什么是貝塞爾曲線，它能夠做什么瘫怜？

貝塞爾曲線的名稱來源于一位就職于雷諾的法國工程師Pierre Bézier，他在1962年開始對貝塞爾曲線做了廣泛的宣傳，他使用這種只需要很少的控制點就能生成復(fù)雜平滑曲線的方法來進行汽車車體的工業(yè)設(shè)計饵溅，因為它控制簡便卻具有極強的描述能力，所以在工業(yè)設(shè)計和計算機圖形學(xué)等相關(guān)領(lǐng)域得到了廣泛應(yīng)用妇萄，比如我們電腦常用的繪圖軟件PhotoShop里的鋼筆工具蜕企，這也是貝塞爾曲線的應(yīng)用之一。

簡單點來說冠句，貝塞爾曲線就是能用數(shù)學(xué)公式將一條曲線很精準(zhǔn)的表現(xiàn)出來轻掩。

那么在Android開發(fā)中，貝塞爾曲線可以幫我們做出什么效果呢懦底？這里舉幾個例子唇牧，簡單點的它可以幫助我們做出很自然的平滑動畫，比如在一個頁面中畫出波浪動畫，餓了么購物車的商品加入動畫等丐重，復(fù)雜點的比如QQ消息氣泡的拖拽消失等腔召。

關(guān)于貝塞爾曲線，我們需要知道什么扮惦？

首先我們需要知道這幾個詞：
數(shù)據(jù)點：一條路徑的起始點和結(jié)束點
控制點：決定一條路徑的曲線軌跡臀蛛，根據(jù)控制點的個數(shù)我們可以把貝塞爾曲線分成一階、二階崖蜜、三階和多階貝塞爾曲線浊仆。
其中n階貝塞爾曲線=n-1個控制點，也就是一階貝塞爾曲線是0個控制點也就是一條直線纳猪，二階貝塞爾曲線是1個控制點氧卧，以此類推。
在Android開發(fā)中氏堤，系統(tǒng)已經(jīng)幫我們封裝好了二階和三階的對應(yīng)實現(xiàn)方法沙绝，我們只管調(diào)用就行，當(dāng)然在開發(fā)中鼠锈，我們有時會遇到需要實現(xiàn)多階貝塞爾曲線的情況闪檬，這時我們可以把多階進行分解，變成多個二階或者三階的貝塞爾曲線购笆，再以后的博客里我會再提到粗悯，這里先做一個入門的介紹，畢竟不能一口氣吃成大胖子同欠。
來看下關(guān)于貝塞爾曲線的展示：
一階貝塞爾曲線：

一階貝塞爾曲線

給定對應(yīng)的P0和P1样傍，分別是起始點和結(jié)束點，對應(yīng)的表達式：

一階貝塞爾表達式

二階貝塞爾曲線：

二階貝塞爾曲線

給定對應(yīng)的P0和P2铺遂，分別是起始點和結(jié)束點衫哥，P1為控制點，對應(yīng)的表達式：

二階貝塞爾表達式

三階貝塞爾曲線：

三階貝塞爾曲線

給定對應(yīng)的P0和P3襟锐，分別是起始點和結(jié)束點撤逢，P1，P2為控制點粮坞，對應(yīng)的表達式：

三階貝塞爾表達式

以上的曲線圖紅色軌跡即為貝塞爾曲線運動軌跡,而綠色的軌跡即為貝塞爾曲線的切線蚊荣，想了解更多的朋友可以參考下維基百科： 貝塞爾曲線
這里有一個貝塞爾曲線的動態(tài)演示圖，大家玩玩感受一下：貝塞爾曲線的動態(tài)演示圖

具體代碼實現(xiàn)

好了莫杈，大概介紹完貝塞爾曲線的概念后互例，作為開發(fā)者，應(yīng)該手癢癢的想拿去鍵盤用代碼實現(xiàn)一波了吧姓迅？
由于一階貝塞爾曲線沒有控制點敲霍，就是一條直線俊马，沒什么好說的 丁存，這里我打算從二階貝塞爾曲線開始說起肩杈，谷歌官方對開發(fā)者還是很不錯的，已經(jīng)提前幫我們封裝好關(guān)于二階和三階貝塞爾曲線的實現(xiàn)方法解寝，我們先來看下API：

