Interpolating Curve


I want to drow a curve passing truw n points.

For example : How to drow a circle
with only 6 or 12 points ?


For a circle it’s simple. All you need is two points: the center and a point on the circumference.

For general curves I’ll have to think about it.

The only ways i know about to interpolate points (pass through the points) is curve interpolation using Lagrange polynomals, or B-Splines.

B-Splines are the way to go as Lagrange polynomals are not as smooth and regular as B-Splines.

For the B-Splines, if the multiplicity of the control-points is set to n-1 (n = number of intervals), the curve will interpolate, otherwise it will only approximate a curve near the points.

If you don’t want to go through the points, Bezier-curves are also an option and they are generally easier (and less expensive) to compute.

I guess a google-search on Curve Interpolation , B-Spline/Bezier curves or NURBS should come up with some information.



[This message has been edited by Sven Clauw (edited 05-25-2001).]

[This message has been edited by Sven Clauw (edited 05-25-2001).]

Be forewarned, this is a big topic, the subject of Compute aided graphics design (CAGD). If you want to pas a line THROUGH n points with reasonable continuity, use HERMITE INTERPOLATION.

Bezier curves, B-Splines and Non Uniform Rational B splines/surfaces (NURBs) have control points that do not necessarily go through the n points.

[This message has been edited by iss (edited 05-27-2001).]