前幾天在“Android繪圖之漸隱動畫”一文中通過畫線實現了漸隱動畫，但裡面有個問題，畫筆較粗（大於1）時線段之間會有裂隙，我又改進了一下。這次效果好多了。

先看效果吧：

然後我們來說說基本的做法：

• 根據畫筆寬度，計算每一條線段兩個頂點對應的四個點，四點連線，包圍線段，形成一個路徑。
• 後一條線段的路徑的前兩個點，取（等於）前一條線段的後兩點，這樣就銜接起來了。

把Path的Style修改為FILL，效果是這樣的：

可以看到一個個四邊形，連成了路徑。

好啦，現在說說怎樣根據兩點計算出包圍它們連線的路徑所需的四個點。

先看一張圖：

在這張圖裡，黑色細線是我們拿到的兩個觸控點相連得到的。當畫筆寬度大於1（比如為10）時，其實經過這條黑線的兩個端點並且與這條黑線垂直相交的兩條線（藍線），就可以計算出來，藍線的長度就是畫筆的寬度，結合這些就可以計算出紅色的四個點。而紅色的四個點就圍住了線段，形成路徑。

這裡面用到兩點連線的公式，採用點斜式：

y = k*x + b

黑線的斜率是：

k = (y2 - y1) / (x2 - x1)

垂直相交的兩條線的斜率的關係是：

k1 * k2 = -1

所以，藍線的斜率就可以計算出來了。有了斜率和線上的一個點，就可以求出這條線的點斜式中的b，點斜式就出來了。

然後，利用兩點間距離公式：

已知一個點，這個點與另一個點的距離（畫筆寬度除以2），斜率，代入兩點間距離公式和藍線的點斜式，就可以計算出兩個紅色的點了。

計算時用到的是一元二次方程a*x*x + bx + c = 0，求 x 時用的公式是：

好啦，最後，上程式碼：

package com.example.disappearinglines;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import android.graphics.RectF;
import android.os.Handler;
import android.os.Message;
import android.os.SystemClock;
import
 
 android.support.annotation.NonNull;
import android.util.AttributeSet;
import android.util.Log;
import android.util.TypedValue;
import android.view.MotionEvent;
import android.view.View;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Iterator;
import java.util.List;
import java.util.ListIterator;

/**
 * Created by foruok，歡迎關注我的訂閱號“程式視界”.
 */

public class DisappearingDoodleView extends View {
    public static float convertDipToPx(Context context, float fDip) {
        float fPx = TypedValue.applyDimension(TypedValue.COMPLEX_UNIT_DIP, fDip,
                context.getResources().getDisplayMetrics());
        return fPx;
    }

    final static String TAG = "DoodleView";
    class LineElement {
        static final public int ALPHA_STEP = 8;
        public LineElement(float pathWidth){
            mPaint = new Paint();
            mPaint.setARGB(255, 255, 0, 0);
            mPaint.setAntiAlias(true);
            mPaint.setStrokeWidth(0);
            mPaint.setStrokeCap(Paint.Cap.BUTT);
            mPaint.setStyle(Paint.Style.FILL);
            mPath = new Path();
            mPathWidth = pathWidth;
            for(int i= 0; i < mPoints.length; i++){
                mPoints[i] = new PointF();
            }
        }

        public void setPaint(Paint paint){
            mPaint = paint;
        }

        public void setAlpha(int alpha){
            mPaint.setAlpha(alpha);
            mPathWidth = (alpha * mPathWidth) / 255;
        }

        private boolean caculatePoints(float k, float b, float x1, float y1, float distance, PointF pt1, PointF pt2){
            //point-k formula
            //  y= kx + b
            //distance formula of two points
            //  distance*distance = Math.pow((x - x1), 2) + Math.pow((y - y1), 2)
            //    |
            //    V
            //  ax*x + bx + c = 0;
            //    |
            //    V
            //  x = (-b +/- Math.sqrt( b*b - 4*a*c ) ) / (2*a)
            double a1 = Math.pow(k, 2) + 1;
            double b1 = 2* k * (b - y1) - 2 * x1;
            double c1 = Math.pow(x1, 2) + Math.pow(b - y1, 2) - Math.pow(distance, 2);
            double criterion = Math.pow(b1, 2) - 4*a1*c1;
            if(criterion > 0) {
                criterion = Math.sqrt(criterion);
                pt1.x = (float) ((-b1 + criterion) / (2 * a1));
                pt1.y = k * pt1.x + b;
                pt2.x = (float) ((-b1 - criterion) / (2 * a1));
                pt2.y = k * pt2.x + b;
                return true;
            }
            return false;
        }

