In Summary...
Summary:
- piecewise cubic is generally sufficient
- define conditions on the curves and their continuity
- solve the linear system; if knot spacing is uniform, you obtain a constant basis matrix, so same basis functions for every piece
- can use a nonuniform knot spacing, changing the u-values, to vary tension
-
Things to know:
- basic curve properties (what are the conditions, controls, and properties for each spline type)
- generic matrix formula for uniform cubic splines x(u) = uBG
- given definition derive a basis matrix (do not memorize matrices themselves)
- how curves are generalized to surfaces