Two-point G1G1 Hermite interpolation in biangular coordinates

•The equations of most curves in biangular coordinate system are not yet known.•We construct G1G1 Hermite interpolating curves in biangular coordinates.•Interpolation problem reduces to choosing suitable functions in biangular coordinates.•The simplest linear equations correspond to the sectrix of Maclaurin.•Proposed interpolation method may reduce the computational cost in some cases.

We construct G1G1 Hermite interpolating curves in biangular coordinates, and provide sufficient conditions for their convexity. In a biangular coordinate system, the problem reduces to that of choosing suitable functions interpolating the biangular coordinates of the curve at its end points. The simplest linear equations, γ=((1−t)α,tβ)γ=((1−t)α,tβ), in biangular coordinates correspond to a sectrix of Maclaurin, which we extend by introducing two shape parameters that pull the curve towards the sides of its triangular envelope. In addition, we consider a class of curves whose biangular coordinates have a constant sum, and we analyze their shape and curvature.

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