geometry - Converting a cubic bezier curves into a cardinal spline and back -


i've read many articles describe how convert cardinal or canonical splines cubic bezier curves, such this one.

is there way reverse, i.e. convert set of cubic bezier curves cardinal spline? know, example, endpoints of each curve on spline.

what i'm looking way roundtrip through 2 representations minimal loss of information. ideally solution should stable, going cubic bezier => cardinal spline => cubic bezier => cardinal spline should result in same (or same) curves after second operation.

imagine cubic curve between points b , e.
if defined cardinal spline tension parameter s, tangent vectors in these points are

tb = s * (e - a)
te = s * (f - b)

if curve defined bezier one, tangent vectors

tb = 3 * (c - b)
te = 3 * (e - d)

if curve same, values of tangents equal, , can find control points of bezier, if a,b,e,f,s known. , vice versa - can find a,f points cardinal spline, if b,c,d,e,s known. example, first control point of bezier is

c = b + s * (e - a) / 3

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