On the Parameterization and the Geometry of the Configuration Space of a Single Planar Robot

Different poses of 3D models are very often given in different positions and orientations in space. Since most of the computer graphics algorithms do not satisfy geometric invariance, it is very important to bring shapes into a canonical coordinate frame before any processing. In this paper we consider the problem of finding the best alignment between two or more different poses of the same object represented by triangle meshes sharing the same connectivity. Firstly, we developed a method to select a region of interest (ROI) which has a perfect alignment over the two poses (up to a rigid movement). Secondary, we solved a simplified version of the Largest Common Point-set (LCP) problem with a-priori knowledge about point correspondence, in order to align the ROIs. We eventually align the poses performing least square rigid registration. Our method makes no assumption about the starting positions of the objects and can also be used with more than two poses at once. It is fast, non-iterative, easy to reproduce and brings the poses into the best alignment whatever the initial positions are.