二階貝塞爾曲線:
對應(yīng)的實現(xiàn)方式是：Path.quadTo和Path.rQuadTo扩然，它們分別對應(yīng)的是絕對坐標(biāo)和相對坐標(biāo)，兩者是可以互相轉(zhuǎn)換的聋伦。

 /**
     * Add a quadratic bezier from the last point, approaching control point
     * (x1,y1), and ending at (x2,y2). If no moveTo() call has been made for
     * this contour, the first point is automatically set to (0,0).
     *
     * @param x1 The x-coordinate of the control point on a quadratic curve
     * @param y1 The y-coordinate of the control point on a quadratic curve
     * @param x2 The x-coordinate of the end point on a quadratic curve
     * @param y2 The y-coordinate of the end point on a quadratic curve
     */
    public void quadTo(float x1, float y1, float x2, float y2) {
        isSimplePath = false;
        native_quadTo(mNativePath, x1, y1, x2, y2);
    }

首先我們先運用Path.moveTo將坐標(biāo)移動到起始點夫偶，然后這里x1，y1代表的是控制點的x觉增，y坐標(biāo)兵拢，x2，y2代表結(jié)束點逾礁，我們來寫個例子：

package com.lcw.view;

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

/**
 * 自定義View(二階貝塞爾曲線)
 * Create by: chenwei.li
 * Date: 2017/4/21
 * Time: 下午11:47
 * Email: lichenwei.me@foxmail.com
 */

public class BezierQuadView extends View {

    //開始點和結(jié)束點
    private int mStartXPoint;
    private int mStartYPoint;
    private int mEndXPoint;
    private int mEndYPoint;
    //控制點
    private int mConXPoint;
    private int mConYPoint;

    //路徑和畫筆
    private Path mPath;
    private Paint mPaint;


    //輔助線畫筆,寫字畫筆
    private Paint mLinePaint;
    private Paint mTextPaint;


    public BezierQuadView(Context context) {
        super(context);
        init(context);
    }


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

    public BezierQuadView(Context context, AttributeSet attrs, int defStyleAttr) {
        super(context, attrs, defStyleAttr);
        init(context);
    }

    /**
     * 進行初始化的一些操作
     */
    private void init(Context context) {
        //獲取屏幕的寬高
        WindowManager windowManager = (WindowManager) context.getSystemService(Context.WINDOW_SERVICE);
        DisplayMetrics displayMetrics = new DisplayMetrics();
        windowManager.getDefaultDisplay().getMetrics(displayMetrics);
        int screenHeight = displayMetrics.heightPixels;
        int screenWidth = displayMetrics.widthPixels;

        //設(shè)置各點的位置
        mStartXPoint = screenWidth / 4;
        mStartYPoint = screenHeight / 2;
        mEndXPoint = screenWidth * 3 / 4;
        mEndYPoint = screenHeight / 2;
        mConXPoint = screenWidth / 2;
        mConYPoint = screenHeight / 2 - 400;
        //路徑,畫筆設(shè)置
        mPath = new Path();
        mPaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mPaint.setColor(Color.BLUE);
        mPaint.setStyle(Paint.Style.STROKE);
        mPaint.setStrokeWidth(8);

        //輔助線畫筆
        mLinePaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mLinePaint.setColor(Color.GRAY);
        mLinePaint.setStyle(Paint.Style.STROKE);
        mLinePaint.setStrokeWidth(3);

        //寫字畫筆
        mTextPaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mTextPaint.setColor(Color.BLACK);
        mTextPaint.setStyle(Paint.Style.STROKE);
        mTextPaint.setTextSize(20);


    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        mPath.reset();
        //賽貝爾曲線
        mPath.moveTo(mStartXPoint, mStartYPoint);
        mPath.quadTo(mConXPoint, mConYPoint, mEndXPoint, mEndYPoint);
        canvas.drawPath(mPath, mPaint);

        //輔助線
        canvas.drawLine(mStartXPoint, mStartYPoint, mConXPoint, mConYPoint, mLinePaint);
        canvas.drawLine(mConXPoint, mConYPoint, mEndXPoint, mEndYPoint, mLinePaint);

