1. max
bigger
small

2. max

3. Explodes!!!
max

7. Rotate by theta_x (theta degrees about x-axis)
Rotate by pi/2 around y axis (Note previous +x axis).
Rotate by theta_z (undoing initial theta_x)
(theta is constant, subscript just indicates axis of rotation.)

8. Two Frames with Different Topology

9. Instantaneous Self-intersection

10. Unknot

11. Bad
Approximation!
Self-intersect?

12. Good Approximation! Respects Embedding: Curvature (local) &
Separation (global)
Error bounds!! =>
Nbhd_2 about curve.
But recognizing unknot in NP (Hass, L, P, 1998)!!