1、贝塞尔曲线

  • 贝塞尔曲线（Bézier curve），又称贝兹曲线或贝济埃曲线，是应用于二维图形应用程序的数学曲线。一般的矢量图形软件通过它来精确画出曲线，贝兹曲线由线段与节点组成，节点是可拖动的支点，线段像可伸缩的皮筋，我们在绘图工具上看到的钢笔工具就是来做这种矢量曲线的。贝塞尔曲线是计算机图形学中相当重要的参数曲线，在一些比较成熟的位图软件中也有贝塞尔曲线工具，如 PhotoShop 等。在 Flash4 中还没有完整的曲线工具，而在 Flash5 里面已经提供出贝塞尔曲线工具。

  • 二阶贝塞尔曲线示意图

  • 三阶贝塞尔曲线示意图

  • 贝塞尔路径（UIBezierPath）是 iOS UIKit 框架中对 Quartz 2D 绘图的封装。实际操作起来，使用贝塞尔路径，更为方便。用法与 CGContextRef 类似，但是 OC 对其进行了封装，更加面向对象。

  • 贝塞尔路径常用的方法

    	// 设置起始点
    
	- (void)moveToPoint:(CGPoint)point;

	// 添加直线到一点
    
	- (void)addLineToPoint:(CGPoint)point;

	// 封闭闭路径
    
	- (void)closePath;

	// 返回一个描述椭圆的路径
    
	+ (UIBezierPath *)bezierPathWithOvalInRect:(CGRect)rect;

	// 贝塞尔曲线
    
	- (void)addQuadCurveToPoint:(CGPoint)endPoint controlPoint:(CGPoint)controlPoint;

	// 三次贝塞尔曲线
    
	- (void)addCurveToPoint:(CGPoint)endPoint controlPoint1:(CGPoint)controlPoint1 controlPoint2:(CGPoint)controlPoint2;

	// 绘制圆弧
    
	- (void)addArcWithCenter:(CGPoint)center radius:(CGFloat)radius startAngle:(CGFloat)startAngle endAngle:(CGFloat)endAngle clockwise:(BOOL)clockwise;

2、基本图形的绘制

3、二三阶贝塞尔曲线示例

3.1 二阶贝塞尔曲线示例

  • QBezierPathView.h

    	@interface QBezierPathView : UIView

	@end

  • QBezierPathView.m

    	@interface QBezierPathView ()

	/// 路径
    
	@property (nonatomic, strong) UIBezierPath *path;

	/// 起始点
    
	@property (nonatomic, assign) CGPoint startP;

	/// 终止点
    
	@property (nonatomic, assign) CGPoint endP;

	/// 控制点
    
	@property (nonatomic, assign) CGPoint controlP;

	/// 线的颜色
    
	@property (nonatomic, strong) UIColor *pathColor;

	/// 线的宽度
    
	@property (nonatomic, assign) CGFloat pathWidth;

	/// 当前触摸的点
    
	@property (nonatomic, assign) NSUInteger currentTouchP;

	@end

	@implementation QBezierPathView

	/// 初始化
    
	- (instancetype)initWithFrame:(CGRect)frame {

	    if (self = [super initWithFrame:frame]) {

	        // 设置初始值

	        self.startP    = CGPointMake(20, 300);
    
	        self.endP      = CGPointMake(250, 300);
    
	        self.controlP  = CGPointMake(100, 100);

	        self.pathColor = [UIColor redColor];
    
	        self.pathWidth = 2;
    
	    }
    
	    return self;
    
	}

	/// 绘制二阶贝塞尔曲线
    
	- (void)drawRect:(CGRect)rect {

	    // 绘制贝塞尔曲线

	    self.path = [UIBezierPath bezierPath];
    
	    [self.path moveToPoint:self.startP];

	    [self.path addQuadCurveToPoint:self.endP controlPoint:self.controlP];

	    self.path.lineWidth = self.pathWidth;
    
	    [self.pathColor setStroke];
    
	    [self.path stroke];

