Two-point Hermite interpolation in biangular coordinates

We construct 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, , 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.