Application of the Dupin cyclide in temple architecture

Sal'kov, Nikolay

doi:10.1088/1742-6596/1546/1/012042

Cited by 8 publications

(8 citation statements)

References 9 publications

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“…The variety of shapes of quasi-rotation surfaces can serve as a source of inspiration for the architect as well as yield a specific solution to a problem. In this case, as with other cyclic surfaces in architecture described in papers [12][13][14], the design process is simplified by the fact that the basic element of the load bearing construction is a circular frame.…”

Section: Discussionmentioning

confidence: 99%

Application of quasi-rotation surface segments in architectural prototyping

Beglov

Rustamyan

Verbitskiy

2022

J. Phys.: Conf. Ser.

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The present paper details an approach to modeling of quasi-rotation surface segments with pre-defined conditions. The desired surfaces and their segments are formed parametrically through Maple computer algebra system. Various analytical approaches to trimming of the excessive parts of quasi-rotation surfaces are indicated. Geometric modeling is performed with use of a previously developed algorithm. An example illustrating the initial stage of design of an overpass between two separate buildings is provided. The design objective contains the basic geometric parameters of the desired architectural element. Three control models were created with the same initial parameters through basic CAD software methods. All of the constructed models are thin-walled. Mechanical properties of the scale 3D models of the target element were compared in equal conditions by means of CAD software. The prototype created through the use of a quasi-rotation surface segment was the most resistant to load. The paper also features a rendered concept of a complex of three towers connected with three overpasses. The acquired results allow us to conclude that quasi-rotation is an effective method of formation of models of architectural elements.

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Section: Discussionmentioning

confidence: 99%

Application of quasi-rotation surface segments in architectural prototyping

Beglov

Rustamyan

Verbitskiy

2022

J. Phys.: Conf. Ser.

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“…It is known that a ray is reflected form a surface in the same direction as if it was reflected from a surface tangent to such surface at the point of incidence. Such optical properties of surfaces are vital in architecture [7].…”

Section: Discussionmentioning

confidence: 99%

Plane Tangent to Quasi-Rotation Surface

Beglov

Panchuk

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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The analysis of a surface generated by quasi-rotation of a straight line around a circle is provided in the present paper. The considered case features a straight generatrix belonging to the plane of a circular axis of quasi-rotation and intersecting it in two points. A geometric method of determination of a point belonging to a surface given its projection on the axis plane is demonstrated. Geometric construction of the curves of intersection between the considered surface and a conic surface is presented. A method of determination of points belonging to the considered surface as points belonging to the curve of intersection of two conic surfaces is acquired. Step-by-step constructions illustrating the solution of the problem of determination of a plane tangent to the considered surface in a given point are provided. The problem is solved through the methods of descriptive geometry. Every construction is performed according to an analytic algorithm, not involving approximate methods of determination of the sought points. The construction is carried out in a CAD system through the use of tools “straight line by two points” and “circle by center and point”. The presented solution to the defined problem is connected to the solution to the problem of determination of the rays reflected from the considered surface. The results of the paper expose the geometric properties of surfaces of quasi-rotation. The provided constructions can serve as the basis for the research of optical properties of the considered surfaces.

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“…Spheres ∆ and Γ are tangent to each other in point N, and this is the first point equidistant to both of them. Spheres ∆ i and Γ i of radiuses R + t i and r + t i have common parallels 𝛥 1 ∩ 𝛤 1 = 11′, 𝛥 2 ∩ 𝛤 2 = 22′, 𝛥 3 ∩ 𝛤 3 = 33′ etc. generating the "positive" sheet of the two-sheet hyperboloid of revolution.…”

Section: Glp Of Tangent Spheres: Distance Between the Centers Of The ...mentioning

confidence: 99%

“…A frame designed of GLP surfaces can be optimized with methods documented in paper [2]. At the moment, various studies on modeling and application of complex surfaces are being held [3,4].…”

Section: Introductionmentioning

confidence: 99%

Geometric modeling and study of properties of surfaces equidistant to two spheres

Vyshnepolsky

Kadykova

Peh

2022

J. Phys.: Conf. Ser.

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The paper considers the geometric locus of points equidistant to two spheres of different diameters. If these spheres are concentric, the sought multitude constitutes a single surface – a sphere of diameter equal to arithmetic mean of the diameters of the given spheres. In other cases the geometric locus of points equidistant to two spheres of different diameters constitutes two surfaces. In case the spheres intersect, are tangent or distant to each other, the first of these surfaces is a two-sheet hyperboloid of revolution that degenerates into a plane in case the spheres are equal. In case the spheres intersect, the second of the surfaces is an ellipsoid of revolution that degenerates into a straight line if the spheres are tangent to each other. In the case of distant spheres, the second of the surfaces is a two-sheet hyperboloid of revolution. In case the spheres contain one another, the sough geometric locus constitutes two co-axial co-focused ellipsoids of revolution. The equations defining the mentioned surfaces are presented. The regularities in shape and location of these surfaces were studied; the formulas for the major and the minor axes of the ellipsoids and the vertices of the two-sheet hyperboloids of revolution were derived.

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Application of the Dupin cyclide in temple architecture

Cited by 8 publications

References 9 publications

Application of quasi-rotation surface segments in architectural prototyping

Application of quasi-rotation surface segments in architectural prototyping

Plane Tangent to Quasi-Rotation Surface

Geometric modeling and study of properties of surfaces equidistant to two spheres

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