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History
- In parallel to the Costa's work, Camillo investigated the
parallel nature of the Cosserat surface and analyzed in his
Mestrado's thesis the potential
of improving the algorithm's performance with a GPU
implementation.
- Costa deepened the investigation on the application of the surface
deformation model to triangular meshes in
his Mestrado's thesis. He dove
into the
estimation of the covarian derivatives of surface deformation and
spin tensors at each vertex of a triangular mesh, since those physical
quantities are crucial to the deformation model.
- With use of Qt, Pinho implemented
in his Mestrado's thesis an
interface to the surface deformation model proposed by De Melo.
He also investigated a way to improve its implementation
in order to make its running time comparable with the
mass-spring system. He applied an explicit time integration
schema. Inspired by the work of
Szymon Rusinkiewicz,
Batagelo proposed in his Doutorado's thesis
a noval procedure for computing principal curvatures
and principal directions. On the basis of this work,
an algorithm
that estimates per-vertex metric and curvature tensors for the principal
directions was implemented. This allows Pinho to carry out some
experiments with triangular meshes. He faced several problems
related with the estimation of the covariant derivatives of several
physical quantities.
- De Melo proposed in his Doutorado's
thesis to model a deformable surface as a Cosserat surface
and presented an implementation for a rectangular mesh. A
finite-difference spatial discretization and semi-implicit time
integration schemas were used.
- Malheiros investigated in
his Mestrado's thesis a more
intuitive way to manipulate directly an implicitly defined soft
object. He implemented a system called Prototype Implicit
Modeler to allow modeling interactively an object from a set of
spherical primitives. He was so envolved with the interaction
techniques that he participated intensively in the design of
the first version of the manipulation toolkit
MTK.
- In his Mestrado's thesis, Ramos
analyzed thoroughly the model proposed by Terzopoulos et al. by performing
a large range of simulations on the Eter. He intended not
only to validate it, but also to devise a more systematic way to
specify the values for the model parameters in order to get the expected
visual effects. During his experimentations, he perceived that it is
difficult to obtain with the system a realistic behavior for surfaces which
have resistance against bending. One possible problem source may come
from the lack in the control of the relationship between the metric
and curvature tensors of a surface while it is deforming - it is known
that the metric and curvature tensors must satisfy certain
compatibility differential equations known as Gauss formula and
Mainardi-Codazzi equations. His exhaustive tests confirmed the
conjecture, but he observed that the compatibility equations are not
sufficient for producing nice animations.
- The elastically deformable model proposed by Terzopoulos, Platt,
Barr, and Fleischer relates the Lagrangian motion equation (physics of
deformation) with the metric and curvature tensors of the deforming
surface (geometric properties). The metric tensors measure the
variation of the area of the deforming surface and the curvature
tensors give us the amount that a surface bends while it is
deforming. Its potential for providing a more intuitive way to specify
the desired deformation has motivated Horta to implement during his Mestrado's thesis the algorithm presented
in the paper entitled "Elastically Deformable Models" (ACM Computer
Graphics 21/4, p. 205-214, 1987) in C language. The Meschach Library is used
for performing calculations on matrices and vectors, and for solving
systems of linear equations (dense and sparse). The system is named
Eter.
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