	    // 绘制辅助线

	    self.path = [UIBezierPath bezierPath];

	    self.path.lineWidth = 1;
    
	    [[UIColor grayColor] setStroke];

	    CGFloat lengths[] = {5};
    
	    [self.path setLineDash:lengths count:1 phase:1];

	    [self.path moveToPoint:self.controlP];
    
	    [self.path addLineToPoint:self.startP];
    
	    [self.path stroke];

	    [self.path moveToPoint:self.controlP];
    
	    [self.path addLineToPoint:self.endP];
    
	    [self.path stroke];

	    // 绘制辅助点及信息

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.startP radius:4 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path fill];

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.endP radius:4 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path fill];

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.controlP radius:3 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    self.path.lineWidth = 2;
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path stroke];

	    CGRect startMsgRect = CGRectMake(self.startP.x + 8, self.startP.y - 7, 50, 20);
    
	    [@"起始点" drawInRect:startMsgRect withAttributes:nil];

	    CGRect endMsgRect = CGRectMake(self.endP.x + 8, self.endP.y - 7, 50, 20);
    
	    [@"终止点" drawInRect:endMsgRect withAttributes:nil];

	    CGRect control1MsgRect = CGRectMake(self.controlP.x + 8, self.controlP.y - 7, 50, 20);
    
	    [@"控制点" drawInRect:control1MsgRect withAttributes:nil];
    
	}

	/// 触摸开始
    
	- (void)touchesBegan:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 获取触摸点位置
    
	    CGPoint startPoint = [touches.anyObject locationInView:self];

	    CGRect startR   = CGRectMake(self.startP.x   - 4, self.startP.y   - 4, 8, 8);
    
	    CGRect endR     = CGRectMake(self.endP.x     - 4, self.endP.y     - 4, 8, 8);
    
	    CGRect controlR = CGRectMake(self.controlP.x - 4, self.controlP.y - 4, 8, 8);

	    // 判断当前触摸点
    
	    if (CGRectContainsPoint(startR, startPoint)) {
    
	        self.currentTouchP = 1;
    
	    } else if (CGRectContainsPoint(endR, startPoint)) {
    
	        self.currentTouchP = 2;
    
	    } else if (CGRectContainsPoint(controlR, startPoint)) {
    
	        self.currentTouchP = 3;
    
	    }
    
	}

	/// 触摸移动
    
	- (void)touchesMoved:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 获取触摸点位置
    
	    CGPoint touchPoint = [touches.anyObject locationInView:self];

	    // 限制触摸点的边界

	    if (touchPoint.x < 0) {
    
	        touchPoint.x = 0;
    
	    }

	    if (touchPoint.x > self.bounds.size.width) {
    
	        touchPoint.x = self.bounds.size.width;
    
	    }

	    if (touchPoint.y < 0) {
    
	        touchPoint.y = 0;
    
	    }

	    if (touchPoint.y > self.bounds.size.height) {
    
	        touchPoint.y = self.bounds.size.height;
    
	    }

	    // 设置当前触摸点的值
    
	    switch (self.currentTouchP) {
    
	        case 1:
    
	            self.startP = touchPoint;
    
	            break;

	        case 2:
    
	            self.endP = touchPoint;
    
	            break;

	        case 3:
    
	            self.controlP = touchPoint;
    
	            break;

	        default:
    
	            break;
    
	    }

	    // 刷新
    
	    [self setNeedsDisplay];
    
	}

	/// 触摸结束
    
	- (void)touchesEnded:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 释放之前的触摸点
    
	    self.currentTouchP = 0;
    
	}

	/// 触摸取消
    
	- (void)touchesCancelled:(NSSet *)touches withEvent:(nullable UIEvent *)event {
    
	    [self touchesEnded:touches withEvent:event];
    
	}

	@end

  • ViewController.m

    	CGRect frame = CGRectMake(20, 50, self.view.bounds.size.width - 40, 400);

	QBezierPathView *pathView = [[QBezierPathView alloc] initWithFrame:frame];

	pathView.backgroundColor = [UIColor whiteColor];
    
	pathView.layer.borderWidth = 1;

