自定义视图与贝塞尔曲线

Posted 2020-07-26 Fishyer

APK下载地址

1.贝塞尔曲线

以下公式中：
B(t)为t时间下 点的坐标；
P0为起点,Pn为终点,Pi为控制点

一阶贝塞尔曲线(线段)：

意义：由 P0 至 P1 的连续点， 描述的一条线段

二阶贝塞尔曲线(抛物线)：

原理：由 P0 至 P1 的连续点 Q0，描述一条线段。
由 P1 至 P2 的连续点 Q1，描述一条线段。
由 Q0 至 Q1 的连续点 B(t)，描述一条二次贝塞尔曲线。

经验：P1-P0为曲线在P0处的切线。

三阶贝塞尔曲线:

通用公式：

高阶贝塞尔曲线：

4阶曲线：

5阶曲线：

1.1.生成贝塞尔曲线-迭代法

下面我们用代码来生成贝塞尔曲线，来展示如何贝塞尔曲线的生成原理：

package com.che.testapp.view;

import android.animation.FloatEvaluator;
import android.animation.ValueAnimator;
import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.View;
import android.view.animation.LinearInterpolator;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Random;

/**
 * 生成贝塞尔曲线-迭代法
 * <p/>
 * 作者：余天然 on 16/6/14 下午2:10
 */
public class BezierGenerater1 extends View {

    private Paint paint;
    private int centerX, centerY;
    private List<PointF> points;
    private FloatEvaluator evaluator;
    private float fraction;
    private Map<Integer, Integer> colors;
    private List<PointF> destPoints;

    public BezierGenerater1(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);
        evaluator = new FloatEvaluator();
        startAnim();
    }

    //初始化数据点和控制点的位置
    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        centerX = w / 2;
        centerY = h / 2;
        points = new ArrayList<>();
        points.add(new PointF(centerX - 150, centerY));
        points.add(new PointF(centerX - 50, centerY - 300));
        points.add(new PointF(centerX + 50, centerY + 300));
        points.add(new PointF(centerX + 150, centerY));
        colors = new HashMap<>();
        for (int i = 0; i < points.size(); i++) {
            colors.put(i, getRanColor());
        }
        destPoints = new ArrayList<>();
        destPoints.add(points.get(0));
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        //静态的
        drawPoint(canvas, points, Color.BLACK);
        drawLine(canvas, points, Color.GRAY);
        //动态的
        List<PointF> subData = getSubData(points, fraction);
        drawData(canvas, subData, fraction);
    }

    // 绘制数据点
    private void drawPoint(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(20);
        for (int i = 0; i < data.size(); i++) {
            PointF pointF = data.get(i);
            canvas.drawPoint(pointF.x, pointF.y, paint);
        }
    }

    //绘制基准线
    private void drawLine(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(4);
        for (int i = 0; i < data.size() - 1; i++) {
            PointF start = data.get(i);
            PointF end = data.get(i + 1);
            canvas.drawLine(start.x, start.y, end.x, end.y, paint);
        }
    }

    //绘制路径
    private void drawPath(Canvas canvas, List<PointF> data) {
        Path path = new Path();
        PointF start = data.get(0);
        path.moveTo(start.x, start.y);
        for (int i = 1; i < data.size() - 1; i++) {
            PointF point = data.get(i);
            path.lineTo(point.x, point.y);
        }
        paint.setColor(Color.RED);
        paint.setStrokeWidth(4);
        canvas.drawPath(path, paint);
    }

    //迭代绘制集合
    private void drawData(Canvas canvas, List<PointF> data, float fraction) {
        if (data.size() == 1) {
            drawPoint(canvas, data, Color.BLACK);
            destPoints.add(data.get(0));
            drawPath(canvas, destPoints);
        } else {
            drawLine(canvas, data, colors.get(data.size() - 1));
            //迭代
            List<PointF> subData = getSubData(data, fraction);
            drawData(canvas, subData, fraction);
        }
    }

    private void startAnim() {
        ValueAnimator animator = ValueAnimator.ofFloat(0, 100);
        animator.setInterpolator(new LinearInterpolator());
        animator.setDuration(5000);
        animator.addUpdateListener(new ValueAnimator.AnimatorUpdateListener() {
            @Override
            public void onAnimationUpdate(ValueAnimator animation) {
                fraction = animation.getAnimatedFraction();
                invalidate();
            }

