Quasi-Isotropic Initial Triangulation of NURBS Surfaces

Abstract

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.