Grid generation on free-form surface using guide line advancing and surface flattening method

Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifest the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on "guide line" and "surface flattening" methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete NURBS (Non-Uniform Rational B-Spline) surface is firstly divided into a number of patches, and a discrete free-form surface formed by mapping dividing points onto the surface. The free-form surface was then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the 2D surface, with grids formed by applying a guide-line method. Subsequently, the intersections of the guide-lines and the complex boundary are obtained, and the guide-lines divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the 3D surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes bypresenting realistic examples to demonstrate the practical effectiveness of the proposed method.

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“…The most recent method for the synthesis of free-form grid structures was proposed by Gao et al (2017a).…”

Section: Fig3 Compass Methodsmentioning

confidence: 99%

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Jun

Shepherd

et al. 2019

J. Comput. Civ. Eng.

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“…15(b) and Fig. 15(c) are the grids obtained by the map-guideline method according to Gao et al [22], which combines the mapping method and the guideline method. The specific process is to first arrange a certain number of straight lines according to a certain distance on a plane, then map the straight lines to the given surface, and then the obtained curves on the surface are divided into equal parts according to a certain distance or number of segments.…”

Section: Case Two ---Admirant Entrance Buildingmentioning

confidence: 99%

“…For example, Ding [20] proposed a new method for a free-form surface grid generation, referred to as the iso-parametric line dividing method, which is based on a non-uniform rational B-spline (NRUBS) curve. Wei [21] and Gao [22] proposed a grid generation method over the free-form surface, which combines the surface flattening technique and mapping theory. Shepherd and Richens [23] proposed a Subdivision Surface method, which provides a useful platform for combining creative architectural design with intelligent engineering to produce aesthetically pleasing designs on financially and environmentally limited agendas.…”

Section: Introductionmentioning

confidence: 99%

A novel progressive grid generation method for free-form grid structure design and case studies

Liu

Feng

Tsavdaridis

2021

Journal of Building Engineering

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“…In order to improve the flattening quality of sheet metal with free-form surface, Liu et al [14] proposed a flattening system, and the key technologies such as mesh quality measuring criterion, centre triangle indexing algorithm, coordinate transforming principle, and initial flattening method were elaborated. Gao et al [15] presented a grid generation methodology which combined surface flattening technique with guide line method. Danaila et al [16] presented two practical methods to draw the development of a surface unable to be developed applying classical methods of descriptive geometry, the toroidal surface, frequently met in technical practice.…”

Section: Introductionmentioning

confidence: 99%

A free‐form surface flattening algorithm that minimizes geometric deformation energy

Zheng

Liu

Lou

et al. 2022

IET Image Processing

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Based on the analysis of the advantages and disadvantages of existing surface flattening algorithms, this paper proposes a free‐form surface flattening algorithm that minimizes geometric deformation by combining the advantages of the geometric flattening method and the mechanical energy flattening method to address the problems of many iterations, large changes in convergence, and weak visualization of deformation. The point cloud surface is meshed using the triangular slice search method, and the 3D surface mesh is wrapped around the surface using geometric mapping relationships. The initial correction and deformation analysis of the ring flatten graphic are carried out according to the average flattening error, and a global geometric deformation energy model is established to obtain the energy‐minimizing unfolding conditions and optimize the initial flattening graph by iterative optimization. The verification of the algorithm shows that the algorithm is general, has good robustness, high flattening accuracy, and visualizes the flattening deformation. The method is suitable for some design occasions of machining, such as the flattening calculation of automobile outer cladding parts and sheet metal parts. It is especially suitable for the flattening calculation of ring‐like parts, and is a good guide for the design calculation and stamping process of sheet‐metal‐like parts.

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Grid generation on free-form surface using guide line advancing and surface flattening method

Cited by 26 publications

References 13 publications

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

A novel progressive grid generation method for free-form grid structure design and case studies

A free‐form surface flattening algorithm that minimizes geometric deformation energy

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