New Things
- dT/ds (derivative of the Unit Tangent with respect to S) = rate of change in direction as we move along the curve.
- ||dT/ds|| = “curviness” of the curve, curvature
- κ = Curvature = ∥∥dT/ds∥∥
- ρ = 1/κ = Radius of curvature
Curvature
- Here, we see that when looking at curvature, you can imagine a circle that is tangent to a space curve.
- A sharper curve would indicate a smaller tangent circle
- A straight part of the curve would indicate that there is zero curvature
- The radius of curvature (ρ) is the radius of that tangent circle
Torsion
τ = Torsion = twistiness of the curve = rate of change of direction at B as we move along the curve = ||dB/ds|| ⇐ GENERAL FORM
- Derivation for Torsion
