Heterogeneous parametric trivariate fillets

Masalha, Ramy; Cirillo, Emiliano; Elber, Gershon

doi:10.1016/j.cagd.2021.101970

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…Among the applications discussed, the enforcement of the weak continuity is probably the more interesting from a geometric modeling point of view. In a recent work [28], Masalha and colleagues proposed a procedure for creating heterogeneous parametric trivariate fillets. Despite the interesting geometric algorithms proposed, the obtained fillets are not connected to the original objects and therefore new fillets need to be created every time a deformation applies to the input objects.…”

Section: Discussionmentioning

confidence: 99%

Region extraction in mesh intersection

Antolín¹,

Buffa²,

Cirillo³

2021

Preprint

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Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special case of intersection detection among two unstructured meshes. While classical region extraction algorithms for line drawings and mesh intersection algorithms have proved to be able to deal with many applications, the advances in Isogeometric Analysis require a generalization of such problem to the case in which the regions to be extracted are bounded by an arbitrary number of curved segments. In this work we present a novel region extraction algorithm that allows a precise numerical integration of functions defined in different spline spaces. The presented algorithm has several interesting applications in contact problems, mortar methods, and quasi-interpolation problems.

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Section: Discussionmentioning

confidence: 99%

Region extraction in mesh intersection

Antolín¹,

Buffa²,

Cirillo³

2021

Preprint

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“…Fan et al [11] designed a honeycomb lattice structure and a sandwich structure with better mechanical properties than the solid structure, but the model is only two-dimensional. Masalha et al [12] studied several algorithms to construct heterogeneous or trivariate fillets that support smooth filleting operation. The results verify the feasibility of the algorithms.…”

Section: Related Workmentioning

confidence: 99%

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Chen¹,

Liang²,

Ye³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Lattice structures with excellent physical properties have attracted great research interest. In this paper, a novel volume parametric modeling method based on the skeleton model is proposed for the construction of threedimensional lattice structures. The skeleton model is divided into three types of nodes. And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes. The unit-cell is assembled with distinct nodes according to the geometric features. The final lattice structure is created by the periodic arrangement of unit-cells. Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method. The quality is assessed in terms of the value of the Jacobian matrix. Moreover, the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

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“…Following Masalha et al (2021), given two adjacent freeform surfaces in IR 3 , the half Boolean sum operator constructs a trivariate in which two of its boundaries interpolate the two input surfaces. Herein, we also consider a variant of this operator for a surface from two adjacent curves in IR 2 or IR 3 , in Section 3.1, and a trivariate from two/three adjacent surfaces in IR 3 , in Section 3.2.…”

Section: Half Boolean Summentioning

confidence: 99%

“…As part of this work, we consider three geometric constructors: ruling, Boolean sum, and half Boolean sum, a simpler variation of the Boolean sum that was introduced in Masalha et al (2021). We will first consider the case of planar input curves that construct a planar surface, and then, the spatial case where the input curves and/or surfaces in IR 3 synthesize a trivariate.…”

Section: Introductionmentioning

confidence: 99%