# Curved foldings with common creases and crease patterns

@article{Honda2020CurvedFW, title={Curved foldings with common creases and crease patterns}, author={Atsufumi Honda and Kosuke Naokawa and Kentaro Saji and Masaaki Umehara and Kotaro Yamada}, journal={ArXiv}, year={2020}, volume={abs/1911.07166} }

## 4 Citations

Designing Generalized Cylinder with Characteristic Base Curve in Euclidean 3-space

- Engineering
- 2022

Designing a surface from a given curve under some special conditions is an important problem in many practical applications. The purpose of this article is to design a generalized cylinder whose base…

Generalized Cylinder with Geodesic and Line of Curvature Parameterizations

- EngineeringFundamental Journal of Mathematics and Applications
- 2022

On the existence of four or more curved foldings with common creases and crease patterns

- ArtBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 2021

<jats:p>Consider an oriented curve <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Gamma $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
…

A generalization of Zakalyukin's lemma, and symmetries of surface singularities

- Mathematics
- 2021

Zakalyukin’s lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption. The purpose of…

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Curved foldings with common creases and crease patterns

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Isometric deformations of cuspidal edges

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Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field $\nu$ is well-defined as a smooth vector…

Flat surfaces along cuspidal edges

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We consider developable surfaces along the singular set of a cuspidal edge surface which are regarded as flat approximations of the cuspidal edge surface. For the study of singularities of such…

On the existence of four or more curved foldings with common creases and crease patterns

- ArtBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 2021

<jats:p>Consider an oriented curve <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Gamma $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
…

Local differential geometry of cuspidal edge and swallowtail

- Mathematics
- 2020

We investigate the local differential geometric invariants of cuspidal edge and swallowtail from the view point of singularity theory. We introduce finite type invariants of such singularities (see…

Cuspidal edges with the same first fundamental forms along a common closed space curve

- Mathematics
- 2019

Along an embedded space curve $C$, local existence of four distinct cuspidal edges with the same first fundamental forms was shown in the authors' previous work. Here, if $C$ is closed, we show the…

Cuspidal edges with the same first fundamental forms along a knot

- MathematicsJournal of Knot Theory and Its Ramifications
- 2020

Letting [Formula: see text] be a compact [Formula: see text]-curve embedded in the Euclidean [Formula: see text]-space ([Formula: see text] means real analyticity), we consider a [Formula: see…

Folded developables

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1982

A plane, inextensible sheet may be folded or creased along a curved line to produce two connected but distinct developable surfaces. Various theorems applying to this folding process are identified…

Duality on generalized cuspidal edges preserving singular set images and first fundamental forms

- Mathematics
- 2019

In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\boldsymbol R^3$ preserving their singular set images and first…