Two Types of Continuity
Parametric Continuity: Ck
- x(u), y(u), z(u) each individually continuous through kth derivative
- (value, slope, 2nd derivative, …)
- Important for motion curves (parameter is time).
Geometric Continuity: Gk
- curve in xyz (independent of u) continuous through kth derivative
- (position, tangent, curvature, …)
- Important if the parameter is irrelevant.
A curve can be Ck without being Gk and vice versa!
- can you think of examples?