Fully Automated Subdivision Surface Parametrization for Topology Optimized Structures and Frame Structures Using Euclidean Distance Transformation and Homotopic Thinning

Truss Parametrization of Topology Optimization Results with Curve Skeletons and Meta Balls

“…Recent skeleton-based reverse engineering approaches choose to extrude primitive cross-sections along these skeleton lines (Cuillière et al, 2018;Nana et al, 2017;Stangl and Wartzack, 2015) or apply free form surface reconstruction (Bremicker et al, 1991;Denk et al, 2021b). Afterward, the shape is assembled using an implicit representation CSG of these cylindrical primitives (Cuillière et al, 2018;Nana et al, 2017) or connecting the control points of the explicit free form surfaces (Bremicker et al, 1991;Denk et al, 2021b). The fundamental concept of these medial balls of the unification of each ball is covered by the unification of cylinders and spheres (Cuillière et al, 2018;Nana et al, 2017) or the selection of reasonable control point positions (Bremicker et al, 1991;Denk et al, 2021b).…”

“…If this verification fails, automatic adjustment is required, especially for optimization results with a large number of branches, as often occurs in thermal topology optimization (Joo et al, 2018). Converting topology optimization results into such parametrization is one of the recent research challenges, which can be solved by curve (Denk et al, 2021b;Yin et al, 2020) or surface skeletons (Denk et al, 2021c). The original concept of skeletons is derived from Blum's medial skeletons (Blum, 1967).…”

“…The original shape itself can be fully restored by the unification of these balls. Recent skeleton-based reverse engineering approaches choose to extrude primitive cross-sections along these skeleton lines (Cuillière et al, 2018;Nana et al, 2017;Stangl and Wartzack, 2015) or apply free form surface reconstruction (Bremicker et al, 1991;Denk et al, 2021b). Afterward, the shape is assembled using an implicit representation CSG of these cylindrical primitives (Cuillière et al, 2018;Nana et al, 2017) or connecting the control points of the explicit free form surfaces (Bremicker et al, 1991;Denk et al, 2021b).…”

“…Afterward, the shape is assembled using an implicit representation CSG of these cylindrical primitives (Cuillière et al, 2018;Nana et al, 2017) or connecting the control points of the explicit free form surfaces (Bremicker et al, 1991;Denk et al, 2021b). The fundamental concept of these medial balls of the unification of each ball is covered by the unification of cylinders and spheres (Cuillière et al, 2018;Nana et al, 2017) or the selection of reasonable control point positions (Bremicker et al, 1991;Denk et al, 2021b). CSG can lead to an implicit representation with sharp edges, while free form surfaces can leads to a smooth but explicit representation (Bremicker et al, 1991;Denk et al, 2021b).…”

“…The fundamental concept of these medial balls of the unification of each ball is covered by the unification of cylinders and spheres (Cuillière et al, 2018;Nana et al, 2017) or the selection of reasonable control point positions (Bremicker et al, 1991;Denk et al, 2021b). CSG can lead to an implicit representation with sharp edges, while free form surfaces can leads to a smooth but explicit representation (Bremicker et al, 1991;Denk et al, 2021b). An implicit smooth shape descriptor is desirable due to advances in topology modification or the use of Boolean operations.…”