Developable Approximation via Gauss Image Thinning

Binninger, Alexandre; Verhoeven, Floor; Herholz, Philipp; Sorkine‐Hornung, Olga

doi:10.1111/cgf.14374

Cited by 16 publications

(6 citation statements)

References 38 publications

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“…The initial cross-field is updated after each sketch to allow the patch decomposition to conform to the newly inserted constraints. We handle sketches in the same manner as Pietroni et al [2021] handle sharp features. Our method allows real-time editing for small models (up to 3000 triangles) and takes a few seconds to process larger models.…”

Section: Resultsmentioning

confidence: 99%

“…four corners per patch for quadrangulation, which is too stringent for pattern making. We adapt the method by Pietroni et al [2021] to suit the different setting of garment design and fabrication, where the topology requirements are different and textile based distortion measures must be bounded.…”

Section: Related Workmentioning

confidence: 99%

“…Path tracing. To trace field-oriented paths, we use the graphbased approach proposed by Nuvoli et al [2019] and Pietroni et al [2021]. First, we interpolate the cross-field on vertices (considering their invariance to 90-degree rotations).…”

Section: Patch Layout Creationmentioning

confidence: 99%

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Computational pattern making from 3D garment models

et al. 2022

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We propose a method for computing a sewing pattern of a given 3D garment model. Our algorithm segments an input 3D garment shape into patches and computes their 2D parameterization, resulting in pattern pieces that can be cut out of fabric and sewn together to manufacture the garment. Unlike the general state-of-the-art approaches for surface cutting and flattening, our method explicitly targets garment fabrication. It accounts for the unique properties and constraints of tailoring, such as seam symmetry, the usage of darts, fabric grain alignment, and a flattening distortion measure that models woven fabric deformation, respecting its anisotropic behavior. We bootstrap a recent patch layout approach developed for quadrilateral remeshing and adapt it to the purpose of computational pattern making, ensuring that the deformation of each pattern piece stays within prescribed bounds of cloth stress. While our algorithm can automatically produce the sewing patterns, it is fast enough to admit user input to creatively iterate on the pattern design. Our method can take several target poses of the 3D garment into account and integrate them into the sewing pattern design. We demonstrate results on both skintight and loose garments, showcasing the versatile application possibilities of our approach.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Computational pattern making from 3D garment models

et al. 2022

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“…Alternative approaches apply the condition that a developable surface has a one-dimensional Gauss image, i.e it is a network of curves in the Gauss sphere [16]. Based on this definition, the recent work of Binninger et al [17] proposed a novel algorithm based on iterative deformation of a given surface by 'thinning' its Gauss image.…”

Section: (A) Clothes As Developable Surfacesmentioning

confidence: 99%

Mathematics meets the fashion industry on path to product innovation and sustainability

Magri

Ciarletta

2023

Proc. R. Soc. A.

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Mathematics remains an endless source of inspiration for both the conception and the fabrication of clothes and fashion products. Over the last century, the prominent role of mathematics in the fashion industry has evolved together with the progress in computational resources and fabrication technologies. Nowadays, mathematics not only provides useful theoretical and computational tools to assist design and fabrication, but also acts as a catalyst of creativeness. This survey discusses the latest advances on mathematical models and methods in the fashion industry, restricting our attention to clothing design and multi-scale modelling, and their applications for digital manufacturing of textiles and garments. Particular focus is given to the usage of mathematics to drive product innovation and to reduce the environmental impact of the fashion industry in order to meet the Sustainable Development Goals of the United Nations.

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“…A more recent approach to creating developable surfaces is through the approximation of existing shapes with developables. Proposed methods include cutting surfaces into developable pieces [Sharp and Crane 2018], fitting developable patches to a surface [Ion et al 2020], and flowing existing surfaces to reduce a discrete developability measure [Binninger et al 2021;Kohlbrenner et al 2021;Liu and Jacobson 2021;Sellán et al 2020;Stein et al 2018].…”

Section: Introductionmentioning

confidence: 99%

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

Verhoeven

Vaxman

Hoffmann³

et al. 2022

ACM Trans. Graph.

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We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input that connect the PQ strips. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling-based representations of developable surfaces while still obtaining developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its isolines are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight isolines is non-linear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle-based interactive freeform modeling of developable shapes.

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Developable Approximation via Gauss Image Thinning

Cited by 16 publications

References 38 publications

Computational pattern making from 3D garment models

Computational pattern making from 3D garment models

Mathematics meets the fashion industry on path to product innovation and sustainability

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

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