	[self.view addSubview:pathView];

  • 效果

3.2 三阶贝塞尔曲线示例

  • QBezierPathView.h

    	@interface QBezierPathView : UIView

	@end

  • QBezierPathView.m

    	@interface QBezierPathView : UIView
    
	@interface QBezierPathView ()

	/// 路径
    
	@property (nonatomic, strong) UIBezierPath *path;

	/// 起始点
    
	@property (nonatomic, assign) CGPoint startP;

	/// 终止点
    
	@property (nonatomic, assign) CGPoint endP;

	/// 控制点
    
	@property (nonatomic, assign) CGPoint controlP1;
    
	@property (nonatomic, assign) CGPoint controlP2;

	/// 线的颜色
    
	@property (nonatomic, strong) UIColor *pathColor;

	/// 线的宽度
    
	@property (nonatomic, assign) CGFloat pathWidth;

	/// 当前触摸的点
    
	@property (nonatomic, assign) NSUInteger currentTouchP;

	@end

	@implementation QBezierPathView

	/// 初始化
    
	- (instancetype)initWithFrame:(CGRect)frame {

	    if (self = [super initWithFrame:frame]) {

	        // 设置初始值

	        self.startP    = CGPointMake(20, 300);
    
	        self.endP      = CGPointMake(250, 300);
    
	        self.controlP1  = CGPointMake(100, 100);
    
	        self.controlP2  = CGPointMake(200, 350);

	        self.pathColor = [UIColor redColor];
    
	        self.pathWidth = 2;
    
	    }
    
	    return self;
    
	}

	/// 绘制二阶贝塞尔曲线
    
	- (void)drawRect:(CGRect)rect {

	    // 绘制贝塞尔曲线

	    self.path = [UIBezierPath bezierPath];
    
	    [self.path moveToPoint:self.startP];

	    [self.path addCurveToPoint:self.endP controlPoint1:self.controlP1 controlPoint2:self.controlP2];

	    self.path.lineWidth = self.pathWidth;
    
	    [self.pathColor setStroke];
    
	    [self.path stroke];

	    // 绘制辅助线

	    self.path = [UIBezierPath bezierPath];

	    self.path.lineWidth = 1;
    
	    [[UIColor grayColor] setStroke];

	    CGFloat lengths[] = {5};
    
	    [self.path setLineDash:lengths count:1 phase:1];

	    [self.path moveToPoint:self.controlP1];
    
	    [self.path addLineToPoint:self.startP];
    
	    [self.path stroke];

	    [self.path moveToPoint:self.controlP1];
    
	    [self.path addLineToPoint:self.controlP2];
    
	    [self.path stroke];

	    [self.path moveToPoint:self.controlP2];
    
	    [self.path addLineToPoint:self.endP];
    
	    [self.path stroke];

	    // 绘制辅助点及信息

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.startP radius:4 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path fill];

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.endP radius:4 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path fill];

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.controlP1 radius:3 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    self.path.lineWidth = 2;
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path stroke];

	    self.path = [UIBezierPath bezierPathWithArcCenter:self.controlP2 radius:3 startAngle:0 endAngle:M_PI * 2 clockwise:YES];
    
	    self.path.lineWidth = 2;
    
	    [[UIColor blackColor] setStroke];
    
	    [self.path stroke];

	    CGRect startMsgRect = CGRectMake(self.startP.x + 8, self.startP.y - 7, 50, 20);
    
	    [@"起始点" drawInRect:startMsgRect withAttributes:nil];

	    CGRect endMsgRect = CGRectMake(self.endP.x + 8, self.endP.y - 7, 50, 20);
    
	    [@"终止点" drawInRect:endMsgRect withAttributes:nil];

	    CGRect control1MsgRect = CGRectMake(self.controlP1.x + 8, self.controlP1.y - 7, 50, 20);
    
	    [@"控制点1" drawInRect:control1MsgRect withAttributes:nil];

	    CGRect control2MsgRect = CGRectMake(self.controlP2.x + 8, self.controlP2.y - 7, 50, 20);
    
