General skinning techniques aim to deform the surface of an articulated model following the pose change of a skeleton. Their rapidity makes them ideal tools for real-time animation purposes. However, popular skinning algorithms are simple, but they tend to generate undesirable geometric artefacts. In our work, we consider skeletons given in the form of sphere-mesh models controlling both the pose and morphology of the shape that is either described as a mesh or a raw point set. We propose a novel skinning method that encodes the point set details above a bundle of baselines covering the sphere-mesh. In particular, we propose a geometrical model of the baseline and detail direction evolution during bone twisting and joints bending rotations. Our approach works directly on point sets and thus preserves the accuracy of the initial sampling. It further avoids computing a weight per point or a costly explicit muscle modelling step. We evaluate our method on several articulated body point sets, showing that it creates fewer artefacts than classical methods.