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Dirk Gregorius

Editing Bezier Splines while maintaining C1 Continuity

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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.




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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.

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