Yes / This work presents an efficient and fast method for achieving cyclic animation using Partial Differential Equations (PDEs). The boundary-value nature associ- ated with elliptic PDEs offers a fast analytic solution technique for setting up a framework for this type of animation. The surface of a given character is thus cre- ated from a set of pre-determined curves, which are used as boundary conditions so that a number of PDEs can be solved. Two different approaches to cyclic ani- mation are presented here. The first consists of using attaching the set of curves to a skeletal system hold- ing the animation for cyclic motions linked to a set mathematical expressions, the second one exploits the spine associated with the analytic solution of the PDE as a driving mechanism to achieve cyclic animation, which is also manipulated mathematically. The first of these approaches is implemented within a framework related to cyclic motions inherent to human-like char- acters, whereas the spine-based approach is focused on modelling the undulatory movement observed in fish when swimming. The proposed method is fast and ac- curate. Additionally, the animation can be either used in the PDE-based surface representation of the model or transferred to the original mesh model by means of a point to point map. Thus, the user is offered with the choice of using either of these two animation repre- sentations of the same object, the selection depends on the computing resources such as storage and memory capacity associated with each particular application.

No / In this work we propose a modelling technique for producing cyclic motions of human body. The surface of the human body has been created from a set of pre-configured curves that were used as the set of boundary conditions to solve a number of partial differential equations (PDE). These boundary curves are attached to a skeletal system that holds the animation for cyclic motions. An important function of the method described here is the use of mathematical expressions within Maya software for generating the cyclic motion leading to a very realistic movement. Thus, the user can interactively manipulate the position and movement of various body parts to achieve various cyclic motions. Finally the animation can be transferred to either the original mesh model from where the boundary curves associated with the PDE surface were extracted or to another mesh model with equivalent topology.