        });
        animator.start();
    }

    //生成随机颜色
    private int getRanColor() {
        return 0xff000000 | new Random().nextInt(0x00ffffff);
    }

    //获取子数据源
    private List<PointF> getSubData(List<PointF> data, float fraction) {
        List<PointF> subData = new ArrayList<>();
        for (int i = 0; i < data.size() - 1; i++) {
            PointF start = data.get(i);
            PointF end = data.get(i + 1);
            float x = evaluator.evaluate(fraction, start.x, end.x);
            float y = evaluator.evaluate(fraction, start.y, end.y);
            subData.add(new PointF(x, y));
        }
        return subData;
    }
}

1.2.生成贝塞尔曲线-De Casteljau算法

package com.che.testapp.view;

import android.animation.ValueAnimator;
import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.View;
import android.view.animation.LinearInterpolator;

import java.util.ArrayList;
import java.util.List;

/**
 * 生成贝塞尔曲线-De Casteljau算法
 * <p/>
 * 作者：余天然 on 16/6/14 下午2:10
 */
public class BezierGenerater2 extends View {

    private Paint paint;
    private int centerX, centerY;
    private List<PointF> points;
    private float fraction;
    private List<PointF> destPoints;

    public BezierGenerater2(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);
    }

    //初始化数据点和控制点的位置
    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        centerX = w / 2;
        centerY = h / 2;
        points = new ArrayList<>();
        points.add(new PointF(centerX - 150, centerY));
        points.add(new PointF(centerX - 50, centerY - 300));
        points.add(new PointF(centerX + 50, centerY + 300));
        points.add(new PointF(centerX + 150, centerY));
        destPoints = new ArrayList<>();
        destPoints.add(points.get(0));
        startAnim();
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        //静态的
        drawPoint(canvas, points, Color.BLACK);
        drawLine(canvas, points, Color.GRAY);
        //动态的
        drawPath(canvas, destPoints);
    }

    // 绘制数据点
    private void drawPoint(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(20);
        for (int i = 0; i < data.size(); i++) {
            PointF pointF = data.get(i);
            canvas.drawPoint(pointF.x, pointF.y, paint);
        }
    }

    //绘制基准线
    private void drawLine(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(4);
        for (int i = 0; i < data.size() - 1; i++) {
            PointF start = data.get(i);
            PointF end = data.get(i + 1);
            canvas.drawLine(start.x, start.y, end.x, end.y, paint);
        }
    }

    //绘制路径
    private void drawPath(Canvas canvas, List<PointF> data) {
        Path path = new Path();
        PointF start = data.get(0);
        path.moveTo(start.x, start.y);
        for (int i = 1; i < data.size() - 1; i++) {
            PointF point = data.get(i);
            path.lineTo(point.x, point.y);
        }
        paint.setColor(Color.RED);
        paint.setStrokeWidth(4);
        canvas.drawPath(path, paint);
    }

    private void startAnim() {
        ValueAnimator animator = ValueAnimator.ofFloat(0, 100);
        animator.setInterpolator(new LinearInterpolator());
        animator.setDuration(5000);
        animator.addUpdateListener(new ValueAnimator.AnimatorUpdateListener() {
            @Override
            public void onAnimationUpdate(ValueAnimator animation) {
                fraction = animation.getAnimatedFraction();
                PointF pointF = deCasteljau(fraction, points);
                destPoints.add(pointF);
                invalidate();
            }
        });
        animator.start();
    }

    //深复制
    private List<PointF> copyData(List<PointF> points) {
        List<PointF> data = new ArrayList<>();
        for (int i = 0; i < points.size(); i++) {
            PointF point = points.get(i);
            data.add(new PointF(point.x, point.y));
        }
        return data;
    }

    //De Casteljau算法
    public PointF deCasteljau(float fraction, List<PointF> points) {
        List<PointF> data = copyData(points);
        final int n = data.size();
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < n - i; j++) {
                data.get(j).x = (1 - fraction) * data.get(j).x + fraction * data.get(j + 1).x;
                data.get(j).y = (1 - fraction) * data.get(j).y + fraction * data.get(j + 1).y;
            }
        }
        return data.get(0);
    }

