But, since you mention a sequence of arcs, you may be interested to know that a very common usage of splines is to create a sequence of low-order splines, such as cubic. A cubic Bezier is a 4-point spline that you can think of as a curve defined by 2 end points and 2 tangents. Place a bunch of those back to back, and you can have an arbitrarily long curve where the effect of moving any point in the curve is localized to 2 segments of the chain, and none of the other segments will change.
Using a higher order spline where moving any point will affect the whole curve is pretty uncommon in practice, I think. At least for practice that includes modeling and animating in film & video games.
For example: http://www.moreprocess.com/computer-graphics/interpolation-a...
There are a bunch of interpolating splines.
But, since you mention a sequence of arcs, you may be interested to know that a very common usage of splines is to create a sequence of low-order splines, such as cubic. A cubic Bezier is a 4-point spline that you can think of as a curve defined by 2 end points and 2 tangents. Place a bunch of those back to back, and you can have an arbitrarily long curve where the effect of moving any point in the curve is localized to 2 segments of the chain, and none of the other segments will change.
Using a higher order spline where moving any point will affect the whole curve is pretty uncommon in practice, I think. At least for practice that includes modeling and animating in film & video games.