Drawing Cardinal Splines

A cardinal spline is a curve that passes smoothly through a given set of points. To draw a cardinal spline, create a Graphics object and pass the address of an array of points to the DrawCurve method. The following example draws a bell-shaped cardinal spline that passes through five designated points:

Dim points As Point() = { _
   New Point(0, 100), _
   New Point(50, 80), _
   New Point(100, 20), _
   New Point(150, 80), _
   New Point(200, 100)}
      
Dim pen As New Pen(Color.FromArgb(255, 0, 0, 255))
e.Graphics.DrawCurve(pen, points)
[C#]
Point[] points = {
   new Point(0, 100),
   new Point(50, 80),
   new Point(100, 20),
   new Point(150, 80),
   new Point(200, 100)};

Pen pen = new Pen(Color.FromArgb(255, 0, 0, 255));
e.Graphics.DrawCurve(pen, points);

The following illustration shows the curve and five points.

You can use the DrawClosedCurve method of the Graphics class to draw a closed cardinal spline. In a closed cardinal spline, the curve continues through the last point in the array and connects with the first point in the array.

The following example draws a closed cardinal spline that passes through six designated points:

Dim points As Point() =  { _
   New Point(60, 60), _
   New Point(150, 80), _
   New Point(200, 40), _
   New Point(180, 120), _
   New Point(120, 100), _
   New Point(80, 160)}
      
Dim pen As New Pen(Color.FromArgb(255, 0, 0, 255))
e.Graphics.DrawClosedCurve(pen, points)
[C#]
Point[] points = {
   new Point(60, 60),
   new Point(150, 80),
   new Point(200, 40),
   new Point(180, 120),
   new Point(120, 100),
   new Point(80, 160)};

Pen pen = new Pen(Color.FromArgb(255, 0, 0, 255));
e.Graphics.DrawClosedCurve(pen, points);

The following illustration shows the closed spline along with the six points.

You can change the way a cardinal spline bends by passing a tension argument to the DrawCurve method. The following example draws three cardinal splines that pass through the same set of points:

Dim points As Point() =  { _
   New Point(20, 50), _
   New Point(100, 10), _
   New Point(200, 100), _
   New Point(300, 50), _
   New Point(400, 80)}
      
Dim pen As New Pen(Color.FromArgb(255, 0, 0, 255))
e.Graphics.DrawCurve(pen, points, 0F)
e.Graphics.DrawCurve(pen, points, 0.6F)
e.Graphics.DrawCurve(pen, points, 1F)
[C#]
Point[] points = {
   new Point(20, 50),
   new Point(100, 10),
   new Point(200, 100),
   new Point(300, 50),
   new Point(400, 80)};

Pen pen = new Pen(Color.FromArgb(255, 0, 0, 255));
e.Graphics.DrawCurve(pen, points, 0.0f);
e.Graphics.DrawCurve(pen, points, 0.6f);
e.Graphics.DrawCurve(pen, points, 1.0f);

The following illustration shows the three splines along with their tension values. Note that when the tension is 0, the points are connected by straight lines.