}

1.3.二阶贝塞尔曲线

上面只是展示了贝塞尔曲线是如何生成的，但是实际上，我们使用的时候，是不必我们自己去生成的，直接调用系统api即可，path的quadTo，cubicTo就分别是二阶和三阶的贝塞尔曲线。至于更高阶的，一般用不到，就算真的需要的，用N个三阶的叠加即可。

package com.che.testapp.view;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.MotionEvent;
import android.view.View;

/**
 * 二阶贝塞尔曲线
 * <p/>
 * 两个数据点和一个控制点
 * 公式：B(t) = (1 - t)^2 * P0 + 2t * (1 - t) * P1 + t^2 * P2, t ∈ [0,1]
 * 作者：余天然 on 16/6/14 上午10:27
 */
public class Bezier2 extends View {
    private Paint paint;
    private int centerX, centerY;
    private PointF start, end, control;

    public Bezier2(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);

        start = new PointF(0, 0);
        end = new PointF(0, 0);
        control = new PointF(0, 0);
    }

    //初始化数据点和控制点的位置
    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        centerX = w / 2;
        centerY = h / 2;
        start.x = centerX - 200;
        start.y = centerY;
        end.x = centerX + 200;
        end.y = centerY;
        control.x = centerX;
        control.y = centerY - 100;
    }

    //根据触摸位置更新控制点，并提示重绘
    @Override
    public boolean onTouchEvent(MotionEvent event) {
        control.x = event.getX();
        control.y = event.getY();
        invalidate();
        return true;
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        drawPoint(canvas);
        drawGuideLine(canvas);
        drawBezierCurve(canvas);
    }

    // 绘制数据点和控制点
    private void drawPoint(Canvas canvas) {
        paint.setColor(Color.GRAY);
        paint.setStrokeWidth(20);
        canvas.drawPoint(start.x, start.y, paint);
        canvas.drawPoint(end.x, end.y, paint);
        canvas.drawPoint(control.x, control.y, paint);
    }

    //绘制辅助线
    private void drawGuideLine(Canvas canvas) {
        paint.setStrokeWidth(4);
        canvas.drawLine(start.x, start.y, control.x, control.y, paint);
        canvas.drawLine(control.x, control.y, end.x, end.y, paint);
    }

    //绘制贝塞尔曲线
    private void drawBezierCurve(Canvas canvas) {
        paint.setColor(Color.RED);
        paint.setStrokeWidth(4);
        Path path = new Path();
        path.moveTo(start.x, start.y);
        path.quadTo(control.x, control.y, end.x, end.y);
        canvas.drawPath(path, paint);
    }
}

1.4.三阶贝塞尔曲线

package com.che.testapp.view;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.MotionEvent;
import android.view.View;

import java.util.ArrayList;
import java.util.List;

/**
 * 三阶贝塞尔曲线
 * <p/>
 * 2个数据点和2个控制点
 * 公式：B(t) = P0 * (1-t)^3 + 3 * P1 * t * (1-t)^2 + 3 * P2 * t^2 * (1-t) + P3 * t^3 代
 * 作者：余天然 on 16/6/14 上午10:27
 */
public class Bezier3 extends View {

    private Paint paint;
    private int centerX, centerY;
    private List<PointF> points;

    public Bezier3(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);
    }

    //初始化数据点和控制点的位置
    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        centerX = w / 2;
        centerY = h / 2;
        points = new ArrayList<>();
        points.add(new PointF(centerX - 150, centerY));
        points.add(new PointF(centerX - 50, centerY - 300));
        points.add(new PointF(centerX + 50, centerY + 300));
        points.add(new PointF(centerX + 150, centerY));
    }

    //根据触摸位置更新控制点，并提示重绘
    @Override
    public boolean onTouchEvent(MotionEvent event) {
        PointF control = new PointF(0, 0);
        control.x = event.getX();
        control.y = event.getY();

        double distance1 = getDistance(control, points.get(1));
        double distance2 = getDistance(control, points.get(2));

        if (distance1 < distance2) {
            points.set(1, control);
        } else {
            points.set(2, control);
        }
        invalidate();
        return true;
    }


    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        drawPoint(canvas, points, Color.BLACK);
        drawLine(canvas, points, Color.GRAY);
        drawBezierCurve(canvas);
    }

