
     * circle will be far from both points, giving a near straight path between the points.
     * By setting a minimum angle, this forces the center point to be closer and give an
     * exaggerated curve to the path.
     * <p>The default value is 0.</p>
     *
     * @return  The minimum arc along the circle between two points aligned near horizontally.
     * @attr ref android.R.styleable#ArcMotion_minimumHorizontalAngle
     */
    public float getMinimumHorizontalAngle() {
        return mMinimumHorizontalAngle;
    }

    
Sets the minimum arc along the circle between two points aligned near vertically.
When start and end points are close to vertical, the calculated center point of the
circle will be far from both points, giving a near straight path between the points.
By setting a minimum angle, this forces the center point to be closer and give an
exaggerated curve to the path.

The default value is 0.


Params:
  • angleInDegrees – The minimum angle of the arc on a circle describing the Path
                      between two nearly vertically-separated points.
@attrref android.R.styleable#ArcMotion_minimumVerticalAngle
/**
     * Sets the minimum arc along the circle between two points aligned near vertically.
     * When start and end points are close to vertical, the calculated center point of the
     * circle will be far from both points, giving a near straight path between the points.
     * By setting a minimum angle, this forces the center point to be closer and give an
     * exaggerated curve to the path.
     * <p>The default value is 0.</p>
     *
     * @param angleInDegrees The minimum angle of the arc on a circle describing the Path
     *                       between two nearly vertically-separated points.
     * @attr ref android.R.styleable#ArcMotion_minimumVerticalAngle
     */
    public void setMinimumVerticalAngle(float angleInDegrees) {
        mMinimumVerticalAngle = angleInDegrees;
        mMinimumVerticalTangent = toTangent(angleInDegrees);
    }

    
Returns the minimum arc along the circle between two points aligned near vertically.
When start and end points are close to vertical, the calculated center point of the
circle will be far from both points, giving a near straight path between the points.
By setting a minimum angle, this forces the center point to be closer and give an
exaggerated curve to the path.

The default value is 0.


Returns:The minimum angle of the arc on a circle describing the Path
        between two nearly vertically-separated points.
@attrref android.R.styleable#ArcMotion_minimumVerticalAngle
/**
     * Returns the minimum arc along the circle between two points aligned near vertically.
     * When start and end points are close to vertical, the calculated center point of the
     * circle will be far from both points, giving a near straight path between the points.
     * By setting a minimum angle, this forces the center point to be closer and give an
     * exaggerated curve to the path.
     * <p>The default value is 0.</p>
     *
     * @return The minimum angle of the arc on a circle describing the Path
     *         between two nearly vertically-separated points.
     * @attr ref android.R.styleable#ArcMotion_minimumVerticalAngle
     */
    public float getMinimumVerticalAngle() {
        return mMinimumVerticalAngle;
    }

    
Sets the maximum arc along the circle between two points. When start and end points
have close to equal x and y differences, the curve between them is large. This forces
the curved path to have an arc of at most the given angle.

The default value is 70 degrees.


Params:
  • angleInDegrees – The maximum angle of the arc on a circle describing the Path
                      between the start and end points.
@attrref android.R.styleable#ArcMotion_maximumAngle
/**
     * Sets the maximum arc along the circle between two points. When start and end points
     * have close to equal x and y differences, the curve between them is large. This forces
     * the curved path to have an arc of at most the given angle.
     * <p>The default value is 70 degrees.</p>
     *
     * @param angleInDegrees The maximum angle of the arc on a circle describing the Path
     *                       between the start and end points.
     * @attr ref android.R.styleable#ArcMotion_maximumAngle
     */
    public void setMaximumAngle(float angleInDegrees) {
        mMaximumAngle = angleInDegrees;
        mMaximumTangent = toTangent(angleInDegrees);
    }

    
Returns the maximum arc along the circle between two points. When start and end points
have close to equal x and y differences, the curve between them is large. This forces
the curved path to have an arc of at most the given angle.

The default value is 70 degrees.


