The animation of virtual characters driven by data is one of the key topics in computer graphics . In this context , a motion is classically defined by a list of skeletons over time, each of them is described by a vector of positions and rotations. The 3D mesh is then controlled by the skeletons by a rigging step between the skeleton and the mesh. In this document, we propose to study other representations of the motion through a set of spatial relationships. Two approaches are proposed : the first considers the motion in the metric space and the second characterizes each posture by a differential representation using the Laplacian operator. First, we propose to represent the postures of the motion by a set of distances. The goal is to produce new motions from an editing process or kinematic inversions. We show that this representation allows a simple and intuitive control of the animation of a character. It also has several properties exploitable in the context of motion analysis . This last point is illustrated by an original application of motion retrieval in large databases. Next, we define the motion by a set of graphs. The vertices are characterized by a differential information. Through this representation, we propose a new method to edit a motion coupling constraints of distance and the use the discrete Laplacian operator. This operator preserves the spatial relationships during the edition of the motion and the constraints of distance preserve the properties of the induced skeleton . This concept allows us to propose three applications dedicated to the reconstruction and the edition of motions : (i) an interactive system to edit sequences of skeletons using the discret 3D+t Laplacian operator ; (ii) reconstruction of marker trajectories (iii) animation of mesh constrained by an implicit skeleton and driven by markers trjactories.