        private void swapPoint(PointF pt1, PointF pt2){
            float t = pt1.x;
            pt1.x = pt2.x;
            pt2.x = t;
            t = pt1.y;
            pt1.y = pt2.y;
            pt2.y = t;
        }

        public boolean updatePathPoints(){
            float distance = mPathWidth / 2;
            if(Math.abs(mEndX - mStartX) < 1){
                mPoints[0].x = mStartX + distance;
                mPoints[0].y = mStartY - distance;
                mPoints[1].x = mStartX - distance;
                mPoints[1].y = mPoints[0].y;
                mPoints[2].x = mPoints[1].x;
                mPoints[2].y = mEndY + distance;
                mPoints[3].x = mPoints[0].x;
                mPoints[3].y = mPoints[2].y;
            }else if(Math.abs(mEndY - mStartY) < 1){
                mPoints[0].x = mStartX - distance;
                mPoints[0].y = mStartY - distance;
                mPoints[1].x = mPoints[0].x;
                mPoints[1].y = mStartY + distance;
                mPoints[2].x = mEndX + distance;
                mPoints[2].y = mPoints[1].y;
                mPoints[3].x = mPoints[2].x;
                mPoints[3].y = mPoints[0].y;
            }else{
                //point-k formula
                //y= kx + b
                float kLine = (mEndY - mStartY) / (mEndX - mStartX);
                float kVertLine = -1 / kLine;
                float b = mStartY - (kVertLine * mStartX);
                if(!caculatePoints(kVertLine, b, mStartX, mStartY, distance, mPoints[0], mPoints[1])){
                    String info = String.format(TAG, "startPt, criterion < 0, (%.2f, %.2f)-->(%.2f, %.2f), kLine - %.2f, kVertLine - %.2f, b - %.2f",
                            mStartX, mStartY, mEndX, mEndY, kLine, kVertLine, b);
                    Log.i(TAG, info);
                    return false;
                }
                b = mEndY - (kVertLine * mEndX);
                if(!caculatePoints(kVertLine, b, mEndX, mEndY, distance, mPoints[2], mPoints[3])){
                    String info = String.format(TAG, "endPt, criterion < 0, (%.2f, %.2f)-->(%.2f, %.2f), kLine - %.2f, kVertLine - %.2f, b - %.2f",
                            mStartX, mStartY, mEndX, mEndY, kLine, kVertLine, b);
                    Log.i(TAG, info);
                    return false;
                }
                //reorder points to unti-clockwise
                if(mStartX < mEndX){
                    if(mStartY < mEndY){
                        if(mPoints[0].x < mPoints[1].x){
                            swapPoint(mPoints[0], mPoints[1]);
                        }
                        if(mPoints[2].x > mPoints[3].x){
                            swapPoint(mPoints[2], mPoints[3]);
                        }
                    }else{
                        if(mPoints[0].x > mPoints[1].x){
                            swapPoint(mPoints[0], mPoints[1]);
                        }
                        if(mPoints[2].x < mPoints[3].x){
                            swapPoint(mPoints[2], mPoints[3]);
                        }
                    }
                }else{
                    if(mStartY < mEndY){
                        if(mPoints[0].x < mPoints[1].x){
                            swapPoint(mPoints[0], mPoints[1]);
                        }
                        if(mPoints[2].x > mPoints[3].x){
                            swapPoint(mPoints[2], mPoints[3]);
                        }
                    }else{
                        if(mPoints[0].x > mPoints[1].x){
                            swapPoint(mPoints[0], mPoints[1]);
                        }
                        if(mPoints[2].x < mPoints[3].x){
                            swapPoint(mPoints[2], mPoints[3]);
                        }
                    }
                }
            }

            return true;
        }

        // for the first line
        public void updatePath(){
            //update path
            mPath.reset();
            mPath.moveTo(mPoints[0].x, mPoints[0].y);
            mPath.lineTo(mPoints[1].x, mPoints[1].y);
            mPath.lineTo(mPoints[2].x, mPoints[2].y);
            mPath.lineTo(mPoints[3].x, mPoints[3].y);
            mPath.close();
        }

