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raduvro

convex curvex in 3D

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Consider curves in 2D parametrized by t, say p(t). A segmentation into convex parts of the curve p(t) can be achieved by finding the inflection points using the cross product p'(t) x p"(t) = 0 What about curves in 3D ? the equation p'(t) x p"(t) = 0 still can be solved for t but is that all that needs to be taken into account ? What I mean, can we consider a curve to be convex in 3D or is that notion limited to plane curves only. Do you take other parameters as torsion in 3D ? Please let me know your thoughts on this one, radu

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I'm not sure what would you mean by convexity if the curve is not planar. If it is planar, however, then the formula remains the same, of course. To check whether your curve is planar or not, you need to decide whether the mixed product [p'(t),p''(t),p'''(t)] is always 0 or not (=whether the three vectors are coplanar or not).

edit: of course, you can partition your curve into segments with torsion having the same sign, but it depends on what you want to do after that whether it helps or not.

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