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• Bezier - A Bezier basis generates a 3D curve that passes through every third control vertex. The remaining control vertex positions are used to determine the incoming and outgoing tangent of the curve of the adjacent vertex that the curve does pass through. When using a Bezier basis with curves that contain multiple segments (that is, more than 4 control points), some care should be taken to ensure that incoming and outcoming tangents line up at vertices that are on the rendered curve, or there will be a discontinuity in the smoothness of the curve where it suddenly changes direction.
• B-Spline - While a B-Spline basis function can be somewhat less intuitive to use in that it generates a curve that typically only approximately comes close to passing through the given control vertices, an advantage is that this basis function tends to yield very smooth curves. Discontinuities in the smoothness of the curve are possible if multiple control vertices are repeated consecutively (aka multiplicity).
• Catmull-Rom - This basis function generates a curve that is guaranteed to pass through every interior, non-endpoint control vertex, and it tends to generate smooth curves, although there can sometimes be unexpected "wobbles" in areas of high curvature with this basis function choice (see images below for an example). Using a B-Spline basis instead can smooth out the wobbles, although a B-Spline basis typically produces a curve that does not pass through the control vertices exactly, unlike the Catmull-Rom basis (for non-endpoint control vertices).
• Linear - Specifying linear curves yields straight line segments, continuous linear segments in a curve are joined with a round cap.

 The example below shows how different basis affects the shape of a curve given the exact same control vertices: while control vertices and the curve hull is drown in white, the curve is drawn in yellow.

It is common practice to use B-Spline and Catmull-Rom curves with multiplicity at curves extremities to better control where the curve begins and ends. Note that in order for such types of curve basis to end at the exact position of the first and last curve control vertex, these have to be repeated one more time Catmull-Rom and two more times for B-Splines.

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