    // 绘制数据点
    private void drawPoint(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(20);
        for (int i = 0; i < data.size(); i++) {
            PointF pointF = data.get(i);
            canvas.drawPoint(pointF.x, pointF.y, paint);
        }
    }

    //绘制基准线
    private void drawLine(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(4);
        for (int i = 0; i < data.size() - 1; i++) {
            PointF start = data.get(i);
            PointF end = data.get(i + 1);
            canvas.drawLine(start.x, start.y, end.x, end.y, paint);
        }
    }

    //绘制贝塞尔曲线
    private void drawBezierCurve(Canvas canvas) {
        paint.setColor(Color.RED);
        paint.setStrokeWidth(4);
        Path path = new Path();
        path.moveTo(points.get(0).x, points.get(0).y);
        path.cubicTo(points.get(1).x, points.get(1).y, points.get(2).x, points.get(2).y, points.get(3).x, points.get(3).y);
        canvas.drawPath(path, paint);
    }

    //获取两点的距离
    private double getDistance(PointF start, PointF end) {
        return Math.sqrt((end.y - start.y) * (end.y - start.y) + (end.x - start.x) * (end.x - start.x));
    }
}

1.5.用贝塞尔曲线拟合圆形

四段3阶贝塞尔曲线
每一段拟合90度扇形

公式：B(t) = P0 * (1-t)^3 + 3 * P1 * t * (1-t)^2 + 3 * P2 * t^2 * (1-t) + P3 * t^3

显然，当t=0.5的时候，应该正好在45度的位置上，于是：
sin(pi/4) = 0.125(3x1 - 2) + 0.25(3 - 6x1 ) + 0.5(3x1 )
解出x1=0.55228475或
根据对称性，可得y1=x1;

package com.che.testapp.view;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.MotionEvent;
import android.view.View;

import java.util.ArrayList;
import java.util.List;

/**
 * 贝塞尔曲线-拟合圆形
 * <p/>
 * 作者：余天然 on 16/6/14 上午10:27
 */
public class BezierCircle extends View {

    private Paint paint;
    private int centerX, centerY;
    private List<PointF> points;
    private float magicNumber = 0.55228475f;//(4*(pow(2,1/2)-1)/3
    private float radius = 200;

    public BezierCircle(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);
    }

    //初始化数据点和控制点的位置
    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        super.onSizeChanged(w, h, oldw, oldh);
        centerX = w / 2;
        centerY = h / 2;
        points = new ArrayList<>();
        points.add(new PointF(0, radius));
        points.add(new PointF(radius * magicNumber, radius));
        points.add(new PointF(radius, radius * magicNumber));
        points.add(new PointF(radius, 0));
    }

    //根据触摸位置更新控制点，并提示重绘
    @Override
    public boolean onTouchEvent(MotionEvent event) {
        PointF control = new PointF(0, 0);
        control.x = event.getX()-centerX;
        control.y = event.getY()-centerY;

        double distance1 = getDistance(control, points.get(1));
        double distance2 = getDistance(control, points.get(2));

        if (distance1 < distance2) {
            points.set(1, control);
        } else {
            points.set(2, control);
        }
        invalidate();
        return true;
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        canvas.save();
        canvas.translate(centerX, centerY);
        drawSector(canvas, 0);
        drawSector(canvas, 90);
        drawSector(canvas, 180);
        drawSector(canvas, 270);
        canvas.restore();
    }

    //绘制90度扇形
    private void drawSector(Canvas canvas, float degree) {
        canvas.save();
        canvas.rotate(degree);
        drawPoint(canvas, points, Color.BLACK);
        drawLine(canvas, points, Color.GRAY);
        drawBezierCurve(canvas);
        canvas.restore();
    }

    // 绘制数据点
    private void drawPoint(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(20);
        for (int i = 0; i < data.size(); i++) {
            PointF pointF = data.get(i);
            canvas.drawPoint(pointF.x, pointF.y, paint);
        }
    }

    //绘制基准线
    private void drawLine(Canvas canvas, List<PointF> data, int color) {
        paint.setColor(color);
        paint.setStrokeWidth(4);
        for (int i = 0; i < data.size() - 1; i++) {
            PointF start = data.get(i);
            PointF end = data.get(i + 1);
            canvas.drawLine(start.x, start.y, end.x, end.y, paint);
        }
    }

