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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