[dahart]

It of course depends on what you need, what you’re doing. The cubic Bézier curves with handles are probably the best thing for animation curves, specifically because having handles allow you to break the continuity of the curve, and change direction suddenly. Animators need this when tweaking motion curves on a timeline. Think of abrupt changes in speed, like with collisions.

Splines with tangent handles are much better for font design as well, than splines without handles.

Splines defined by points and not tangents are useful for different reasons, and they’re not great if you want to have sharp changes of angle. You can do it by duplicating control points, but that causes some math mayhem in some situations.

In computer graphics people use the “Catmull-Rom” spline a lot, which is a type of interpolating spline that goes through the control points. https://en.wikipedia.org/wiki/Centripetal_Catmull–Rom_spline

People also use the B-spline as well, which is smoother and nicer than the Catmull-Rom spline, but it’s an approximating spline that doesn’t usually go exactly through the control points. https://en.wikipedia.org/wiki/B-spline

Both of these get used in CG for hair and fur - which is a good example of an application of curves that doesn’t require sharp angles along the splines.