The Construction of the Dupin Cyclides in a Smectic A Polygonal Texture

Figure 3

Two different main curvature radii for two surfaces: a torus and a Dupin cyclide, both characterized by the same value of 𝜇 (𝜇=4 for the drawing). For the figure, 𝑎=5 and 𝑏=4. The two circles correspond to the curvature lines (in green) of radii 𝑅₁ and 𝑅₂, respectively, at any point 𝑀 of each surface; (a) 𝑅₁(torus)=−1 and 𝑅₂(torus)=4 and (b) 𝑅₁(cyclide)=−1 and 𝑅₂(cyclide)=1.

(a)

(b)