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Triathlon

Member

Registered: 2022-04-27

Posts: 2

Linking two Bézier curves

Hi,
I'm in 2D, and I have a Bézier curve defined by three points A, B, C.
I have two other points next to the curve, D and E, and I want to make a second Bézier curve C, D, E (having a common point (C) with the first curve).
My question is : How do I calculate the coordinates of point D to make the second curve continuous (tangent) with the first one.

I guess there are infinite possibilities to position point D to have the second curve continuous with the first one. What can I do?

Thanks

Triathlon

Member

Registered: 2022-04-27

Posts: 2

Re: Linking two Bézier curves

I got an answer :

For Bézier curves, the tangent at the end point is collinear with the direction to the nearest control point. In this case, it means that for the two curves to be tangential, points B, C and D must lie on a straight line.

mathdrop

Member

Registered: 2022-03-07

Posts: 75

Re: Linking two Bézier curves

What is the source of the answer, you have got ?

May you tell us something about the problem, you are trying to solve ?

For instance with a qubic spline,
you could just give the points A, C, E and B, D would not be an issue.
Do you need B ?