        // for middle line
        public void updatePathWithStartPoints(PointF pt1, PointF pt2){
            mPath.reset();
            mPath.moveTo(pt1.x, pt1.y);
            mPath.lineTo(pt2.x, pt2.y);
            mPath.lineTo(mPoints[2].x, mPoints[2].y);
            mPath.lineTo(mPoints[3].x, mPoints[3].y);
            mPath.close();
        }

        public float mStartX = -1;
        public float mStartY = -1;
        public float mEndX = -1;
        public float mEndY = -1;
        public Paint mPaint;
        public Path mPath;
        public PointF[] mPoints = new PointF[4]; //path's vertex
        float mPathWidth;
    }

    private LineElement mCurrentLine = null;
    private List<LineElement> mLines = null;
    private float mLaserX = 0;
    private float mLaserY = 0;
    final Paint mPaint = new Paint();
    private int mWidth = 0;
    private int mHeight = 0;
    private long mElapsed = 0;
    private float mStrokeWidth = 20;
    private float mCircleRadius = 10;
    private Handler mHandler = new Handler(){
        @Override
        public void handleMessage(Message msg){
            DisappearingDoodleView.this.invalidate();
        }
    };

    public DisappearingDoodleView(Context context){
        super(context);
        initialize(context);
    }

    public DisappearingDoodleView(Context context, AttributeSet attrs){
        super(context, attrs);
        initialize(context);
    }

    private void initialize(Context context){
        mStrokeWidth = convertDipToPx(context, 22);
        mCircleRadius = convertDipToPx(context, 10);
        mPaint.setARGB(255, 255, 0, 0);
        mPaint.setAntiAlias(true);
        mPaint.setStrokeWidth(0);
        mPaint.setStyle(Paint.Style.FILL);
    }

    @Override
    protected void onSizeChanged (int w, int h, int oldw, int oldh){
        mWidth = w;
        mHeight = h;
        adjustLasterPosition();
    }

    private void adjustLasterPosition(){
        if(mLaserX - mCircleRadius < 0) mLaserX = mCircleRadius;
        else if(mLaserX + mCircleRadius > mWidth) mLaserX = mWidth - mCircleRadius;
        if(mLaserY - mCircleRadius < 0) mLaserY = mCircleRadius;
        else if(mLaserY + mCircleRadius > mHeight) mLaserY = mHeight - mCircleRadius;
    }

    private void updateLaserPosition(float x, float y){
        mLaserX = x;
        mLaserY = y;
        adjustLasterPosition();
    }
    @Override
    protected void onDraw(Canvas canvas){
        //canvas.drawText("ABCDE", 10, 16, mPaint);
        mElapsed = SystemClock.elapsedRealtime();

        if(mLines != null) {
            updatePaths();
            for (LineElement e : mLines) {
                if(e.mStartX < 0 || e.mEndY < 0 || e.mPath.isEmpty()) continue;
                //canvas.drawLine(e.mStartX, e.mStartY, e.mEndX, e.mEndY, e.mPaint);
                canvas.drawPath(e.mPath, e.mPaint);
            }
            compactPaths();
        }
        canvas.drawCircle(mLaserX, mLaserY, mCircleRadius, mPaint);
    }

    private boolean isValidLine(float x1, float y1, float x2, float y2){
        return Math.abs(x1 - x2) > 1 || Math.abs(y1 - y2) > 1;
    }