	    [@"控制点2" drawInRect:control2MsgRect withAttributes:nil];
    
	}

	/// 触摸开始
    
	- (void)touchesBegan:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 获取触摸点位置
    
	    CGPoint startPoint = [touches.anyObject locationInView:self];

	    CGRect startR    = CGRectMake(self.startP.x   - 4, self.startP.y   - 4, 8, 8);
    
	    CGRect endR      = CGRectMake(self.endP.x     - 4, self.endP.y     - 4, 8, 8);
    
	    CGRect controlR1 = CGRectMake(self.controlP1.x - 4, self.controlP1.y - 4, 8, 8);
    
	    CGRect controlR2 = CGRectMake(self.controlP2.x - 4, self.controlP2.y - 4, 8, 8);

	    // 判断当前触摸点
    
	    if (CGRectContainsPoint(startR, startPoint)) {
    
	        self.currentTouchP = 1;
    
	    } else if (CGRectContainsPoint(endR, startPoint)) {
    
	        self.currentTouchP = 2;
    
	    } else if (CGRectContainsPoint(controlR1, startPoint)) {
    
	        self.currentTouchP = 3;
    
	    } else if (CGRectContainsPoint(controlR2, startPoint)) {
    
	        self.currentTouchP = 4;
    
	    }
    
	}

	/// 触摸移动
    
	- (void)touchesMoved:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 获取触摸点位置
    
	    CGPoint touchPoint = [touches.anyObject locationInView:self];

	    // 限制触摸点的边界

	    if (touchPoint.x < 0) {
    
	        touchPoint.x = 0;
    
	    }

	    if (touchPoint.x > self.bounds.size.width) {
    
	        touchPoint.x = self.bounds.size.width;
    
	    }

	    if (touchPoint.y < 0) {
    
	        touchPoint.y = 0;
    
	    }

	    if (touchPoint.y > self.bounds.size.height) {
    
	        touchPoint.y = self.bounds.size.height;
    
	    }

	    // 设置当前触摸点的值
    
	    switch (self.currentTouchP) {
    
	        case 1:
    
	            self.startP = touchPoint;
    
	            break;

	        case 2:
    
	            self.endP = touchPoint;
    
	            break;

	        case 3:
    
	            self.controlP1 = touchPoint;
    
	            break;

	        case 4:
    
	            self.controlP2 = touchPoint;
    
	            break;

	        default:
    
	            break;
    
	    }

	    // 刷新
    
	    [self setNeedsDisplay];
    
	}

	/// 触摸结束
    
	- (void)touchesEnded:(NSSet<UITouch *> *)touches withEvent:(nullable UIEvent *)event {

	    // 释放之前的触摸点
    
	    self.currentTouchP = 0;
    
	}

	/// 触摸取消
    
	- (void)touchesCancelled:(NSSet *)touches withEvent:(nullable UIEvent *)event {
    
	    [self touchesEnded:touches withEvent:event];
    
	}

	@end

  • ViewController.m

    	CGRect frame = CGRectMake(20, 50, self.view.bounds.size.width - 40, 400);

	QBezierPathView *pathView = [[QBezierPathView alloc] initWithFrame:frame];

	pathView.backgroundColor = [UIColor whiteColor];
    
	pathView.layer.borderWidth = 1;

	[self.view addSubview:pathView];

  • 效果

iOS - Quartz 2D 贝塞尔曲线的更多相关文章

  1. iOS - Quartz 2D 二维绘图

    1.Quartz 2D 简介 Quartz 2D 属于 Core Graphics(所以大多数相关方法的都是以 CG 开头),是 iOS/Mac OSX 提供的在内核之上的强大的 2D 绘图引擎,并且 ...

  2. iOS之UIBezierPath贝塞尔曲线属性简介

    #import <Foundation/Foundation.h> #import <CoreGraphics/CoreGraphics.h> #import <UIKi ...

