Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures
In this paper we propose a method for the genesis of novel geometric surfaces which we named Cassinian directorial surfaces (CDS). They represent spatial geometric locus of points whose product of distances from k fixed directrix lines is constant and given by the parameter S. The modelling of such...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek
2023-01-01
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| Series: | Tehnički Vjesnik |
| Subjects: | |
| Online Access: | https://hrcak.srce.hr/file/444208 |
| _version_ | 1827281742319321088 |
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| author | Maja Petrović Radovan Štulić Marko Jovanović Marko Vučić Branko Malešević |
| author_facet | Maja Petrović Radovan Štulić Marko Jovanović Marko Vučić Branko Malešević |
| author_sort | Maja Petrović |
| collection | DOAJ |
| description | In this paper we propose a method for the genesis of novel geometric surfaces which we named Cassinian directorial surfaces (CDS). They represent spatial geometric locus of points whose product of distances from k fixed directrix lines is constant and given by the parameter S. The modelling of such Cassinian directorial surfaces is based upon two criteria that are the geometric mean as a proportional harmony and the golden ration i.e. the divine proportion. The three particular spatial dispositions of directors-directrices thus enable the design of three types of Cassinian five-directorial surfaces: CDS1 incorporating directrices which coincide with the sides of a regular pentagon; CDS2 incorporating directrices coinciding with the edges of an upright regular pentagonal prism; and CDS3 incorporating directrices which coincide with the skew diagonals of the sides of an upright regular pentagonal prism. In addition, for each type of the surface we propose possible applications of such surfaces as a geometric pattern in designing architectural structures. |
| first_indexed | 2024-04-24T09:06:21Z |
| format | Article |
| id | doaj.art-98c2da2f45464774a9db51e191ded475 |
| institution | Directory Open Access Journal |
| issn | 1330-3651 1848-6339 |
| language | English |
| last_indexed | 2024-04-24T09:06:21Z |
| publishDate | 2023-01-01 |
| publisher | Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek |
| record_format | Article |
| series | Tehnički Vjesnik |
| spelling | doaj.art-98c2da2f45464774a9db51e191ded4752024-04-15T18:52:55ZengFaculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in OsijekTehnički Vjesnik1330-36511848-63392023-01-013051611161910.17559/TV-20220622234115Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural StructuresMaja Petrović0Radovan Štulić1Marko Jovanović2Marko Vučić3Branko Malešević4University of Belgrade - The Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, 11000 Belgrade, SerbiaUniversity of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaUniversity of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaUniversity of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaUniversity of Belgrade, School of Electrical Engineering, Bulevar kralja Aleksandra 73, 11000 Belgrade, SerbiaIn this paper we propose a method for the genesis of novel geometric surfaces which we named Cassinian directorial surfaces (CDS). They represent spatial geometric locus of points whose product of distances from k fixed directrix lines is constant and given by the parameter S. The modelling of such Cassinian directorial surfaces is based upon two criteria that are the geometric mean as a proportional harmony and the golden ration i.e. the divine proportion. The three particular spatial dispositions of directors-directrices thus enable the design of three types of Cassinian five-directorial surfaces: CDS1 incorporating directrices which coincide with the sides of a regular pentagon; CDS2 incorporating directrices coinciding with the edges of an upright regular pentagonal prism; and CDS3 incorporating directrices which coincide with the skew diagonals of the sides of an upright regular pentagonal prism. In addition, for each type of the surface we propose possible applications of such surfaces as a geometric pattern in designing architectural structures.https://hrcak.srce.hr/file/444208architectural structuresCassinian directorial surfacesgeometric meangolden ratiomodelling |
| spellingShingle | Maja Petrović Radovan Štulić Marko Jovanović Marko Vučić Branko Malešević Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures Tehnički Vjesnik architectural structures Cassinian directorial surfaces geometric mean golden ratio modelling |
| title | Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures |
| title_full | Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures |
| title_fullStr | Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures |
| title_full_unstemmed | Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures |
| title_short | Cassinian Directorial Surfaces Modelling as Geometric Pattern in Designing Architectural Structures |
| title_sort | cassinian directorial surfaces modelling as geometric pattern in designing architectural structures |
| topic | architectural structures Cassinian directorial surfaces geometric mean golden ratio modelling |
| url | https://hrcak.srce.hr/file/444208 |
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