Surface triangulation over intersecting geometries

Abstract

SUMMARYA method for the rapid construction of meshes over intersecting triangulated shapes is described. The method is based on an algorithm that automatically generates a surface mesh from intersecting triangulated surfaces by means of Boolean intersection/union operations. After the intersection of individual components is obtained, the exposed surface parts are extracted. The algorithm is intended for rapid interactive construction of non-trivial surfaces in engineering design, manufacturing, visualization and molecular modelling applications. Techniques to make the method fast and general are described. The proposed algorithm is demonstrated on a number of examples, including intersections of multiple spheres, planes and general engineering shapes, as well as generation of surface and volume meshes around clusters of intersecting components followed by the computation of flow field parameters.

Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance

“…Moreover, the Laplacian smoothing that is used to reposition the inserted nodes does not always ensure a valid result [23]. The workflow developed by Shostko et al is also quite similar to our since it computes the intersection lines, removes the intersecting faces and remeshes the created holes using an advancing front mesh generation method [24]. Here, all the points at the intersection between an edge and a triangle are taken into account which results in degenerated triangles.…”

Finite element mesh generation over intersecting curved surfaces by tracing of neighbours

“…Another is to use discrete data structure such as tessellate facets and triangular facets [1]. For engineering applications, surfaces defined by discrete data are widely adopted, for instance, in the presentation of complex molecules [2][3][4][5], engineering design [6], visualization [7] and computational models for analysis by the finite element method [4][5][6]8], etc. There are at least three ways for the construction of complex surface models of triangulated facets.…”

“…The second is parametric mapping approach [17][18][19][20] which mesh the parametric domain followed by a mapping process of the resulting mesh onto the surface. The third approach is to construct models by using Boolean operations such as intersection [6,8] and union between groups of surfaces composed of triangular facets. A great variety of objects can be easily created by selectively putting together various surface parts derived from surface intersections.…”

“…A great variety of objects can be easily created by selectively putting together various surface parts derived from surface intersections. This approach has been explored and applied in the field of finite element mesh generation [21,22], molecules model [6], engineering design [23,24], etc.…”

“…It would be very time consuming if we try to detect intersections by examining all the triangular facets on two groups of surfaces a pair of triangles at a time. The process can be speeded up by using a bounding box technique [6,24] to filter out all triangles of the two groups of surfaces that are too far apart and cannot possibly have intersection. Additional data structure can also be set up to further reduce searching for intersections [23,24].…”