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spline conversion

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I start with a hermite spline with a list of components: time T, point (x, y, z), intan vector (x1, y1, z1), and outtan vector (x2, y2, z2). I want to convert that into a bezier curve in the form of point(T, X), bezier point(t2, x2), bezier point(t3,x3) and repeat that for y and z. I have the conversion of hermite to bezier(the matrix) but my problem is that the berzier curve is in time and offset while the hermite is in 3d. I guess some way I could interpolate through the curve to create an approximation but is there an easier way to create it component for component?

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