bezier | 易学教程

Solution for route or path marking with bends

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问题 I want to give my users an easy way to visually trace a route on a map or a picture. The solution must let the users add control points that they can use to put bends into the route. It should work with html5 canvas - I currently use the Konvajs library so a solution that uses this would be good. In the interests of sharing & learning, if you can suggest solutions using other HTML5 canvas libraries that would be good to see too. Note: This is not the original question posed. However it

Find rightmost/leftmost point of SVG path

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问题 How to find leftmost/rightmost point of SVG C (bezier curve) path segment? I know there is getBoundingClientRect() and getBBox() but none of them apply since they return only single coordinate of the point. Just to avoid XY problem - I want to split single path composed of bezier curves into several paths each monotonously going from left to right (or right to left). It means that on any single path should be no 2 points having equal X coordinate. I understand that required split point may

Is there an iOS equivalent of appendBezierPathWithArcWithCenter

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问题 I'm trying to draw a quarter circle in iOS. In Mac OS, it seems you can use appendBezierPathWithArcWithCenter but this doesn't seem to work in iOS. Does anyone know how to simply draw a quarter circle in iOS? Thanks 回答1: There are two iOS equivalents, one for UIBezierPath and one for CGPath : UIBezierPath equivalent UIBezierPath *path = [UIBezierPath bezierPath]; [path addArcWithCenter:centerPoint radius:radius startAngle:startAngle endAngle:endAngle clockwise:YES]; CGPath equivalent

Android draw circle with Path

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问题 I'm trying to animate drawing out a circle. In my custom view, I have private final Paint mPaint = new Paint() { { setDither(true); setStyle(Paint.Style.STROKE); setStrokeCap(Paint.Cap.ROUND); setStrokeJoin(Paint.Join.ROUND); setColor(Color.BLUE); setStrokeWidth(30.0f); setAntiAlias(true); } }; ... protected void onDraw(Canvas canvas) { super.onDraw(); if (mOval == null) { mOval = new RectF(getLeft(), getTop(), getRight(), getBottom()); } if (mPath == null) { mPath = new Path(); mPath.moveTo

Simplify high-order Bezier curve

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问题 I have an array of control points that represent a Bezier curve. It could be a fifth-order or 100-order Bezier curve, or anything in-between. I am looking for a way to simplify that Bezier curve into multiple cubic Bezier curves. An illustration below shows how tenth-degree curve can be simplified to three-degree curve, but I want to go further and simplify it to several cubic Bezier curves to achieve better approximation. Code example would be very helpful. 回答1: As mohsenmadi already pointed

Writing Name Using Bezier Curves In C#

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问题 I have to make a program that uses C# Generated Graphics to make a replica of my name that I wrote in cursive. Twist is, I have to use Bezier Curves. I've already called a function to make Bezier Curves using 4 points and a gravity concept. My question to you is, What would be the easiest way to make around 10 curves. Here is my function for a Bezier Curve. public static void bezierCurve( Graphics g, double p1x, double p1y, double p2x, double p2y, double p3x, double p3y, double p4x, double

Writing Name Using Bezier Curves In C#

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CG-曲线与曲面-学习笔记

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一、连续性 1. 参数连续性 0阶参数连续性（C 0 ）：是指曲线的几何位置连接，即第一个曲线段的终点与第二个曲线段的起点x,y,z值相等； 1阶参数连续性（C 1 ）：在C 0 的基础上，该始末点的导数相等； 2阶参数连续性（C 2 ）：在C 1 的基础上，该始末点的二阶导相等； 2. 几何连续性（条件不太苛刻） 0阶几何连续性（G 0 ）：同0阶参数连续性； 1阶几何连续性（G 1 ）：在满足G0条件下，两曲线结合处有公共切矢（方向相同，大小成比例）； 2阶几何连续性（G 2 ）：在满足G1条件下，两曲线结合处有公共曲率；二、Bezier曲线与曲面 1. 曲线段拟合函数可以把曲线表示为许多小线段Φ i （x）之和，其中Φ i （x）称为基（混合）函数； 2. Bezier曲线定义其中系数矢量ai（i=0,1,...,n）顺序首尾相接； 3. 贝塞尔基函数的替换->伯恩斯坦（Bernstain）基函数 1972年，剑桥大学的博士生Forrest在《Computer Aided Design》发表了他一生中最著名的论文。Forrest证明了Bezier曲线的基函数可以简化成伯恩斯坦基函数：一个连续函数y=f(x)，任何一个ξ>0，总能找到一个多项式和这个函数足够逼近。伯恩斯坦这套逼近的理论的形式是： 4. Bezier曲线的再定义针对Bezier曲线，给定空间n

Bezier曲线

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一、Bezier曲线 1、背景知识给定 n + 1 个数据点，生成一条曲线，使得该曲线与这些点所描述的形状相符如果要求该曲线通过所有的数据点，则属于插值问题；如果只要求曲线逼近这些数据点，则属于逼近问题在进行汽车外形设计时，先用折线段勾画出汽车的外形大致轮廓，然后用光滑的参数曲线去逼近这个折线多边形，这个折线多边形被称为特征多边形，逼近多边形的曲线被称为Bezier曲线 2、Bezier曲线的定义 Bezier曲线段的参数方程表示为：（其中Pi是控制多边形的n+1个顶点，即构成该曲线的特征多边形） 3、一次Bezier曲线、二次Bezier曲线和三次Bezier曲线二、Bernstein基函数的性质 1、正性（非负性）：只有当t = 0 或 t = 1时为0，其他情况下均大于0 2、权性：基函数有n + 1项，这些基函数的和加起来正好等于1 来源： https://www.cnblogs.com/SChenqi/p/9776777.html

连续bezier曲线的实现

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需求场景一系列的坐标点，划出一条平滑的曲线 3次Bezier曲线基本上大部分绘图工具都实现了3次Bezier曲线，4个点确定一条3次Bezier曲线。以html5中的canvas为例 let ctx = canvas.getContex('2d'); ctx.moveTo(20,20); // 曲线起点 Fom ctx.bezierCurveTo(20,100,200,100,200,20); // 分别为控制点 Ctrl1,Ctrl2, 终点 To 连续Bezier曲线假定给定点的序列List，我们应该以List中的每个点为起点，其下一个点Next为终点绘制Bezier曲线。所以问题变成，如何确定这两个点之间的两个Bezier控制点。每一小段路径From-To的Bezier曲线并不是独立的，其实收到了其前后两个点的影响（Prev，Next）我们在绘制每一段路径的时候，引入其前点Prev，和后点Next共同计算当前Bezier曲线的控制点Ctrl1,Ctrl2 如图所示绘制从From到To的Bezier曲线，引入Prev,Next作参考点。先依次连线4个点，记为线段l1,l2,l3，并求出其中点c1,c2,c3 连接中点，在c1c2上找一点f1, 使 l1:l2 = c1f1:f1c2。也就是 c1f1 = c1c2 * l1/(l1+l2)。我叫它线段比例法