    //绘制贝塞尔曲线
    private void drawBezierCurve(Canvas canvas) {
        paint.setColor(Color.RED);
        paint.setStrokeWidth(4);
        Path path = new Path();
        path.moveTo(points.get(0).x, points.get(0).y);
        path.cubicTo(points.get(1).x, points.get(1).y, points.get(2).x, points.get(2).y, points.get(3).x, points.get(3).y);
        canvas.drawPath(path, paint);
    }

    //获取两点的距离
    private double getDistance(PointF start, PointF end) {
        return Math.sqrt((end.y - start.y) * (end.y - start.y) + (end.x - start.x) * (end.x - start.x));
    }
}

2.自定义视图

贝塞尔曲线就是PS里面的魔棒工具，UI上的很多曲线，其实都是用贝塞尔曲线画的，既然如此，我们只需要知道UI是怎么画的，让她标注好数据点的位置，那我们就可以原样画出UI效果了。

贝塞尔曲线的用处，就是动态绘制平滑曲线！
并且可以实时控制曲线状态，并可以通过改变控制点的状态实时让曲线进行平滑的状态变化。

2.1.气泡拖拽效果

效果图：

上面的图是盗来的，因为我还不会在手机上录制gif,下面的我的demo的截图：

这里:
p1是初始圆的圆心，p2是拖动圆的圆心
X是p1p2线段的中点
AB：与p1p2线段垂直，长度为初始圆的直径
CD：与p1p2线段垂直，长度为拖动圆的直径

绘制流程：
1.绘制p1和p2的圆形
2.根据A，X，D绘制一条2阶贝塞尔曲线
3.根据B，X，C绘制另一条2阶贝塞尔曲线
4.设置path的模式为填充模式

package com.che.testapp.view;

import android.animation.FloatEvaluator;
import android.animation.ValueAnimator;
import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.util.AttributeSet;
import android.view.MotionEvent;
import android.view.View;
import android.view.animation.OvershootInterpolator;

/**
 * 贝塞尔曲线-气泡拖拽
 * <p/>
 * 二条2阶贝塞尔曲线
 * 作者：余天然 on 16/6/14 上午10:27
 */
public class BezierDraggableFlag extends View {
    private Paint paint;
    private int raduis = 40;//气泡的半径
    private double distance;//记录拉动的距离
    private double raduisTmp;//临时的半径
    private int maxDistance = 800;//拉断的距离
    private PointF p1, p2;//圆心
    private PointF pA, pB, pC, pD, pX;//控制点

    private double distanceBackup;
    private PointF p2Backup;

    public BezierDraggableFlag(Context context, AttributeSet attrs) {
        super(context, attrs);
        init();
    }

    //初始化圆心的位置
    private void init() {
        paint = new Paint();
        paint.setAntiAlias(true);

        p1 = new PointF(600, 400);
        p2 = new PointF(600, 400);
    }

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        switch (event.getAction()) {
            case MotionEvent.ACTION_DOWN:
                break;
            case MotionEvent.ACTION_MOVE:
                p2.x = event.getX();
                p2.y = event.getY();
                distance = PointUtil.getDistance(p1, p2);
                invalidate();
                break;
            case MotionEvent.ACTION_UP:
                if (distance < maxDistance) {
                    p2Backup = new PointF(p2.x, p2.y);
                    distanceBackup = distance;
                    startAnim();
                }
                break;
        }
        return true;
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        if (distance < maxDistance) {
            calculatePoint();
            drawBefore(canvas);
        } else {
            drawAfter(canvas);
        }
    }

    //计算控制点的位置
    private void calculatePoint() {
        double raduisScale = 1 - distance / maxDistance;
        raduisTmp = raduis * raduisScale;

        pA = PointUtil.getRotatePoint(p1, p2, raduisTmp, Math.PI / 2);
        pB = PointUtil.getRotatePoint(p1, p2, raduisTmp, -Math.PI / 2);
        pC = PointUtil.getRotatePoint(p2, p1, raduis, -Math.PI / 2);
        pD = PointUtil.getRotatePoint(p2, p1, raduis, Math.PI / 2);
        pX = PointUtil.getCenterPoint(p1, p2);
    }

