History: Ramos's Mestrado Thesis

In this work an OOGL output file format is added to Eter for inspecting the generated results with help of Geomview.

Two control levels are distinguished in order to make easier assigning appropriate value to each parameter in the following equations in order to generate the set of all desirable visual effects:

\begin{displaymath} \mu\frac{{\partial}^{2}\vec{r}}{{\partial}{t}^{2}}+ \gamma\f... ...elta\varepsilon(\vec{r})}{\delta\vec{r}}= \vec{f}(\vec{r},t)~. \end{displaymath}
\begin{displaymath} \epsilon({\bf\vec{r}})=\int_{\Omega}\sum_{i,j}(\eta_{ij}(G_{... ...G^{0}_{ij})^{2}+\xi_{ij}(B_{ij}-B^{0}_{ij})^{2}) da_{1} da_{2} \end{displaymath}

  • Macro Control

    By assigning adequate values for $\mu$, $\gamma$, and $\vec{f}$, one may have an inaccurate, but intuitive control of the object's dynamics. All points in the surface assume equal values of $\mu$ and $\gamma$, considering that the surface is homogeneous with respect to the environment in which it is immersed.

  • Micro Control

    The variations in the local geometry of each point is caused by the material's resistance to variations in stretching and curving. That effect can be controlled by properly setting the elasticity parameters $\eta_{ij}$ and $\xi_{ij}$, respectively.

Moreover, it is presented a heuristic procedure for choosing the range of the parameter values for the model in order to ensure numerical stability without resorting to the reduction in the time integration intervals. The procedure works at least for most of examples we tested.

Finally, aiming at getting an algorithm for determining a set of conditions under which the system of equations is often poorly contitioned, it is implemented a routine that indicates when the Mainardi-Codazzi compatibility equation is violated during the simulation. From exhaustive tests, we may conclude that the violation of the Mainardi-Codazzi always leads to a bad conditioning system. This condition is, however, not sufficient.