Finsleroids with three axes in dimension

We study the dependence of three-axes positive-definite Finsleroid metric functions on the Finsleroid azimuthal angle \(\theta \) in the three-dimensional case, provided the condition of the angle-separation in the involved characteristic functions is fulfilled. The complete set of algebraic and differential equations characterizing the class of three-axes positive-definite Finsleroid metric functions is derived and explicit dependence of the involved characteristic functions on the angle \(\theta \) is obtained.