An Implicit Complexes Framework for Heterogeneous Objects Modelling

Kartasheva, Elena; Adzhiev, Valery; Comninos, Peter; Fryazinov, Oleg; Pasko, Alexander

doi:10.1007/978-3-540-68443-5_1

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…These unit cells have the unit cell size u = 10 mm, the beam diameter d = 1 mm, and the node diameter D = 1.1 mm. F-rep is a powerful geometric modeling technique that greatly expands the complexity of the solid models it can produce [30]. This method, however, introduces additional complexity to the design process itself by providing more complex tools to model solid bodies.…”

Section: Function Representation Applicability For Geometric Modeling...mentioning

confidence: 99%

Beam-Based Lattice Topology Transition With Function Representation

Letov

Zhao

2022

Journal of Mechanical Design

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A lattice structure is a porous periodic structure with unit cells organized according to a pattern. Lattice structures are lightweight parts that are commonly produced by additive manufacturing techniques. Lattice structures require their topology defined which effectively defines the connectivity of their unit cell. Many of these topologies are beam-based, i.e. their unit cell is represented by a network of nodes connected with beams. Such lattice structures require a geometric modeling tool capable of generating their solid model. This paper presents a method to support the topology transition for beam-based lattice structures by controlling the geometric parameters of topologies. This control is made possible with the function representation of the geometry. The work also analyzes how suitable different beam-based lattice topologies are to support the transition. A few case studies are carried out to demonstrate the feasibility of the proposed method.

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Section: Function Representation Applicability For Geometric Modeling...mentioning

confidence: 99%

Beam-Based Lattice Topology Transition With Function Representation

Letov

Zhao

2022

Journal of Mechanical Design

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“…The implicit building of parametric functions defining the intersection and flattened curves is an important property shared by other 3D modeling techniques such as the implicit complex (IC) framework of Kartasheva et al [19] (the third condition of the definition of a graphical cell in the IC). However, CEDG is based on locus-based parametric functions, which differ completely from the IC concept.…”

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confidence: 99%

Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (CeDG)

Prado-Velasco

García-Ruesgas

2023

Symmetry

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Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. CeDG may calculate a parametric implicit functional form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study first presents the theoretical foundations and methodology to calculate those curves. Secondly, a compound hopper is defined and modeled through CeDG (implemented in GeoGebra) and CAD (Solid Edge© 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for he intersection and flattening of surfaces and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study.

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