C#绘制带控制点的Bezier曲线，用于点阵图像及矢量图形

【摘要】不借助第三方, 使用c# + GDI+进行SVG等绘图，绘制带控制点的Bezier曲线。可用于点阵图像及矢量图形（如SVG）绘图。先看效果：
(不知为何，已两次上传图片，无法显示，求助csdn)图注：使用方法二绘制。方法一：
/// <summary>
/// Bezier样条曲线
/// </summary>
public static class BezierSpline
{/// <summary>/// Get open-ended Bezier Spline Control Points./// </summary>/// <param name="knots">Input Knot Bezier spline points.</param>/// <param name="firstControlPoints">Output First Control points/// array of knots.Length - 1 length.</param>/// <param name="secondControlPoints">Output Second Control points/// array of knots.Length - 1 length.</param>/// <exception cref="ArgumentNullException"><paramref name="knots"/>/// parameter must be not null.</exception>/// <exception cref="ArgumentException"><paramref name="knots"/>/// array must contain at least two points.</exception>public static void GetCurveControlPoints(Point[] knots,out Point[] firstControlPoints, out Point[] secondControlPoints){if (knots == null)throw new ArgumentNullException("knots");int n = knots.Length - 1;if (n < 1)throw new ArgumentException("At least two knot points required", "knots");if (n == 1){ // Special case: Bezier curve should be a straight line.firstControlPoints = new Point[1];// 3P1 = 2P0 + P3firstControlPoints[0].X = (2 * knots[0].X + knots[1].X) / 3;firstControlPoints[0].Y = (2 * knots[0].Y + knots[1].Y) / 3;secondControlPoints = new Point[1];// P2 = 2P1 – P0secondControlPoints[0].X = 2 *firstControlPoints[0].X - knots[0].X;secondControlPoints[0].Y = 2 *firstControlPoints[0].Y - knots[0].Y;return;}// Calculate first Bezier control points// Right hand side vectordouble[] rhs = new double[n];// Set right hand side X valuesfor (int i = 1; i < n - 1; ++i)rhs[i] = 4 * knots[i].X + 2 * knots[i + 1].X;rhs[0] = knots[0].X + 2 * knots[1].X;rhs[n - 1] = (8 * knots[n - 1].X + knots[n].X) / 2.0;// Get first control points X-valuesdouble[] x = GetFirstControlPoints(rhs);// Set right hand side Y valuesfor (int i = 1; i < n - 1; ++i)rhs[i] = 4 * knots[i].Y + 2 * knots[i + 1].Y;rhs[0] = knots[0].Y + 2 * knots[1].Y;rhs[n - 1] = (8 * knots[n - 1].Y + knots[n].Y) / 2.0;// Get first control points Y-valuesdouble[] y = GetFirstControlPoints(rhs);// Fill output arrays.firstControlPoints = new Point[n];secondControlPoints = new Point[n];for (int i = 0; i < n; ++i){// First control pointfirstControlPoints[i] = new Point(x[i], y[i]);// Second control pointif (i < n - 1)secondControlPoints[i] = new Point(2 * knots[i + 1].X - x[i + 1], 2 *knots[i + 1].Y - y[i + 1]);elsesecondControlPoints[i] = new Point((knots[n].X + x[n - 1]) / 2,(knots[n].Y + y[n - 1]) / 2);}}/// <summary>/// Solves a tridiagonal system for one of coordinates (x or y)/// of first Bezier control points./// </summary>/// <param name="rhs">Right hand side vector.</param>/// <returns>Solution vector.</returns>private static double[] GetFirstControlPoints(double[] rhs){int n = rhs.Length;double[] x = new double[n]; // Solution vector.double[] tmp = new double[n]; // Temp workspace.double b = 2.0;x[0] = rhs[0] / b;for (int i = 1; i < n; i++) // Decomposition and forward substitution.{tmp[i] = 1 / b;b = (i < n - 1 ? 4.0 : 3.5) - tmp[i];x[i] = (rhs[i] - x[i - 1]) / b;}for (int i = 1; i < n; i++)x[n - i - 1] -= tmp[n - i] * x[n - i]; // Backsubstitution.return x;}
}

方法二：

private void DrawCurve(Graphics g, PointF[] points, float tension)
{
int n=points.Length;
Pen rPen = new Pen(Color.Red, 2f);
Pen blPen= new Pen(Color.Blue, 1f);
Pen bzPen = new Pen(Color.DarkGoldenrod, 2f);
for (int i = 0; i < n; ++i)
{
// draw segment points[i] - points[(i + 1) % n]
var pPrev1 = points[(i - 1 + n) % n];
var p1 = points[i];
var p2 = points[(i + 1) % n];
var pAfter2 = points[(i + 2) % n];

// tangents 切线控制点
var t1 = new PointF(tension * (p2.X - pPrev1.X), tension * (p2.Y - pPrev1.Y));
var t2 = new PointF(tension * (pAfter2.X - p1.X), tension * (pAfter2.Y - p1.Y));

