Statics Aware Grid Shells

Pietroni, Nico; Tonelli, Davide; Puppo, Enrico; Froli, Maurizio; Scopigno, Roberto; Cignoni, Paolo

doi:10.1111/cgf.12590

Cited by 41 publications

(30 citation statements)

References 28 publications

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“…Many problems in this eld share two distinct yet interrelated themes: the assurance of static soundness and the reduction of manufacturing cost. Static soundness has been explored in the context of 3D printing [Langlois et al 2016;Prévost et al 2013;, furniture [Umetani et al 2012], gridshell structures [Pietroni et al 2015], and selfsupporting surfaces [Block and Ochsendorf 2007;de Goes et al 2013;Panozzo et al 2013;Vouga et al 2012]. To reduce manufacturing cost, researchers looked at the use of o -the-shelf parts [Schulz et al 2014], simpli cation of geometric components [Liu et al 2006;Tang et al 2016], and construction using repetitive elements [Fu et al 2010;Huard et al 2014;.…”

Section: Previous Workmentioning

confidence: 99%

Design and volume optimization of space structures

et al. 2017

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Fig. 1. Le : A statically sound space structure designed and optimized with our framework, motivated by the real architectural project shown in Figure 2. Right: The space structure is constructed with six types of customized beams to minimize the total volume of the material used for beams while maintaining moderate manufacturing complexity. Here, a ho er color indicates a larger beam cross-section area. Our framework automatically determines the optimal cross-section areas of the six types of beams as well as the assignment of beam types.We study the design and optimization of statically sound and materially e cient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we rst jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with xed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and e ciency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

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Section: Previous Workmentioning

confidence: 99%

Design and volume optimization of space structures

et al. 2017

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“…Common variants are two directions with πradians RoSy, four directions with π/2 RoSy, or two independent pairs of directions with π RoSy within each pair. These symmetry properties are very natural in many applications, for instance when dealing with principal curvature directions [Hertzmann and Zorin 2000], principal directions of stress or strain tensors [Pietroni et al 2015], conjugate directions [Liu et al 2011;Diamanti et al 2014], or Langer's lines [Marcias et al 2013;Bommes et al 2013b], to name a few.…”

Section: Types Of Directional Fieldsmentioning

confidence: 99%

“…The problem is formulated in the language of DEC in [de Goes et al 2013], where the new metric of the stress tensor is expressed by the hodge star. The metric is also altered by a 2 2 -direction field to deform a mesh in a statics-aware way in [Pietroni et al 2015].…”

Section: Architectural Geometrymentioning

confidence: 99%

Directional field synthesis, design, and processing

Vaxman

Campen

Diamanti

et al. 2017

ACM SIGGRAPH 2017 Courses

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SummaryDirection fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges. PrerequisitesThe audience should have some prior experience with triangle mesh representation of geometric models, and a working knowledge of vector calculus, linear algebra, and general computer graphics fundamentals. Some familiarity with the basics of differential geometry and numerical optimization are helpful, but not required. Intended AudienceThe course targets researchers and developers who seek to understand the concepts and technologies used in direction field and vector field synthesis, learn about the most recent developments, and discern how this powerful tool, which has had impact in a variety of research and application areas, might benefit their area of work. Participants will get a broad overview, and obtain the knowledge on how to choose the proper combination of techniques for many relevant tasks. SourcesThese notes are largely based on the following state-of-the-art report by the lecturers. It has been extended to include updates on the most recent developments. • The course was subsequently given at SIGGRAPH Asia 2016, including demos and real-time coding sessions. The entire course, including the notes, the presentation slides, and the demos, is provided in the following open-source GitHub repository: https://github.com/avaxman/DirectionalFieldSynthesis Further ReadingBeing a relatively young and developing topic, no textbooks covering the various aspects of directional field synthesis in the context of computer graphics and geometry processing are available. The notes of a recent course on vector field processing offer another perspective on parts of the topic, with a focus on the discrete differential geometry aspects:• F. Her current interests are in geometry processing and modeling, specifically on vector field design, surface parametrizations, and inter-surface mappings. David Bommes RWTH Aachen University, GermanyDavid Bommes is an assistant professor in the Computer Science ...

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“…• Regularization: In order to uniform the length of mesh edges, we adopted local global shape optimization as proposed in [17]. This step improved the local shape of the faces of our mesh, making them closer to the faces of Archimedeal solids; this geometric optimization phase greatly contributed to improve the aesthetics of the final grid shell.…”

Section: Remeshingmentioning

confidence: 99%

Conception and parametric design workflow for a timber large-spanned reversible grid shell to shelter the archaeological site of the roman shipwrecks in pisa

Corio¹,

Laccone²,

Pietroni³

et al. 2017

Int. J. CMEM

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Reciprocal structures or nexorade are composed by the assembling of groups of three or more beams mutually connected by mono-lateral T joints in a way that any relative movement is suppressed. This kind of structures can be easily built in relatively unprepared sites, dismantled, transported and re-used even by not specialized handcraft. For these reasons, reciprocal structures have been widely used in the past for military purposes, and nowadays they seem to satisfy very well the different requirements of a quick and temporary shelter of a large archaeological area when they are shaped as grid shells. This paper proposes the design of a reversible, reciprocal framed grid shell to shelter the archaeological site of the Roman Shipwrecks in Pisa. The structure must protect excavations and archaeologists from the weather and provide an easy access to visitors. Additionally, it must allow for easy disassembling and moving to another site. The design choices aim at optimizing both structural efficiency and esthetical qualities. A parametric workflow for both the form finding and the digital fabrication processes has been developed, and a prototype of accommodative steel T-joint for timber reciprocal beams has been realized. Finally, a model using CNC-cutting tested the structural feasibility of such a design approach.

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Statics Aware Grid Shells

Cited by 41 publications

References 28 publications

Design and volume optimization of space structures

Design and volume optimization of space structures

Directional field synthesis, design, and processing

Conception and parametric design workflow for a timber large-spanned reversible grid shell to shelter the archaeological site of the roman shipwrecks in pisa

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