Computer-Aided Design最新文献

Complex architectural structures may be built in a simple and cost-effective way if their geometry respects the fabrication constraints. Examples of such structures are provided by gridshells that are built from straight and flat slats which are bent on site so that they become tangential or normal to the design surface. Tangential slats follow geodesic curves on the surface, while normal slats are attached along asymptotic curves. Extending work by Frei Otto, Julius Natterer and others, who placed the slats tangentially, Eike Schling proposed structures which also contain slats normal to the reference surface. In the present paper we address those gridshells that consist of three families of bent elements, either tangential or normal to the design surface, and are arranged in a triangular web. We propose algorithms for the computational design of such webs that start from a boundary strip and propagate it, partially under additional guidance, to an entire web.

We present several algorithms for evaluating point containment in constructive solid geometry (CSG) trees with unbounded primitives. Three algorithms are presented based on postfix, prefix, and infix notations of the CSG binary expression tree. We show that prefix and infix notations enable short-circuiting logic, which reduces the number of primitives that must be checked during point containment. To evaluate the performance of the algorithms, each algorithm was implemented in the OpenMC Monte Carlo particle transport code, which relies on CSG to represent solid bodies through which subatomic particles travel. Two sets of tests were carried out. First, the execution time to generate a rasterized image of a 2D slice of three CSG models of varying complexity was measured. Use of both prefix and infix notations offered significant speedup over the postfix notation that has traditionally been used in particle transport codes, with infix resulting in a 6$\times$ reduction in execution time relative to postfix for a model of a tokamak fusion device. We then measured the execution time of neutron transport simulations of the same three models using each of the algorithms. The results and performance improvements reveal the same trends as for the rasterization test, with a 5.52$\times$ overall speedup using the infix notation relative to the original postfix notation in OpenMC for the tokamak model.

This paper addresses two problems needed to support four-dimensional ($3d+t$) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface points of the geometry are embedded in a four-dimensional space as the geometry moves in time. The geometry is first tessellated at prescribed time steps and then these tessellations are connected in the parameter space of each geometry entity to form tetrahedra. In contrast to previous work, this approach allows the resolution of the geometry to be controlled at each time step. The only restriction on the algorithm is the requirement that no topological changes to the geometry are made (i.e. the hierarchical relations between all geometry entities are maintained) as the geometry moves in time. The validity of the final mesh topology is verified by ensuring the tetrahedralizations represent a closed 3-manifold. For some analytic problems, the $4d$ volume of the tetrahedralization is also verified. The second problem addressed in this paper is the design of a system to interactively visualize four-dimensional meshes when the $4d$ view changes, including tetrahedra (embedded in $4d$) and pentatopes. Algorithms that either include or exclude a geometry shader are described, and the efficiency of each approach is then compared. Overall, the results suggest that visualizing tetrahedra (either those bounding the domain, or extracted from a pentatopal mesh) using a geometry shader achieves the highest frame rate, realizing interactive frame rates of at least 15 frames per second for meshes with about 50 million tetrahedra.

Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to cater to diverse functional regions in heterogeneous models. Previous studies on blending methods for porous structures have mainly focused on controlling the shape of blending regions, yet they have fallen short in effectively addressing topological errors in blended structures. This paper introduces a new blending method that successfully addresses this issue. Initially, a novel initialization method is proposed, which includes distinct strategies for blending regions of varying complexities. Subsequently, we formulate the challenge of eliminating topological errors as an optimization problem based on persistent homology. Through iterative updates of control coefficients, this optimization problem is solved to generate a blended porous structure. Our approach not only avoids topological errors but also governs the shape and positioning of the blending region while remaining unchanged in the structure outside blending region. The experimental outcomes validate the effectiveness of our method in producing high-quality blended porous structures. Furthermore, these results highlight potential applications of our blending method in biomimetics and the design of high-stiffness mechanical heterogeneous models.