Interactive free-form level-set surface-editing operators

In this paper, we present a computational framework for computational design and additive manufacturing of spatial free-form periodic metasurfaces. The proposed scheme rests on the level-set based topology approach and the conformal mapping theory. A 2D unit cell of metamaterial with tailored effective properties is created using the level-set based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle when mapping the 2D design to a 3D surface. The proposed level-set based optimization methods not only can act as a motivator for design synthesis, but also can be seamlessly hooked with additive manufacturing with no need of CAD reconstructions. The proposed computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces in different fields of interest. The performance of the proposed scheme is illustrated through a benchmark example where a negative-Poisson’s-ratio unit cell pattern is mapped to a 3D human face and fabricated through additive manufacturing.

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Sketch-based shape exploration using multiscale free-form surface editing

Artificial intelligence for engineering design analysis and manufacturing ◽

10.1017/s0890060412000182 ◽

2012 ◽

Vol 26 (3) ◽

pp. 337-350

Author(s):

Günay Orbay ◽

Mehmet Ersın Yümer ◽

Levent Burak Kara

Keyword(s):

Computer Aided Design ◽

Free Form ◽

Levels Of Detail ◽

Solid Models ◽

Free Form Surface ◽

Conceptual Flexibility ◽

Aided Design ◽

Free Form Surfaces ◽

Surface Editing ◽

Different Levels

AbstractThe hierarchical construction of solid models with current computer-aided design systems provide little support in creating and editing free-form surfaces commonly encountered in industrial design. In this work, we propose a new design exploration method that enables sketch-based editing of free-form surface geometries where specific modifications can be applied at different levels of detail. This multilevel detail approach allows the designer to work from existing models and make alterations at coarse and fine representations of the geometry, thereby providing increased conceptual flexibility during modeling. At the heart of our approach lies a multiscale representation of the geometry obtained through a spectral analysis on the discrete free-form surface. This representation is accompanied by a sketch-based surface editing algorithm that enables edits to be made at different levels. The seamless transfer of modifications across different levels of detail facilitates a fluid exploration of the geometry by eliminating the need for a manual specification of the shape hierarchy. We demonstrate our method with several design examples.

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Displacement Calculation of Heart Walls in ECG Sequences Using Level Set Segmentation and B-Spline Free Form Deformations

Computer Vision and Graphics - Lecture Notes in Computer Science ◽

10.1007/978-3-642-15907-7_33 ◽

2010 ◽

pp. 268-275

Author(s):

Andrzej Skalski ◽

Paweł Turcza ◽

Tomasz Zieliński

Keyword(s):

Level Set ◽

Free Form ◽

B Spline ◽

Level Set Segmentation

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Parametric Topology Optimization Toward Rational Design and Efficient Prefabrication for Additive Manufacturing

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4042580 ◽

2019 ◽

Vol 141 (4) ◽

Cited By ~ 1

Author(s):

Long Jiang ◽

Hang Ye ◽

Chi Zhou ◽

Shikui Chen

Keyword(s):

Topology Optimization ◽

Additive Manufacturing ◽

Level Set ◽

Rational Design ◽

Computational Cost ◽

Significant Advance ◽

Free Form ◽

Geometric Complexity ◽

Original Design ◽

Design And Manufacturing

The significant advance in the boosted fabrication speed and printing resolution of additive manufacturing (AM) technology has considerably increased the capability of achieving product designs with high geometric complexity and provided tremendous potential for mass customization. However, it is also because of geometric complexity and large quantity of mass-customized products that the prefabrication (layer slicing, path planning, and support generation) is becoming the bottleneck of the AM process due to the ever-increasing computational cost. In this paper, the authors devise an integrated computational framework by synthesizing the parametric level set-based topology optimization method with the stereolithography (SLA)-based AM process for intelligent design and manufacturing of multiscale structures. The topology of the design is optimized with a distance-regularized parametric level set method considering the prefabrication computation. With the proposed framework, the structural topology optimization not only can create single material structure designs but also can generate multiscale, multimaterial structures, offering the flexibility and robustness of the structural design that the conventional methods could not provide. The output of the framework is a set of mask images that can be directly used in the AM process. The proposed approach seamlessly integrates the rational design and manufacturing to reduce the numerical complexity of the computationally expensive prefabrication process. More specifically, the prefabrication-friendly design and optimization procedure are devised to drastically eliminate the redundant computations in the traditional framework. Two test examples, including a free-form 3D cantilever beam and a multiscale meta-structure, are utilized to demonstrate the performance of the proposed approach. Both the simulation and experimental results verified that the new rational design could significantly reduce the prefabrication computation cost without affecting the original design intent or sacrificing the original functionality.

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Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)

10.1115/detc2021-67819 ◽

2021 ◽

Author(s):

Xiaoqiang Xu ◽

Shikui Chen ◽

Xianfeng David Gu ◽

Michael Yu Wang

Keyword(s):

Topology Optimization ◽

Heat Conduction ◽

Level Set ◽

Rectangular Domain ◽

Free Form ◽

Topology Optimization Problem ◽

Parameter Domain ◽

Covariant Derivatives ◽

3D Topology ◽

Free Form Surfaces

Abstract In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The proposed concept is proved through two examples of heat conduction on manifolds.

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Topology Optimization of Conformal Structures Using Extended Level Set Methods and Conformal Geometry Theory

Volume 2B: 44th Design Automation Conference ◽

10.1115/detc2018-85655 ◽

2018 ◽

Author(s):

Qian Ye ◽

Yang Guo ◽

Shikui Chen ◽

Xianfeng David Gu ◽

Na Lei

Keyword(s):

Topology Optimization ◽

Level Set ◽

Differential Operators ◽

Conformal Geometry ◽

Level Set Methods ◽

Free Form ◽

Computational Framework ◽

Covariant Derivatives ◽

Free Form Surface ◽

Free Form Surfaces

In this paper, we propose a new method to approach the problem of structural shape and topology optimization on manifold (or free-form surfaces). A manifold is conformally mapped onto a 2D rectangle domain, where the level set functions are defined. With conformal mapping, the corresponding covariant derivatives on a manifold can be represented by the Euclidean differential operators multiplied by a scalar. Therefore, the topology optimization problem on a free-form surface can be formulated as a 2D problem in the Euclidean space. To evolve the boundaries on a free-form surface, we propose a modified Hamilton-Jacobi equation and solve it on a 2D plane following the conformal geometry theory. In this way, we can fully utilize the conventional level-set-based computational framework. Compared with other established approaches which need to project the Euclidean differential operators to the manifold, the computational difficulty of our method is highly reduced while all the advantages of conventional level set methods are well preserved. We hope the proposed computational framework can provide a timely solution to increasing applications involving innovative structural designs on free-form surfaces in different engineering fields.

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