// interior Bezier control points
var c1 = new PointF(p1.X + t1.X / 3.0f, p1.Y + t1.Y / 3.0f);
var c2 = new PointF(p2.X - t2.X / 3.0f, p2.Y - t2.Y / 3.0f);

//画贝塞尔曲线
g.DrawBezier(bzPen, p1, c1, c2, p2);

//画关键点到切线控制点的直线
g.DrawLine(blPen, p1, c1);
g.DrawEllipse(rPen, p1.X - 2, p1.Y - 2, 4, 4);
g.DrawEllipse(rPen, c1.X - 2, c1.Y - 2, 4, 4);

g.DrawLine(blPen, p2, c2);
g.DrawEllipse(rPen, p2.X - 2, p2.Y - 2, 4, 4);
g.DrawEllipse(rPen, c2.X - 2, c2.Y - 2, 4, 4);

g.FillEllipse(new SolidBrush(Color.Green), new RectangleF(p1.X-2, p1.Y-2, 4, 4));

}
}

方法二的调用方法：

//这里使用的是Panel上绘图，其他控件（如PictureBox)道理一样。

Graphics g = pnlWorkArea.CreateGraphics();
g.Clear(Color.White);
g.CompositingQuality = CompositingQuality.HighQuality;
g.InterpolationMode = InterpolationMode.HighQualityBicubic;
g.SmoothingMode = SmoothingMode.HighQuality;
g.TextRenderingHint = TextRenderingHint.AntiAliasGridFit;
PointF[] points = { new PointF(568,200),new PointF(168,110),new PointF(60,186),new PointF(300,191),new PointF(600,300),new PointF(800,431),new PointF(300,650), new PointF(568, 200) };
float tension=0.68f;
DrawCurve(g, points, tension);

这里有一个不错的链接：

C# GraphicsPath AddBeziers(params System.Drawing.Point[] points)

C# GraphicsPath AddBeziers(System.Drawing.PointF[] points)

源码也可以在此下载：C#带控制点的贝塞尔Bezier曲线算法(源码)-C#文档类资源-CSDN下载

C#绘制带控制点的Bezier曲线，用于点阵图像及矢量图形相关推荐

计算机图形学：Bezier曲线的绘制
1.实验目的掌握Bezier曲线的定义原理及绘制过程定义: 贝塞尔曲线(Bezier 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 ...
rms | 如何绘制模型带置信区间的预测曲线
前段时间,有读者咨询如何绘制带置信区间的预测曲线.本篇介绍的rms工具包可以很简便地解决这个问题. 该包是Regression Modeling Strategies的附加学习资源,小编从网上找到了这 ...
android曲线位移动画,Bezier曲线在Android动画中的应用
Android动画的开发中,为了达到更加酷炫的效果,常常需要自定义运动轨迹,或者绘制花式复杂的曲线,这正是Bezier曲线大显神通的地方,本文将带你了解Bezier曲线在Android开发中的一些应用 ...
bezier曲线_Bezier算法
个人博客: vectormoon's blogwww.vectormoon.net bezier算法的背景 vm公司设计出了一个原型车--moon,这样的: 产品经理一看觉得有点抽象,他使用了Bez ...
计算机图形学E10——Bezier曲线
其他计算机图形学实验见链接 #include<gl/glut.h> #include<iostream> #include<algorithm> #include ...
开源项目推荐：Bezier曲线、B-Spline和NURBS的区别与《THE NURBS BOOK 2nd》简介，曲线拟合可视化工具
一.基本概念 B-Spline:B样条曲线 NURBS(Non Uniform Rational B-Spline):非均匀有理B样条曲线 B样条曲线有三种类型: 当起始点和终止点的重复度为最高次数加 ...
Bezier曲线、B样条和NURBS的基本概念
最不能理解的一点,一讨论软件的曲面,曲线功能,最后就变成曲线.曲面的数学原理的讨论了,但是里面也没数学好的,讨论的结果可想而知. 我不是数学家,我不懂这么复杂的方程,只要好用就行了. 在CAD中,设计 ...
Bezier曲线曲面绘制
知识点: Bezier曲面性质 Bezier曲线简单理解代码参考:https://blog.csdn.net/wpxu08/article/details/70208395 曲线 #include ...
lisp 非对称缓和曲线_利用AutoLISP语言绘制带缓和曲线的铁路曲线平面图
利用 AutoLISP 语言绘制带缓和曲线的铁路曲线平面图 [ 摘要 ] 通过 AutoLISP 编程方法的剖析 , 探讨了基于 Visual LISP(VLISP) 编程软件环境下 , 利用 Aut ...

C#绘制带控制点的Bezier曲线，用于点阵图像及矢量图形

C#绘制带控制点的Bezier曲线，用于点阵图像及矢量图形相关推荐

最新文章

热门文章