A distance-based approach for human posture simulations

Human-like characters can be modeled by suitable skeletal structures, which basically consist in trees where edges represent bones and vertices are joints between two adjacent bones. Motion is then defined as variations of the joints' configuration (i.e., partial rotations) over time, which also influences joint positions. However, this representation does not allow to easily represent the relationship between joints that are not directly connected by a bone. This work is therefore based on the premise that variations of the relative distances between such joints are important to represent complex human motions. While the former representations are currently used in practice for playing and analyzing motions, the latter can help in modeling a new class of problems where the relationships in human motions need to be simulated. Our main interest in this work is in adapting previously captured human postures (one frame of a given motion) with the aim of satisfying a certain number of geometrical constraints, which turn out to be easily definable in terms of distances. We present a novel procedure for approximating the relative inter-joint distances for skeletal structures having arbitrary features and respecting a predefined posture. This set of inter-joint distances defines an instance of the Distance Geometry Problem (DGP), that we tackle with a non-monotone spectral gradient method.