Non-linear shape optimization using local subspace projections

Weiss, Tomer; Hafner, Christian; Rist, Florian; Birsak, Michael; Wimmer, Michael; Kobbelt, Leif

doi:10.1145/2897824.2925886

Cited by 40 publications

(28 citation statements)

References 27 publications

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“…Some of them attempt to design mechanical toy and automata [45,4], articulated models [1,28], external supporting structures [25,7,30]. The other algorithms are proposed to improve printing efficiency [31,34] and quality [10,37], shape details enhancement [21], and dynamic stability [2,18,19,33]. In contrast, our work is proposed to reduce the material cost, fix the structural weak regions, and optimize static stability of the object.…”

Section: Related Workmentioning

confidence: 99%

“…Although the volume of the model is optimized in their method, they also do not consider the structural strength of the model. Musialski et al [18,19] propose shape optimization frameworks, which can achieve both static and dynamic stability. Although [19] takes into account structural strength in shape optimization, it is difficult for them to handle structural weak regions.…”

Section: Related Workmentioning

confidence: 99%

“…Musialski et al [18,19] propose shape optimization frameworks, which can achieve both static and dynamic stability. Although [19] takes into account structural strength in shape optimization, it is difficult for them to handle structural weak regions. In this work, we propose an algorithm system to simultaneously optimize stability, material usage, and enhance weak parts.…”

Section: Related Workmentioning

confidence: 99%

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Cross section-based hollowing and structural enhancement

Wang

Qian

et al. 2017

Vis Comput

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Recently, 3D printing has become a powerful tool for personal fabrication. However, the price of some materials are still high which limits its applications in home users. To optimize the volume of the model, while not largely affecting the strength of the objects, researchers propose algorithms to divide the model with different kind of light weight structures, such as frame structure, honeycomb-cell structure, truss structure, medial axis tree, etc. However, these algorithms are not suitable for the model whose internal space needs to be reused. In addition, the structural strength and static stability of the models, obtained with modern 3D model acquirement methods, are not guaranteed. In consequence, some models are too fragile to print, and cannot be survived in daily usage, handling, and transportation, or cannot stand in a stable.To handle the mentioned problems, an algorithm system is proposed based on cross sections in this work. The structural weak cross sections are enhanced and structural strong cross sections are adaptively hollowed to meet a given structural strength, static stability, printability, etc., while the material usage is minimized. The proposed algorithm system has been tested on several typical 3D models. The experimental results demonstrate the effectiveness and practicability of our system.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Cross section-based hollowing and structural enhancement

Wang

Qian

et al. 2017

Vis Comput

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“…Methods have also been developed to achieve desired reflectance [WPMR09, MAG*09, LDPT13]. Musialski et al [MAB*15, MHR*16] provide generic paradigm for non‐linear shape optimization for fabrication problems.…”

Section: Related Workmentioning

confidence: 99%

Data‐Driven Bending Elasticity Design by Shell Thickness

Zhang

et al. 2016

Computer Graphics Forum

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We present a method to design the deformation behavior of 3D printed models by an interactive tool, where the variation of bending elasticity at different regions of a model is realized by a change in shell thickness. Given a soft material to be used in 3D printing, we propose an experimental setup to acquire the bending behavior of this material on tubes with different diameters and thicknesses. The relationship between shell thickness and bending elasticity is stored in an echo state network using the acquired dataset. With the help of the network, an interactive design tool is developed to generate non‐uniformly hollowed models to achieve desired bending behaviors. The effectiveness of this method is verified on models fabricated by different 3D printers by studying whether their physical deformation can match the designed target shape.

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“…While volumetric or surface mesh representations are more commonly used in computer graphics and computer vision, since its introduction by Blum et al . [Blu67], medial representations have found applications in many 2D/3D geometric problems such as animation [BP07], fabrication [MHR*16], image processing [TD17], shape analysis [SSCO08], and real‐time tracking [TPT16]. The process of converting an input model into a medial representation is generally referred to as the medial axis transform (MAT), and the collection of origins of the spheres in a medial representation form a medial skeleton .…”

Section: Introductionmentioning

confidence: 99%

LSMAT Least Squares Medial Axis Transform

Rebain

Angles

Valentin

et al. 2019

Computer Graphics Forum

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The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independent optimization of each sphere using Gauss–Newton, and its least‐squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real‐data.

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Non-linear shape optimization using local subspace projections

Cited by 40 publications

References 27 publications

Cross section-based hollowing and structural enhancement

Cross section-based hollowing and structural enhancement

Data‐Driven Bending Elasticity Design by Shell Thickness

LSMAT Least Squares Medial Axis Transform

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