LAUSR

Developable Surfaces Through Sweeping Surfaces

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0 Published in 2018 at "Bulletin of the Iranian Mathematical Society"

DOI: 10.1007/s41980-018-0177-8

Abstract: This paper studies the rotation minimizing frames that are associated with spatial curves and the sweeping surfaces which are generated by these frames. Then the necessary and sufficient condition for sweeping surface to be developable… read more here.

Keywords: surface; surfaces sweeping; developable surfaces; sweeping surfaces ... See more keywords

Gauss Map Based Curved Origami Discretization

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0 Published in 2018 at "Journal of Mechanisms and Robotics"

DOI: 10.1115/1.4041631

Abstract: This paper addresses the problem of discretizing the curved developable surfaces that are satisfying the equivalent surface curvature change discretizations. Solving basic folding units occurs in such tasks as simulating the behavior of Gauss mapping.… read more here.

Keywords: discretization; gauss; curved surface; developable surfaces ... See more keywords

Geometry of Developable Surfaces of Frenet Type Framed Base Curves from the Singularity Theory Viewpoint

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14050975

Abstract: In this paper, we consider Frenet type framed base curves that may have singular points and define one-parameter developable surfaces associated with such curves. By using the singularity theory, we classify the generic singularities of… read more here.

Keywords: type framed; base curves; developable surfaces; frenet type ... See more keywords

Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14112251

Abstract: In this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the osculating developable surface of the timelike surface along the curve. The… read more here.

Keywords: singularities osculating; timelike surfaces; developable surfaces; surface ... See more keywords

Singularities for Timelike Developable Surfaces in Minkowski 3-Space

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1 Published in 2023 at "Symmetry"

DOI: 10.3390/sym15020277

Abstract: In this paper, we consider the singularities and geometrical properties of timelike developable surfaces with Bishop frame in Minkowski 3-space. Taking advantage of the singularity theory, we give the classification of generic singularities of these… read more here.

Keywords: developable surfaces; timelike developable; surfaces minkowski; singularities timelike ... See more keywords