The problem with a smooth curve is that you need to know the curvature at each (3D) point in-between the known points. Which is equivalent to having to calculate the function at each of those points. Or, if you know the formula for the function, taking the partial derivatives and working out from them how far along you can go before continuing on in a straight line would be "too far" from the real curve and putting an adjustment there.
Some people use cubic splines to draw smooth curves. I my view, cubic splines "look pretty" but are unjustified if determining the actual value at any particular intermediate point is going to happen. Don't confuse the approximation with the real thing.