How to create a curve using interpolating points

Hi all,In my project I want to create surface out of curve.So in order to do that I want to create curves from points.When creating curves it does’t go through my points.Is there any solution to do this.I can’t use nurbs since it does not interpolate.Any suggection.I’m using Opengl with Qt.

To me this seems more like a math/geometry question than an OpenGL one, a forum focused on the former may get you better answers.
My understanding is you are looking for interpolation instead of approximation curves. They differ in how closely they are required to follow the positions defined by their control points. This Wikipedia page shows the derivation for interpolating cubic splines.