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。 /// <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 + P3
      firstControlPoints[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 – P0
      secondControlPoints[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 vector
    double[] rhs = new double[n];

    // Set right hand side X values
    for (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-values
    double[] x = GetFirstControlPoints(rhs);

    // Set right hand side Y values
    for (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-values
    double[] y = GetFirstControlPoints(rhs);

    // Fill output arrays.
    firstControlPoints = new Point[n];
    secondControlPoints = new Point[n];
    for (int i = 0; i < n; ++i)
    {
      // First control point
      firstControlPoints[i] = new Point(x[i], y[i]);
      // Second control point
      if (i < n - 1)
        secondControlPoints[i] = new Point(2 * knots
          [i + 1].X - x[i + 1], 2 *
          knots[i + 1].Y - y[i + 1]);
      else
        secondControlPoints[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)​​