The Frenet apparatus is a recently developed framework for constructing high order geometry-conforming immersed finite element (GC-IFE) functions for interface problems. In this report, we present computational details for constructing the local GC-IFE bases on interface elements, including procedures based on singular value decomposition to produce a GC-IFE basis with a desirable orthonormal feature. A sample implementation in Matlab is provided to illustrate involved construction procedures and facilitate adoption of the GC-IFE method.