Open Science Research Excellence
%0 Journal Article
%A Oscar E. Ruiz and  Carlos Cadavid and  Juan G. Lalinde and  Ricardo Serrano and  Guillermo Peris-Fajarnes
%D 2008 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 20, 2008
%T Gabriel-constrained Parametric Surface Triangulation
%V 20
%X The Boundary Representation of a 3D manifold contains
FACES (connected subsets of a parametric surface S : R2 -!
R3). In many science and engineering applications it is cumbersome
and algebraically difficult to deal with the polynomial set and
constraints (LOOPs) representing the FACE. Because of this reason, a
Piecewise Linear (PL) approximation of the FACE is needed, which is
usually represented in terms of triangles (i.e. 2-simplices). Solving the
problem of FACE triangulation requires producing quality triangles
which are: (i) independent of the arguments of S, (ii) sensitive to the
local curvatures, and (iii) compliant with the boundaries of the FACE
and (iv) topologically compatible with the triangles of the neighboring
FACEs. In the existing literature there are no guarantees for the point
(iii). This article contributes to the topic of triangulations conforming
to the boundaries of the FACE by applying the concept of parameterindependent
Gabriel complex, which improves the correctness of the
triangulation regarding aspects (iii) and (iv). In addition, the article
applies the geometric concept of tangent ball to a surface at a point to
address points (i) and (ii). Additional research is needed in algorithms
that (i) take advantage of the concepts presented in the heuristic
algorithm proposed and (ii) can be proved correct.
%P 568 - 575