Calculus

곡률, 비틀림률

Kreamsoup 2021. 10. 25. 16:09

$$\text{곡률}$$
$$\kappa(t)=|\frac{dT}{ds}|=\frac{|T'(t)|}{|r'(t)|}=\frac{|r'(t) \times r''(t)|}{|r'(t)|^3}$$

$$\text{비틀림률}$$
$$\tau(t)=-\frac{dB}{ds}\cdot N = -\frac{B'(t)\cdot N(t)}{|r'(t)|} = \frac{[r'\times r'']}{|r'\times r''|^2}\cdot r'''$$