    //拉断之后的绘制
    private void drawAfter(Canvas canvas) {
        paint.setColor(Color.RED);
        paint.setStyle(Paint.Style.FILL);
        paint.setStrokeWidth(4);
        canvas.drawCircle(p2.x, p2.y, raduis, paint);
    }

    //拉断之前的绘制
    private void drawBefore(Canvas canvas) {
        //端点
//        paint.setColor(Color.GRAY);
//        paint.setStyle(Paint.Style.STROKE);
//        paint.setStrokeWidth(20);
//        canvas.drawPoint(p1.x, p1.y, paint);
//        canvas.drawPoint(p2.x, p2.y, paint);
//        canvas.drawPoint(pX.x, pX.y, paint);

        //辅助线
        paint.setColor(Color.GRAY);
        paint.setStyle(Paint.Style.STROKE);
        paint.setStrokeWidth(4);
        canvas.drawLine(p1.x, p1.y, p2.x, p2.y, paint);

        //文字
//        paint.setColor(Color.BLACK);
//        paint.setStyle(Paint.Style.FILL);
//        paint.setStrokeWidth(2);
//        paint.setTextSize(30);
//        canvas.drawText("A", pA.x, pA.y, paint);
//        canvas.drawText("B", pB.x, pB.y, paint);
//        canvas.drawText("C", pC.x, pC.y, paint);
//        canvas.drawText("D", pD.x, pD.y, paint);
//        canvas.drawText("X", pX.x, pX.y, paint);
//        canvas.drawText("p1", p1.x, p1.y, paint);
//        canvas.drawText("p2", p2.x, p2.y, paint);

        //圆形
        paint.setColor(Color.RED);
        paint.setStyle(Paint.Style.FILL);
        paint.setStrokeWidth(4);
        canvas.drawCircle(p1.x, p1.y, (float) raduisTmp, paint);
        canvas.drawCircle(p2.x, p2.y, raduis, paint);

        //贝塞尔曲线
        paint.setColor(Color.RED);
        paint.setStyle(Paint.Style.FILL);
        paint.setStrokeWidth(4);
        Path path = new Path();
        path.moveTo(pA.x, pA.y);
        path.quadTo(pX.x, pX.y, pD.x, pD.y);
        path.lineTo(pC.x, pC.y);
        path.quadTo(pX.x, pX.y, pB.x, pB.y);
        path.lineTo(pA.x, pA.y);
        canvas.drawPath(path, paint);
    }


    //放开之后，如果没有拉断，就恢复初始状态
    private void startAnim() {
        final FloatEvaluator evaluator = new FloatEvaluator();
        ValueAnimator animator = ValueAnimator.ofFloat(0, 100);
        animator.setInterpolator(new OvershootInterpolator());
        animator.setDuration(100);
        animator.addUpdateListener(new ValueAnimator.AnimatorUpdateListener() {
            @Override
            public void onAnimationUpdate(ValueAnimator animation) {
                float fraction = animation.getAnimatedFraction();
                p2.x = evaluator.evaluate(fraction, p2Backup.x, p1.x);
                p2.y = evaluator.evaluate(fraction, p2Backup.y, p1.y);
                distance = evaluator.evaluate(fraction, distance, 0);
                invalidate();
            }

        });
        animator.start();
    }


}

这里用到了一个工具类：

package com.che.testapp.view;

import android.graphics.PointF;

/**
 * 点计算工具类
 * <p/>
 * 作者：余天然 on 16/6/15 下午2:33
 */
public class PointUtil {

    //获取旋转后的点
    public static PointF getRotatePoint(PointF p1, PointF p2, double raduis, double radians) {
        double oldRadians = getPointDegree(p1, p2);
        double newRadians = oldRadians + radians;
        float x = (float) (raduis * Math.cos(newRadians));
        float y = (float) (raduis * Math.sin(newRadians));
        return 
以上是关于自定义视图与贝塞尔曲线的主要内容，如果未能解决你的问题，请参考以下文章
 
 必须要理解掌握的贝塞尔曲线（原创）
 贝塞尔曲线的使用
 Android贝塞尔曲线的理解与应用
 n阶贝塞尔曲线
 Android UI贝塞尔曲线 ① ( 一阶贝塞尔曲线 | 二阶贝塞尔曲线 )
 用三阶贝塞尔曲线拟合圆