Topologically Reliable Approximation of Trimmed Polynomial Surface Patches

A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

“…In particular, a narrow interval is obtained in case of a successful operation whereas a wide interval reveals a risk [ 117 ]. This concept may be modified to rounded intervals to assure that the computed endpoints always contain the exact interval, see e.g., [ 3 , 57 , 193 ]. Interval arithmetic may also be combined with backward error analysis [ 255 ].…”

“…In general, tessellations do not require an element connectivity or shape regular elements. However, several authors have presented the construction of conforming meshes for trimmed patches that yield triangles with good aspect ratios [ 55 , 57 , 58 ].…”

On the meshing of trimmed 3D surfaces

“…Another surface tessellation algorithm based on unstructured Delaunay triangulation constructed 2D triangulation domains, which got mapped onto 3D space later, preserving element quality [30].…”

On Wk,p‐manifolds and Wk,p‐surfaces for analysis of the convergence of mesh‐based approximation

“…Thus, mesh-based surface modeling techniques in engineering and computer graphics generally partition manifolds and surfaces into chart sets "disjointly," via boundary curves, often called "trimming curves." Examples of this approach appear in Shimada et al [18], Anglada et al [1], Cho et al [4,5], Klein [11], George and Borouchaki [8], and Borouchaki et al [2]. The disjoint coverings used in this approach are insufficient to define a C k -manifold or surface.…”