        //文字
        canvas.drawPoint(mStartXPoint, mStartYPoint, mPaint);
        canvas.drawText("起始點", mStartXPoint, mStartYPoint + 30, mTextPaint);
        canvas.drawPoint(mEndXPoint, mEndYPoint, mPaint);
        canvas.drawText("結(jié)束點", mEndXPoint, mEndYPoint + 30, mTextPaint);
        canvas.drawPoint(mConXPoint, mConYPoint, mPaint);
        canvas.drawText("控制點", mConXPoint, mConYPoint - 30, mTextPaint);

    }

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        switch (event.getAction()){
            case MotionEvent.ACTION_MOVE:
                mConXPoint= (int) event.getX();
                mConYPoint=(int)event.getY();
                invalidate();
                break;
        }
        return true;
    }
}

三階貝塞爾曲線:
對應(yīng)的實現(xiàn)方式是：Path.cubicTo和Path.rCubicTo说铃，它們分別對應(yīng)的是絕對坐標(biāo)和相對坐標(biāo)，兩者是可以互相轉(zhuǎn)換的嘹履。

    /**
     * Add a cubic bezier from the last point, approaching control points
     * (x1,y1) and (x2,y2), and ending at (x3,y3). If no moveTo() call has been
     * made for this contour, the first point is automatically set to (0,0).
     *
     * @param x1 The x-coordinate of the 1st control point on a cubic curve
     * @param y1 The y-coordinate of the 1st control point on a cubic curve
     * @param x2 The x-coordinate of the 2nd control point on a cubic curve
     * @param y2 The y-coordinate of the 2nd control point on a cubic curve
     * @param x3 The x-coordinate of the end point on a cubic curve
     * @param y3 The y-coordinate of the end point on a cubic curve
     */
    public void cubicTo(float x1, float y1, float x2, float y2,
                        float x3, float y3) {
        isSimplePath = false;
        native_cubicTo(mNativePath, x1, y1, x2, y2, x3, y3);
    }

來看下運行效果圖：

二階貝塞爾曲線.png

首先我們先運用Path.moveTo將坐標(biāo)移動到起始點腻扇，然后這里x1，y1代表的是控制點1的x砾嫉，y坐標(biāo)幼苛，x2，y2代表的是控制點2的x焕刮，y坐標(biāo)舶沿，x3，y3代表結(jié)束點配并，我們來寫個例子：

package com.lcw.view;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.util.AttributeSet;
import android.util.DisplayMetrics;
import android.view.View;
import android.view.WindowManager;

/**
 * 自定義View(三階貝塞爾曲線)
 * Create by: chenwei.li
 * Date: 2017/4/21
 * Time: 下午11:47
 * Email: lichenwei.me@foxmail.com
 */

public class BezierCubicView extends View {

    //開始點和結(jié)束點
    private int mStartXPoint;
    private int mStartYPoint;
    private int mEndXPoint;
    private int mEndYPoint;
    //控制點
    private int mConOneXPoint;
    private int mConOneYPoint;
    private int mConTwoXPoint;
    private int mConTwoYPoint;

    //路徑和畫筆
    private Path mPath;
    private Paint mPaint;


    //輔助線畫筆,寫字畫筆
    private Paint mLinePaint;
    private Paint mTextPaint;


    public BezierCubicView(Context context) {
        super(context);
        init(context);
    }


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

    public BezierCubicView(Context context, AttributeSet attrs, int defStyleAttr) {
        super(context, attrs, defStyleAttr);
        init(context);
    }

    /**
     * 進行初始化的一些操作
     */
    private void init(Context context) {
        //獲取屏幕的寬高
        WindowManager windowManager = (WindowManager) context.getSystemService(Context.WINDOW_SERVICE);
        DisplayMetrics displayMetrics = new DisplayMetrics();
        windowManager.getDefaultDisplay().getMetrics(displayMetrics);
        int screenHeight = displayMetrics.heightPixels;
        int screenWidth = displayMetrics.widthPixels;