Returns:The maximum angle of the arc on a circle describing the Path
        between the start and end points.
@attrref android.R.styleable#ArcMotion_maximumAngle
/**
     * Returns the maximum arc along the circle between two points. When start and end points
     * have close to equal x and y differences, the curve between them is large. This forces
     * the curved path to have an arc of at most the given angle.
     * <p>The default value is 70 degrees.</p>
     *
     * @return The maximum angle of the arc on a circle describing the Path
     *         between the start and end points.
     * @attr ref android.R.styleable#ArcMotion_maximumAngle
     */
    public float getMaximumAngle() {
        return mMaximumAngle;
    }

    private static float toTangent(float arcInDegrees) {
        if (arcInDegrees < 0 || arcInDegrees > 90) {
            throw new IllegalArgumentException("Arc must be between 0 and 90 degrees");
        }
        return (float) Math.tan(Math.toRadians(arcInDegrees / 2));
    }

    @Override
    public Path getPath(float startX, float startY, float endX, float endY) {
        // Here's a little ascii art to show how this is calculated:
        // c---------- b
        //  \        / |
        //    \     d  |
        //      \  /   e
        //        a----f
        // This diagram assumes that the horizontal distance is less than the vertical
        // distance between The start point (a) and end point (b).
        // d is the midpoint between a and b. c is the center point of the circle with
        // This path is formed by assuming that start and end points are in
        // an arc on a circle. The end point is centered in the circle vertically
        // and start is a point on the circle.

        // Triangles bfa and bde form similar right triangles. The control points
        // for the cubic Bezier arc path are the midpoints between a and e and e and b.

        Path path = new Path();
        path.moveTo(startX, startY);

        float ex;
        float ey;
        float deltaX = endX - startX;
        float deltaY = endY - startY;

        // hypotenuse squared.
        float h2 = deltaX * deltaX + deltaY * deltaY;

        // Midpoint between start and end
        float dx = (startX + endX) / 2;
        float dy = (startY + endY) / 2;

        // Distance squared between end point and mid point is (1/2 hypotenuse)^2
        float midDist2 = h2 * 0.25f;

        float minimumArcDist2 = 0;

        boolean isMovingUpwards = startY > endY;

        if (deltaY == 0) {
            ex = dx;
            ey = dy + (Math.abs(deltaX) * 0.5f * mMinimumHorizontalTangent);
        } else if (deltaX == 0) {
            ex = dx + (Math.abs(deltaY) * 0.5f * mMinimumVerticalTangent);
            ey = dy;
        } else if ((Math.abs(deltaX) < Math.abs(deltaY))) {
            // Similar triangles bfa and bde mean that (ab/fb = eb/bd)
            // Therefore, eb = ab * bd / fb
            // ab = hypotenuse
            // bd = hypotenuse/2
            // fb = deltaY
            float eDistY = Math.abs(h2 / (2 * deltaY));
            if (isMovingUpwards) {
                ey = endY + eDistY;
                ex = endX;
            } else {
                ey = startY + eDistY;
                ex = startX;
            }

            minimumArcDist2 = midDist2 * mMinimumVerticalTangent
                    * mMinimumVerticalTangent;
        } else {
            // Same as above, but flip X & Y and account for negative eDist
            float eDistX = h2 / (2 * deltaX);
            if (isMovingUpwards) {
                ex = startX + eDistX;
                ey = startY;
            } else {
                ex = endX - eDistX;
                ey = endY;
            }

            minimumArcDist2 = midDist2 * mMinimumHorizontalTangent
                    * mMinimumHorizontalTangent;
        }
        float arcDistX = dx - ex;
        float arcDistY = dy - ey;
        float arcDist2 = arcDistX * arcDistX + arcDistY * arcDistY;

        float maximumArcDist2 = midDist2 * mMaximumTangent * mMaximumTangent;

        float newArcDistance2 = 0;
        if (arcDist2 != 0 && arcDist2 < minimumArcDist2) {
            newArcDistance2 = minimumArcDist2;
        } else if (arcDist2 > maximumArcDist2) {
            newArcDistance2 = maximumArcDist2;
        }
        if (newArcDistance2 != 0) {
            float ratio2 = newArcDistance2 / arcDist2;
            float ratio = (float) Math.sqrt(ratio2);
            ex = dx + (ratio * (ex - dx));
            ey = dy + (ratio * (ey - dy));
        }
        float control1X = (startX + ex) / 2;
        float control1Y = (startY + ey) / 2;
        float control2X = (ex + endX) / 2;
        float control2Y = (ey + endY) / 2;
        path.cubicTo(control1X, control1Y, control2X, control2Y, endX, endY);
        return path;
    }
}