Construction of spline curves on smooth manifolds by action of Lie groups

Abstract

Polynomials for blending parametric curves in Lie groups are defined. Properties of these polynomials are proved. Blending parametric curves in Lie groups with these polynomials is considered. Then application of the proposed technique to construction of spline curves on smooth manifolds is presented. As an example, construction of spherical spline curves using the proposed approach is depicted.