Re: Basic : Bezier Problems

I'm not familiar with Bézier curves, but from what it says on wikipedia it's not going to go through the 4 points used to generate it. The 4 points act like guide points that determine the curve, but do not lie on it.

If you want any arbitrary curve that goes trough any four points, you could just use a fourth degree polynomial. (That extends to n points and an n degree polynomial.)

Did you need a particular type of curve? I'm not sure I understand your question (or its context).

Re: Basic : Bezier Problems

MathHead,

I want to use a Bezier or Catmull-ROM to go through the 4 points. And there is a reason for it to use a bezier curve.

The example i gave in the first post apparently, the bezier curve goes through the 1st and last point but not 3rd and 4th. And i guess it creates a convex hull. Therefore, I would like to know how to find the control point for point 2 & point 3, so that the curve goes through point 1, 2,3,4.

Re: Basic : Bezier Problems

Given two points that line on curve , and given , find .

If we let , then

We now have two equations and two variables to solve for. The answers will be in terms of , and I'm not sure how to go about deriving from , but I hope it's a start.