Generating spirals with predefined boundary conditions

Spirality, considered as monotonicity of curvature, is preserved under inversions. This property is used to construct a spiral transition curve with predefined curvature elements at the end points. These boundary conditions define two invariant values: Coxeter's inversive distance and the width of the lense. To solve the problem, it is sufficient to realize corresponding values on two curvature elements of any known spiral. The rest is achieved by inversion. In particular, any boundary conditions, compatible with spirality, can be satisfied by inverting an arc of logarithmic spiral. Bibl. – 9 titles.