Biarcs and bilens

Biarc curves are considered from the standpoints of the theory of spirals and Möbius maps. Parametrization and reference formulae, covering the whole variety of biarcs, are proposed. A region is constructed, enclosing all spirals with common circles of curvature at the endpoints. This region, named bilens, is bounded by two biarcs.

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► Simplest spirals, biarcs curves, are explored from the viewpoints of the theory of spirals and Möbius maps.
► Parametrization is proposed for the whole variety of biarcs.
► Region is constructed, bounded by two biarcs and enclosing all spirals with given G2G2 Hermite data.