Powerfull and flexible way is using bezier curves,

"Quadratic" bezier is a curve done using 3 points just like in your example,
"cubic" bezier is a curve done using 4 points.

Code:
function Calculate_Quadratic_Bezier(A, B, C: taffinevector; T: Single): taffinevector;
var
 Sn : single;
begin
   t:=1-t;
   Sn:=1-t;
   result.X := A.x*t*t + B.x*2*t*Sn + C.x*sn*sn;
   result.Y := A.y*t*t + B.y*2*t*Sn + C.y*sn*sn;
   result.Z := A.z*t*t + B.z*2*t*Sn + C.z*sn*sn;
end;

function Calculate_Cubic_Bezier(A, B, C, D: taffinevector; T: Single): taffinevector;
var
 Sn : single;
begin
   t:=1-t;
   Sn:=1-t;
   result.X := A.x*t*t*t + B.x*3*t*t*Sn + C.x*3*t*Sn*Sn + D.x*Sn*Sn*Sn;
   result.Y := A.y*t*t*t + B.y*3*t*t*Sn + C.y*3*t*Sn*Sn + D.y*Sn*Sn*Sn;
   result.Z := A.z*t*t*t + B.z*3*t*t*Sn + C.z*3*t*Sn*Sn + D.z*Sn*Sn*Sn;
end;
That also works for 2d points, just ignore Z component.

The "T" parameter is a value between 0..1 that allow you to calc the next point coordinate in the curve as much points you want in your curve, for example if you want to use 100 points for draw your curve then calc each point position using t values from 0.01 to 1.00; if you want to draw a curve with lets say 20 points then you do somthing like f:=1/20 and then use f as a factor into a 20 step loop for calc the points.

Full explanation with awesome animations can be found here:

http://en.wikipedia.org/wiki/B%C3%A9zier_curve