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Quasi-isotropic initial triangulation of NURBS surfaces
Isotropic triangulation of NURBS surfaces provides high quality triangular meshes, where
all triangles are equilateral. This isotropy increases representation quality and analysis
accuracy. We introduce a new algorithm to generate quasi-isotropic triangulation on
NURBS surfaces at once, with no prior meshing. The procedure consists of one front made
of vertexes that advances in a divergence manner avoiding front collision. Vertexes are
calculated by intersecting arcs whose radius is estimated by trapezoidal rule integration of
directional derivatives. The parameter space is discretized in partitions such that the error
of trapezoidal rule is controlled efficiently. A new space, called pattern space, is used to
infer the direction of the arcs’ intersection. Derivatives, whose analytical computation is
expensive, are estimated by NURBS surface fitting procedures, which increases the speed
of the process. The resultant algorithm is robust and efficient. The mesh achieved
possesses most of the triangles equilateral and with high uniformity of sizes. The
performance is evaluated by measuring angles, vertex valences and size uniformity in
different numerical examples