The attached source code project draws spline curves between two points. Its a cubic spline fitting means program start drawing curve after four clicks.

To run the project, download and unzip the attached file, build and run the project and click on the form.

Main source code:

public struct point
{
public int x;
public int y;
public void setxy(int i,int j)
{
x=i;
y=j;
}
public void clearxy()
{
x=0;
y=0;
}
}
public void BSPLINE(point p1,point p2,point p3,point p4,int divisions)
{
double []a=new double[4];
double []b=new double[4];
a[0] = ( -p1.x + 3*p2.x - 3*p3.x + p4.x)/6.0;
a[1] = ( 3*p1.x - 6*p2.x + 3*p3.x )/6.0;
a[2] = (-3*p1.x + 3*p3.x )/6.0;
a[3] = ( p1.x + 4*p2.x + p3.x )/6.0;
b[0] = ( -p1.y + 3*p2.y - 3*p3.y + p4.y)/6.0;
b[1] = ( 3*p1.y - 6*p2.y + 3*p3.y )/6.0;
b[2] = (-3*p1.y + 3*p3.y )/6.0;
b[3] = ( p1.y + 4*p2.y + p3.y )/6.0;
spline_out_x[0] = a[3];
spline_out_y[0] = b[3];
for (int i = 1 ; i < divisions ; i++)
{
float t;
t = ((float) i) / ((float) divisions);
spline_out_x[i] = a[3] + t*(a[2] + t*(a[1] + t*a[0]));
spline_out_y[i] = b[3] + t*(b[2] + t*(b[1] + t*b[0]));
}
}
public void plus_draw(int x,int y,int pen_width,Color cl )
{
Graphics g = Graphics.FromHwnd(this.Handle);
g.DrawLine(new Pen(cl,pen_width) ,x-3,y,x+3,y);
g.DrawLine(new Pen(cl,pen_width) ,x,y-3,x,y+3);
}
public void Form_MouseUp(object sender, System.Windows.Forms.MouseEventArgs e)
{
if (Movement_Click>3)
{
pt[0]=pt[1];
pt[1]=pt[2];
pt[2]=pt[3];
pt[3].setxy(e.X,e.Y);
int no_of_interpolated_points=(int)(Math.Sqrt(Math.Pow((pt[2].x-pt[1].x),2)+Math.Pow((pt[2].y-pt[1].y),2)));
BSPLINE(pt[0],pt[1],pt[2],pt[3],no_of_interpolated_points);
for (int i=0;i<no_of_interpolated_points;i++)
plus_draw((int )spline_out_x[i],(int)spline_out_y[i],2,Color.Blue);
}
else
{
pt[Movement_Click].setxy(e.X,e.Y);
}
Movement_Click=Movement_Click+1;
plus_draw(e.X,e.Y,1,Color.Red);
}