Christian Gentil

Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited

Abstract. Voluntary arm-raising movement performed during the upright human stance position imposes a perturbation to an already unstable bipedal posture characterised by a high body centre of mass (CoM). Inertial forces due to arm acceleration and displacement of the CoM of the arm which alters the CoM position of the whole body represent the two sources of disequilibrium. A current model of postural control explains equilibrium maintenance through the action of anticipatory postural adjustments (APAs) that would offset any destabilising effect of the voluntary movement. The purpose of this paper was to quantify, using computer simulation, the postural perturbation due to arm raising movement. The model incorporated four links, with shoulder, hip, knee and ankle joints constrained by linear viscoelastic elements. The input of the model was a torque applied at the shoulder joint. The simulation described mechanical consequences of the arm-raising movement for different initial conditions. The variables tested were arm inertia, the presence or not of gravity field, the initial standing position and arm movement direction. Simulations showed that the mechanical effect of arm-raising movement was mainly local, that is to say at the level of trunk and lower limbs and produced a slight forward displacement of the CoM (1.5 mm). Backward arm-raising movement had the same effect on the CoM displacement as the forward arm-raising movement. When the mass of the arm was increased, trunk rotation increased producing a CoM displacement in the opposite direction when compared to arm movement performed without load. Postural disturbance was minimised for an initial standing posture with the CoM vertical projection corresponding to the ankle joint axis of rotation. When the model was reduced to two degrees of freedom (ankle and shoulder joints only) the postural perturbation due to arm-raising movement increased compared to the four-joints model. On the basis of these results the classical assumption that APAs stabilise the CoM is challenged.

The Local Fractional Derivative of Fractal Curves

Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.

Joining Primal/Dual Subdivision Surfaces

In this article we study the problem of constructing an intermediate surface between two other surfaces defined by different iterative construction processes. This problem is formalised with Boundary Controlled Iterated Function System model. The formalism allows us to distinguish between subdivision of the topology and subdivision of the mesh. Although our method can be applied to surfaces with quadrangular topology subdivision, it can be used with any mesh subdivision (primal scheme, dual scheme or other.) Conditions that guarantee continuity of the intermediate surface determine the structure of subdivision matrices. Depending on the nature of the initial surfaces and coefficients of the subdivision matrices we can characterise the differential behaviour at the connection points between the initial surfaces and the intermediate one. Finally we study the differential behaviour of the constructed surface and show the necessary conditions to obtain an almost everywhere differentiable surface.

Modeling of human posturokinetic movements by a linear feedback system: relations among feedback coefficients.

This study describes a method of modeling human trunk and whole body backward bending and suggests a possible neural control strategy. The hypothesis was that the control system can be modeled as a linear feedback system, in which the torque acting at a given joint is a function of the state variables (angular positions and angular velocities). The linear system enabled representation of the feedback system by a gain matrix. The matrix was computed from the kinematics recorded by a movement analysis system and from the joint torques calculated by inverse dynamics. To validate the control model, a comparison was made between the angular kinematics yielded by the model and the experimental data. Moreover, for all subjects, the same relationships between feedback coefficients were found although gain values were different. The study showed that the feedback system is an appropriate model of the strategy from performing an accurate controlled trunk or whole body backward bending in the sagittal plane.

Barycentric Combinations Based Subdivision Shaders

We present a new representation of uniform subdivision surfaces based on Iterated Functions Systems formalism. Main advantages of this new representation are the formalization of topological subdivision, multiscale representation of limit surface, separation of iterative space where the attractor is computed once for all and modeling space where the attractor is projected many times. An important consequence of this approach is that all uniform subdivision schemes are handled in the same way whatever there are primal or dual, approximating or interpolating. Subdivision surfaces are no longer viewed as a set of rules but as a list of barycentric combinations to apply on neighborhoods of the coarse mesh. These combinations are representative subsets of the attractor which is deduced from a Controlled Iterated Functions System automaton. From this new point of view we present in this paper a straightforward implementation to directly compute a tessellation of the subdivision surface from a control mesh. This implementation takes full advantage of Graphics Processing Units high capability of computation and Tessellation Stage of OpenGL/GLSL rendering pipeline to generate on the fly a tessellation of the limit surface with a chosen Level of Details.

Boundary Controlled Iterated Function Systems

Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a powerful tool allowing creation of an object with a prescribed topology (e.g. surface patch) independent of its geometrical texture. We also show how to impose constraints on the IFS transformations to guarantee the production of smooth shapes.