    @Override
    public boolean onTouchEvent(MotionEvent event){
        float x = event.getX();
        float y = event.getY();

        int action = event.getAction();
        if(action == MotionEvent.ACTION_UP){// end one line after finger release
            if(isValidLine(mCurrentLine.mStartX, mCurrentLine.mStartY, x, y)){
                mCurrentLine.mEndX = x;
                mCurrentLine.mEndY = y;
                addToPaths(mCurrentLine);
            }
            //mCurrentLine.updatePathPoints();
            mCurrentLine = null;
            updateLaserPosition(x, y);
            invalidate();
            return true;
        }

        if(action == MotionEvent.ACTION_DOWN){
            mLines = null;
            mCurrentLine = new LineElement(mStrokeWidth);

            mCurrentLine.mStartX = x;
            mCurrentLine.mStartY = y;
            updateLaserPosition(x, y);
            return true;
        }

        if(action == MotionEvent.ACTION_MOVE) {
            if(isValidLine(mCurrentLine.mStartX, mCurrentLine.mStartY, x, y)){
                mCurrentLine.mEndX = x;
                mCurrentLine.mEndY = y;
                addToPaths(mCurrentLine);

                mCurrentLine = new LineElement(mStrokeWidth);
                mCurrentLine.mStartX = x;
                mCurrentLine.mStartY = y;

                updateLaserPosition(x, y);
            }else{
                //do nothing, wait next point
            }
        }

        if(mHandler.hasMessages(1)){
            mHandler.removeMessages(1);
        }
        Message msg = new Message();
        msg.what = 1;
        mHandler.sendMessageDelayed(msg, 0);

        return true;
    }

    private void addToPaths(LineElement element){
        if(mLines == null) {
            mLines = new ArrayList<LineElement>() ;
        }
        mLines.add(element);
    }

    private void updatePaths() {
        int size = mLines.size();
        if (size == 0) return;


        LineElement line = null;
        int j = 0;
        for (; j < size; j++) {
            line = mLines.get(j);
            if (line.updatePathPoints()) break;
        }

        if (j == size) {
            mLines.clear();
            return;
        } else {
            for (j--; j >= 0; j--) {
                mLines.remove(0);
            }
        }

        line.updatePath();
        size = mLines.size();

        LineElement lastLine = null;
        for (int i = 1; i < size; i++) {
            line = mLines.get(i);
            if (line.updatePathPoints()){
                if (lastLine == null) {
                    lastLine = mLines.get(i - 1);
                }
                line.updatePathWithStartPoints(lastLine.mPoints[3], lastLine.mPoints[2]);
                lastLine = null;
            }else{
                mLines.remove(i);
                size = mLines.size();
            }
        }
    }

    public void compactPaths(){

        int size = mLines.size();
        int index = size - 1;
        if(size == 0) return;
        int baseAlpha = 255 - LineElement.ALPHA_STEP;
        int itselfAlpha;
        LineElement line;
        for(; index >=0 ; index--, baseAlpha -= LineElement.ALPHA_STEP){
            line = mLines.get(index);
            itselfAlpha = line.mPaint.getAlpha();
            if(itselfAlpha == 255){
                if(baseAlpha <= 0 || line.mPathWidth < 1){
                    ++index;
                    break;
                }
                line.setAlpha(baseAlpha);
            }else{
                itselfAlpha -= LineElement.ALPHA_STEP;
                if(itselfAlpha <= 0 || line.mPathWidth < 1){
                    ++index;
                    break;
                }
                line.setAlpha(itselfAlpha);
            }
        }

        if(index >= size){
            // all sub-path should disappear
            mLines = null;
        }
        else if(index >= 0){
            //Log.i(TAG, "compactPaths from " + index + " to " + (size - 1));
            mLines = mLines.subList(index, size);
        }else{
            // no sub-path should disappear
        }

        long interval = 40 - SystemClock.elapsedRealtime() + mElapsed;
        if(interval < 0) interval = 0;
        Message msg = new Message();
        msg.what = 1;
        mHandler.sendMessageDelayed(msg, interval);
    }
}

這樣自繪，效率不太好，還沒想怎麼去改進，哪位有辦法，可以留言給我。^_^

參考：