Smooth Conjugate Net vs. Curvature-Line Parametrization

Question

so I was wondering what a smooth conjugate net exactly is, intuitively? Also, what exactly is a curvature-line parametrization? What would it mean that a smooth conjugate net is orthogonal? Why is it then a curvature-line parametrization?

Best

Fluffs

Answer 1

This figure is alone quite informative:

Kambe, Tsutomu. Geometrical Theory of Dynamical Systems and Fluid Flows. No. 23. World Scientific, 2004.

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A second source, with spectacular images:

Liu, Yang, Weiwei Xu, Jun Wang, Lifeng Zhu, Baining Guo, Falai Chen, and Guoping Wang. "General planar quadrilateral mesh design using conjugate direction field." In ACM Transactions on Graphics (TOG), vol. 30, no. 6, p. 140. ACM, 2011. (PDF download.)

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