Isogeometric segmentation: The case of contractible solids without non-convex edges

Isogeometric segmentation: Construction of auxiliary curves

“…Let c(u), 0 ≤ u ≤ 1, be a spline curve of degree p ≥ 1 and associated with a knot vector U given by (2). Assume that c fulfils Condition (C − 2).…”

“…For context, we briefly outline the strategy described in [2,3] for segmenting a solid. For our purposes, a solid is represented by a collection of trimmed surfaces, together with incidence [2,3], a segmentation of the solid into topological hexahedra was given in [19] and shown to be suitable for isogeometric analysis.…”

“…For our purposes, a solid is represented by a collection of trimmed surfaces, together with incidence [2,3], a segmentation of the solid into topological hexahedra was given in [19] and shown to be suitable for isogeometric analysis. For the examples of that paper, a preliminary version of the present paper's method was used to produce the auxiliary curves.…”

“…In [2,3] the search for a cutting loop is ''combinatorial'' in the sense that it only results in a description of the list of faces, edges and vertices the closed curve passes through. The cutting loop generally consists of a combination of edges already existing in the solid's edge graph, as well as new auxiliary edges that need to be added to split some faces into two.…”

“…In [2,3] we initiated the development of a method for isogeometric segmentation, that is, the segmentation of a contractible boundary represented solid into boundary represented topological hexahedra (sufficiently smooth images of cubes). In order to be suitable for isogeometric analysis, the number of topological • Search the edge graph of the solid (the graph formed by the edges shared by trimmed surfaces) for a cutting loop: a closed curve in the boundary of the solid which can be used as the boundary of a surface that splits the solid into two simpler solids (see Fig.…”