  3. iOS - Quartz 2D 第三方框架 Charts 绘制图表

    1.Charts 简介 使用第三方框架 Charts 绘制 iOS 图表.GitHub 源码 Charts Charts 是一款用于绘制图表的框架,可以绘制柱状图.折线图.K线图.饼状图等.Chart ...

  4. IOS Quartz 2D 学习(1)

    IOS提供两种创建图形的途径: 1.OpenGL. 2.Quartz.Core Animation.UIKit图形支持. UIKit的图形系统 1.视图绘画周期: DrawRect方法,在任何时候,当 ...

  5. iOS - Quartz 2D 画板绘制

    1.绘制画板 1.1 绘制简单画板 PaintBoardView.h @interface PaintBoardView : UIView @end PaintBoardView.m @interfa ...

  6. iOS - Quartz 2D 手势截屏绘制

    1.绘制手势截屏 具体实现代码见 GitHub 源码 QExtension QTouchClipView.h @interface QTouchClipView : UIView /** * 创建手势 ...

  7. iOS - Quartz 2D 下载进度按钮绘制

    1.绘制下载进度按钮 具体实现代码见 GitHub 源码 QExtension QProgressButton.h @interface QProgressButton : UIButton /// ...

  8. iOS 2D绘图详解（Quartz 2D）之路径(点,直线,虚线,曲线,圆弧,椭圆,矩形)

    前言:一个路径可以包含由一个或者多个shape以及子路径subpath,quartz提供了很多方便的shape可以直接调用.例如:point,line,Arc(圆弧),Curves(曲线),Ellip ...

  9. IOS用CGContextRef画各种图形(文字、圆、直线、弧线、矩形、扇形、椭圆、三角形、圆角矩形、贝塞尔曲线、图片)

    ... 首先了解一下CGContextRef: An opaque type that represents a Quartz 2D drawing environment. Graphics Con ...

随机推荐

  1. CF 246E. Blood Cousins Return [dsu on tree STL]

    题意: 一个森林,求k级后代中多少种不同的权值 用set维护每个深度出现的权值 一开始一直在想删除怎么办,后来发现因为当前全局维护的东西里都是当前子树里的,如果要删除那么当前一定是轻儿子,直接清空se ...

  2. 数据提交成功后如何避免alert被window.location.reload()影响

    数据提交成功用alert提示,但页面立马就重载了 alert("提交成功!"); window.location.reload(); 如何避免? 方法一: setTimeout 延 ...

  3. CentOS上安装GitBlit服务

    简单介绍 在上一篇文章中,已经简单的介绍了如何在CentOS的服务器上搭建git服务器.但是这种方式实现的服务器功能比较弱,操作起来也比较繁琐.在网上搜索了一圈,感觉Gitblit比较符合我的需求.接 ...

  4. nodejs http post 请求带参数

    // We need this to build our post string var querystring = require('querystring'); var http = requir ...

  5. php 生成缩略图

    $src = '4.jpg'; list($width,$height) = getimagesize($src); $im = imagecreatefromjpeg($src); $panl = ...

  6. php生成文字水印和图片水印

    生成文字水印   //文字水印 /*打开图片*/ //1.配置图片路径 $src = "4.jpg"; //2.获取图片的信息(得到图片的基本信息) $info = getimag ...

  7. dedecms调用文章内容

    使用织梦建站时,有时候需要调用某一文档的内容,但织梦默认没有相应的标签,这时就需要我们使用sql语句去抓取了. {dede:sql sql="SELECT aid,typeid,body F ...

  8. CENTOS6.6下redis3.2集群搭建

    本文来自我的github pages博客http://galengao.github.io/ 即www.gaohuirong.cn [参考:]http://blog.csdn.net/zhu_tian ...

  9. PHP实现WebService的简单示例和实现步骤

    首先我创建的文件有: api.php api的接口类文件 api.wsdl 我创建产生的最后要调用的接口文件 cometrue.php 注册service api类内容的所有内容的执行文件 creat ...

  10. git使用步骤

    1报名出处: git config --global user.name lhp  用户名 git config --global user.email a@.qq.com 邮箱 2.建立项目文件夹: ...