Sign in to follow this  
Dirk Gregorius

Editing Bezier Splines while maintaining C1 Continuity

Recommended Posts

I have constructed a (cubic) Bezier spline from some input points by building a Catmull Rom spline first and then convert it to a Bezier spline. I want to manipulate the individual control vertices now, but maintain C1 continuity.

 

The best I came up with so far is this:

- If I manipulate a knot I can use the same strategy as used for Catmull Rom splines (e.g. compute the tangent and update also the incoming and outgoing vertex)

- If I manipulate an 'internal' control vertex I might just apply the equal and opposite translation to the corresponding vertex to keep them aligned.

 

I googled for spline/curve editing/manipulation, but couldn't find anything useful so I was wondering if anyone can point me into the right direction.

 

Thanks,

-Dirk 

Share this post


Link to post
Share on other sites

To maintain C1 continuity between consecutive (cubic) Bézier splines you have to maintain the following equations:

 

P3(i-1) - P2(-1) = P1(i) - P0(i)

P3(i-1) = P0(i)

 

where the index in the parenthesis represents the index of the curve in the spline. The derivative/tangent at the beginning (end) of Bézier curve is in fact parallel to the edge between the first two (last two) control points. If the two curves have different degree you have to multiply each part of the equation with the degree of the corresponding curve.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this