        //設(shè)置各點的位置
        mStartXPoint = screenWidth / 4;
        mStartYPoint = screenHeight / 2;
        mEndXPoint = screenWidth * 3 / 4;
        mEndYPoint = screenHeight / 2;
        mConOneXPoint = screenWidth / 2 - 300;
        mConOneYPoint = screenHeight / 2 - 400;
        mConTwoXPoint = screenWidth / 2 + 100;
        mConTwoYPoint = screenHeight / 2 - 400;
        //路徑,畫筆設(shè)置
        mPath = new Path();
        mPaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mPaint.setColor(Color.BLUE);
        mPaint.setStyle(Paint.Style.STROKE);
        mPaint.setStrokeWidth(8);

        //輔助線畫筆
        mLinePaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mLinePaint.setColor(Color.GRAY);
        mLinePaint.setStyle(Paint.Style.STROKE);
        mLinePaint.setStrokeWidth(3);

        //寫字畫筆
        mTextPaint = new Paint(Paint.ANTI_ALIAS_FLAG);
        mTextPaint.setColor(Color.BLACK);
        mTextPaint.setStyle(Paint.Style.STROKE);
        mTextPaint.setTextSize(20);


    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        //賽貝爾曲線
        mPath.moveTo(mStartXPoint, mStartYPoint);
        mPath.cubicTo(mConOneXPoint, mConOneYPoint,mConTwoXPoint,mConTwoYPoint,mEndXPoint, mEndYPoint);
        canvas.drawPath(mPath, mPaint);

        //輔助線
        canvas.drawLine(mStartXPoint, mStartYPoint, mConOneXPoint, mConOneYPoint, mLinePaint);
        canvas.drawLine(mConOneXPoint, mConOneYPoint, mConTwoXPoint, mConTwoYPoint, mLinePaint);
        canvas.drawLine(mConTwoXPoint, mConTwoYPoint, mEndXPoint, mEndYPoint, mLinePaint);

        //文字
        canvas.drawPoint(mStartXPoint, mStartYPoint, mPaint);
        canvas.drawText("起始點", mStartXPoint, mStartYPoint + 30, mTextPaint);
        canvas.drawPoint(mEndXPoint, mEndYPoint, mPaint);
        canvas.drawText("結(jié)束點", mEndXPoint, mEndYPoint + 30, mTextPaint);
        canvas.drawPoint(mConOneXPoint, mConOneYPoint, mPaint);
        canvas.drawText("控制點1", mConOneXPoint, mConOneYPoint - 30, mTextPaint);
        canvas.drawPoint(mConTwoXPoint, mConTwoYPoint, mPaint);
        canvas.drawText("控制點2", mConTwoXPoint, mConTwoYPoint - 30, mTextPaint);


    }
}

來看下運行效果圖：

三階貝塞爾曲線.png

現(xiàn)在括荡，我們監(jiān)聽下屏幕的觸摸事件，讓控制點隨著我們手指的移動而移動荐绝，看看會是什么樣的效果：

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        switch (event.getAction()){
            case MotionEvent.ACTION_MOVE:
                mConXPoint= (int) event.getX();
                mConYPoint=(int)event.getY();
                invalidate();
                break;
        }
        return true;
    }

二階貝塞爾曲線演示

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        switch (event.getAction() & MotionEvent.ACTION_MASK) {
            case MotionEvent.ACTION_POINTER_DOWN:
                mFlag = true;
                break;
            case MotionEvent.ACTION_POINTER_UP:
                mFlag = false;
                break;
            case MotionEvent.ACTION_MOVE:
                mConOneXPoint = (int) event.getX(0);
                mConOneYPoint = (int) event.getY(0);
                if (mFlag) {
                    mConTwoXPoint = (int) event.getY(1);
                    mConTwoYPoint = (int) event.getY(1);
                }
                invalidate();
                break;
        }
        return true;
    }

三階貝塞爾曲線演示

怎么樣一汽，曲線的繪制很自然吧，這就是貝塞爾曲線的入門使用了低滩。入門篇到這里就結(jié)束了召夹，下次給朋友們帶來貝塞爾曲線的進階篇。

源碼下載:

這里附上源碼地址（歡迎Star恕沫，歡迎Fork）：源碼下載