This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.

In this article, we propose a unified variational framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton–Jacobi‐based formulations. The key idea is the introduction of an auxiliary domain, geometrically identical to the physical design domain, occupied by fictitious matter which is dynamically excited by the conditions prevailing in the design domain. By assigning kinetic and potential energy to this matter and interpreting the level set function as the generalized coordinate to describe its deformation, the governing equation of motion is determined via Hamilton's principle, yielding a modified wave equation. Appropriate combinations of model parameters enable the recovery of classical physical behaviors, including the standard and biharmonic wave equations. The evolution problem is formulated in weak form using variational methods and implemented in the software environment FreeFEM++. The influence of the numerical parameters is analyzed on the example of minimum mean compliance. The results demonstrate that topological complexity and strut design can be effectively controlled by the respective parameters. Notably, the proposed formulation inherently supports the nucleation of new holes and maintains a well‐defined level set function without requiring explicit re‐initialization procedures, both of which emerge naturally from the physically motivated variational framework. The inclusion of a damping term further enhances numerical stability. To showcase the versatility and robustness of our method, we also apply it to compliant mechanism design and a bi‐objective optimization problem involving self‐weight and compliance minimization under local stress constraints.

During the maintenance period of a future fusion reactor power plant, called DEMOnstration Power Plant (DEMO), remotely handled casks are required to confine and handle DEMO in-vessel components during their transportation between the reactor and the active maintenance facility. In order to limit the dispersion of activated dust, a Contamination Control Door (CCD) is designed to be placed at an interface between separable containments (e.g., vacuum vessels and casks) to inhibit the release of contamination at the interface between them. The remotely operated CCD—technically, a double lidded door system—consists of two separable doors (the cask door and port door) and three different locking mechanisms: (i) between the cask door and cask, (ii) between the cask door and port door and (iii) between the port door and port. The locking mechanisms are selected and assessed according to different criteria, and the structure of the CCD is optimized using an Abaqus Topology Optimization Module. Due to the elastic properties of the CCD, deflections will occur during the lifting procedure, which may lead to malfunctions of the CCD. A test rig is developed to investigate the performance of high-risk components in the CCD in the case of deflections and also malpositioning. Misalignment can be induced along three axes and three angles intentionally to test the single components and items. The aim is to identify a possible range of operating in the case of misalignments. It is expected that the proposed CCD design should be able to operate appropriately in the case of ±3 mm translational misalignments and ±1° rotational misalignments.

With the function RooTri(), we present a simple and robust calculation method for the approximation of the intersection points of a scalar field given as an unstructured point cloud with a plane oriented arbitrarily in space. The point cloud is approximated to a surface consisting of triangles whose edges are used for computing the intersection points. The function contourc() of Matlab is taken as a reference. Our experiments show that the function contourc() produces outliers that deviate significantly from the defined nominal value, while the quality of the results produced by the function RooTri() increases with finer resolution of the examined grid.

In this paper, an alternative design approach to the construction of bridge crane systems is analyzed with respect to the potentials and challenges of use based on two possible construction methods. Compared to conventional crane bridges, which are manufactured as a single part, the innovation of the approach relates to designing the crane bridge in segments and assembling it from standardized individual components, which are small in dimension, to form a plug-in structure. These are then prestressed by means of a tensile member to establish the load-bearing capacity. The motivation of the alternative design concept arises from a challenging manufacturing and costly transportation of common crane bridges. Here, the different design approaches are first presented as to how a segmental crane bridge can be constructed and which function the involved components fulfill. In this context, the novel construction method also gives rise to new constraints that are not covered by the common design standards and are therefore discussed. The paper concludes with a comparative study to identify advantages and disadvantages of both concepts regarding defined criteria with the aim of determining design improvements and elaborates the potentials and challenges of the approach with respect to a future industrial implementation. Moreover, these findings additionally form the basis for further research work in this area.