The most common nowadays is some variety of planar elements:
Double curved roofs cannot be covered with regular planar materials, only with shingles.
Bamboo-shingles from flattened culms. Unfortunately, as exposed to rains and UV-radiation from the sun, they will not last for a long time.
*If exploring new horizons, check out the WIP tag and Natural Rubber!

Hyperbolic Paraboloid roof with half-in-half joints.
This structure can actually be built with rectilinear elements! - but the surface is still
double
curved!
Half-in-half joint
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