Hi
I want to drow a curve passing truw n points.
For example : How to drow a circle
with only 6 or 12 points ?
xav
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.
Greets,
Sven
[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. http://www.cubic.org/~submissive/sourcerer/hermite.htm
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).]