The Flattening of Arbitrary Surfaces by Approximation with Developable Stripes

Kolmanič, Simon; Guid, Nikola

doi:10.1007/978-0-387-35495-8_4

Cited by 4 publications

(12 citation statements)

References 15 publications

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“…Gurunathan [7] and Gan et al [14] also proposed their own methods for surface flattening, but results of the Gurunathan method are basically the same as that of Ref. [23], which is easier to understand, while the Gan method works similar as the methods based on the definition of the Gaussian curvature proposed by [18,19].…”

Section: Methods For Surface Flattening In One Piecementioning

confidence: 76%

“…[23] is similar to the Elber method, but it is not bound to the appointed surface representation. It uses the method proposed by Gurunathan described in the previous section to generate a developable surface between two selected isoparametric curves if possible.…”

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 88%

“…Other methods in this group approximate the original surface with a set of developable surfaces, which are then without distortions unfolded into the plane [23,28,29]. Consequently, the flattening error is no more the difference in the length of isoparametric curves of the secondary flattening direction as by the Bennis method but the approximation error made by the surface approximation with a set of developable surfaces.…”

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 97%

“…Currently, we have found only four methods that fit in this group [22,23,28,29]. Their main idea is to stop the unfolding process, if the distortion in generated flat pattern exceeds an acceptable error limit, and to start elsewhere on the surface.…”

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 97%

“…To do that, we can choose between three basic methods for the surface flattening in one piece: a method based on the definition of the Gaussian curvature on triangulated surfaces [18À21], geodesic curvature preservation flattening [22], and a method for preserving the distances and geodesic curvature by construction of appropriate plane triangles [23]. Regardless of the chosen method, the primary and secondary direction and the flattening origin have to be chosen first (see Fig.…”

Section: Methods For Surface Flattening In One Piecementioning

confidence: 99%

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FlattGen: Teaching tool for surface flattening

Kolmanič¹,

Guid²

2006

Comput. Appl. Eng. Educ.

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In many cases in the industry, we can face a problem, where an object has to be manufactured out of thin plane material. This is especially the case in the car, airplane, shipbuilding, textile, and shoe making industry. In order to manufacture such an object, a pattern has to be generated first. It has to be cut out from plane material and then bend to the final shape. The same problem can be found also in computer graphics, where flat patterns are used to decrease distortions in texture mapping. Therefore, it is important for designers and computer engineers to master the flat pattern generation. In literature, a great number of methods for pattern generation can be found and it is important to know their advantages and weaknesses. In this article, the application FlattGen is presented where the most important flattening methods can be seen and compared to each other. In this way, students can experiment and prepare themselves better for the future work. ß

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Section: Methods For Surface Flattening In One Piecementioning

confidence: 76%

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 88%

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 97%

Section: Methods For Per Partes Surface Flatteningmentioning

confidence: 97%

Section: Methods For Surface Flattening In One Piecementioning

confidence: 99%

See 3 more Smart Citations

FlattGen: Teaching tool for surface flattening

Kolmanič¹,

Guid²

2006

Comput. Appl. Eng. Educ.

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Computer Simulation of New Forms of Shell Structures

Strashnov

2023

Geometry &Amp; Graphics

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Abstract. A large number of new surfaces are presented, formed by congruent curves with variable curvature, but remaining in the same class, and superellipses. All surfaces are included in the class-es Rotation Surfaces, Velaroidal Translaation Surfaces, and Algebraic Surfaces with a Carcass of Three Main Flat Curves. All surfaces of the same class are defined by the same general explicit and para-metric equations, and thanks to the presence of many constants in the superellipse equation, it is possible to obtain a lot of known and new surfaces. Despite the fact that the method of construction of the considered surfaces is known, in the presented article it is il-lustrated and visualized on many examples. The surfaces were constructed using a numeric computing environment MATLAB. The surfaces of a general-view superellipse were built on the basis of a new computer program that allows them to be visualized in a multimedia mode by a set change in the exponents contained in the meridian-superellipse formula. All built rotation surfaces have a common name — superellipsoids of rotation. For the first time it is shown that algebraic surfaces with a given frame in three mutually perpendicular planes, applied in shipbuilding, can also find application in the architecture of public buildings. Superellipses are used as the rigid frame of surfaces. In the overview section of the article on the basis of the available publications it is shown that the geometry of the form affects the stress-deformable state of shells with the proposed medial surfaces. The materials of the article give an opportunity in the future to find the optimal shells outlined on the considered analytical surfaces of three different classes, which are considered in the article, taking into account the criteria of optimality applied in architecture, construction, engineering and shipbuilding.

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Tangential developable surfaces and their application in real structures

Кривошапко

Gil-oulbé

2022

Struct. Mech. of Eng. Const. and Build

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A class of developable surfaces contains cylindrical, conical, and tangential developable surfaces. Tangential developable surfaces are ruled surfaces of zero Gaussian curvature with cuspidal edges. They give great opportunities to architects and engineers for realization of their creative projects. Both the theoretical researches in the area of geometry of torses and strength analysis of shells and the influence of these researches on the application of torses in practice are shown. A presented research demonstrated that torses found the application in shipbuilding, aircraft construction, mechanical engineering, in architecture and building, engineering equipment and communications, in road building, in anti-erosive banks, topography, and cartography, clothing articles of light industry, in sculptural forms, and in modelling with developable surfaces. It was confirmed by the references on great number of published works on the subject, real examples from practice, and by handing in 14 illustrations of real objects.

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The Flattening of Arbitrary Surfaces by Approximation with Developable Stripes

Cited by 4 publications

References 15 publications

FlattGen: Teaching tool for surface flattening

FlattGen: Teaching tool for surface flattening

Computer Simulation of New Forms of Shell Structures

Tangential developable surfaces and their application in real structures

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