mathematical optimization - Moving some of the control points of a bezier curve with minimal change to its length -

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mathematical optimization - Moving some of the control points of a bezier curve with minimal change to its length -

given bezier curve defined p0 (1-t)^3 + 3p1 (1-t)^2 t + 3p2 (1-t) t^2 + p3 t^3 t=0..1, p0, p1, p2, , p3 command points of bezier curve, find how command points adjacent 1 moved need adjusted alter overall length of bezier curve after command points have been moved minimized. if, example, moving p3, want adjust position p2, if moving p2, want adjust positions of both p1 , p3, since both adjacent moved command point. in case there multiple solutions, solution adequate.

i am, ideally, looking algorithm feasible utilize in interactive scheme user may drag 1 point , adjacent ones updated in real time per above description, if no computationally efficient algorithm exists (eg, entire length of resulting bezier curve must recalculated scratch each , every frame), that's matter need know, consider if costs incurred create such interactive scheme non-viable.

mathematical-optimization bezier-curve

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