Curve Fitting
Find Nice-looking curve through these points
Complicated,fluctuated,slow
from mechanics
piece together N-1 cubic curves together smoothly
(1)
(2)
(3)
4N-4 unknowns
4N-4 equations
Gaussian Elimination can do
Let the curves be S as described as fallows,
Curse
we have the properties:
to show how (2) stands:
so,
, such that
and note that:
Spline curve
With the two properties above, all we have to do is to determine Pi through the first differential equations:
which leads us to simple matrix computation.
Solve
, then plug them to Si to finish the approach.