Öz
Helical curves are constructed by the property that their unit tangents make a constant angle with a chosen constant direction. There are relations between polynomial planar curves, helices and Pythagorean-hodograph or shortly PH-curves. The aim of this paper is to obtain a method which generate PH-curves and PH-helical curves from a planar curve in Euclidean Space E^(n+1). Furthermore, some examples are given in E^4 and E^5 to explain the method neatly.
Anahtar Kelimeler
PH-curve helical curve PH-helical curve planar curve polynomial curve
Proje Numarası
FHD-2020-3452
Kaynakça
- M. A. Lancret, Mémoire sur la théorie des courbes à double courbure, Mémoires présentés ‘a l’Institut des Sciences, Letters et arts par divers savants, Tome 1(1802) 416–454.
- W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunchweig, Friedr. Vieweg & Sohn, 1999.
- R. T. Farouki, T. Sakkalis, Pythagorean Hodographs, IBM Journal of Research and Development 34(5) (1999) 736–752.
- R. T. Farouki, T. Sakkalis, Pythagorean-Hodograph Space Curves, Advances in Computational Mathematics 2(1) (1994) 41–66.
- R. T. Farouki, C. Y. Han., C. Manni, A. Sestini, Characterization and Construction of Helical Polynomial Space Curves, Journal of Computational and Applied Mathematics 162(2) (2004) 365–392.
- R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer, Berlin, Heidelberg, 2008.
- R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs I Quaternion and Hopf map representations, Journal of Symbolic Computation 44(2) (2009) 161–179.
- R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs II. Enumeration of Low-Degree Durves, Journal of Symbolic Computation 44(4) (2009) 307–332.
- R. T. Farouki, M. Al-Kandari, T. Sakkalis, Structural Invariance of Spatial Pythagorean Hodographs, Computer Aided Geometric Design 19(6) (2002) 395–407.
- R. T. Farouki, Z. Šír, Rational Pythagorean-Hodograph Space Curves, Computer Aided Geometric Design 28(2) (2011) 78–88.
- H. Pottman, Curve Design with Rational Pythagorean-Hodograph Curves, Advances in Computational Mathematics 3 (1995) 147–170.
- S. Izumiya, N. Takeuchi, Generic Properties of Helices and Bertrand Curves, Journal of Geometry 74 (2002) 97–109.
- Ç. Camcı K. İlarslan, A New Method for Construction of PH-Helical Curves in E^3, Comptes Rendus De L Academıe Bulgare Des Scıences, 72(3) (2019) 301–308.
- H. Gluck, Higher Curvatures of Curves in Euclidean Space, The American Mathematical Monthly 37 (1966) 699–704.
- M. C. Romero-Fuster, E. Sanabria-Codesal, Generalized Helices Twistings and Flattenings of Curves in n-Space, Matematica Contemporanea 17 (1999) 267–280.
- E. Ödamar, H. H. Hacısalihoğlu, A Characterization of Inclined Curves in Euclidean n-Space, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics 24 (1975) 15–23.
- Ç. Camcı K. İlarslan, L. Kula, H. H. Hacısalihoğlu, Harmonic Curvature and General Helices, Chaos Solitons Fractals 40 (2009) 2590–2596.
- K. K. Kubota, Pythagorean Triples in Unique Factorization Domains, The American Mathematical Monthly 79 (1972) 503–505.
Öz
Destekleyen Kurum
Çanakkale Onsekiz Mart Üniversitesi Bilimsel Araştırma Projeleri Koordinasyonu
Proje Numarası
FHD-2020-3452
Kaynakça
- M. A. Lancret, Mémoire sur la théorie des courbes à double courbure, Mémoires présentés ‘a l’Institut des Sciences, Letters et arts par divers savants, Tome 1(1802) 416–454.
- W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunchweig, Friedr. Vieweg & Sohn, 1999.
- R. T. Farouki, T. Sakkalis, Pythagorean Hodographs, IBM Journal of Research and Development 34(5) (1999) 736–752.
- R. T. Farouki, T. Sakkalis, Pythagorean-Hodograph Space Curves, Advances in Computational Mathematics 2(1) (1994) 41–66.
- R. T. Farouki, C. Y. Han., C. Manni, A. Sestini, Characterization and Construction of Helical Polynomial Space Curves, Journal of Computational and Applied Mathematics 162(2) (2004) 365–392.
- R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer, Berlin, Heidelberg, 2008.
- R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs I Quaternion and Hopf map representations, Journal of Symbolic Computation 44(2) (2009) 161–179.
- R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs II. Enumeration of Low-Degree Durves, Journal of Symbolic Computation 44(4) (2009) 307–332.
- R. T. Farouki, M. Al-Kandari, T. Sakkalis, Structural Invariance of Spatial Pythagorean Hodographs, Computer Aided Geometric Design 19(6) (2002) 395–407.
- R. T. Farouki, Z. Šír, Rational Pythagorean-Hodograph Space Curves, Computer Aided Geometric Design 28(2) (2011) 78–88.
- H. Pottman, Curve Design with Rational Pythagorean-Hodograph Curves, Advances in Computational Mathematics 3 (1995) 147–170.
- S. Izumiya, N. Takeuchi, Generic Properties of Helices and Bertrand Curves, Journal of Geometry 74 (2002) 97–109.
- Ç. Camcı K. İlarslan, A New Method for Construction of PH-Helical Curves in E^3, Comptes Rendus De L Academıe Bulgare Des Scıences, 72(3) (2019) 301–308.
- H. Gluck, Higher Curvatures of Curves in Euclidean Space, The American Mathematical Monthly 37 (1966) 699–704.
- M. C. Romero-Fuster, E. Sanabria-Codesal, Generalized Helices Twistings and Flattenings of Curves in n-Space, Matematica Contemporanea 17 (1999) 267–280.
- E. Ödamar, H. H. Hacısalihoğlu, A Characterization of Inclined Curves in Euclidean n-Space, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics 24 (1975) 15–23.
- Ç. Camcı K. İlarslan, L. Kula, H. H. Hacısalihoğlu, Harmonic Curvature and General Helices, Chaos Solitons Fractals 40 (2009) 2590–2596.
- K. K. Kubota, Pythagorean Triples in Unique Factorization Domains, The American Mathematical Monthly 79 (1972) 503–505.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Proje Numarası | FHD-2020-3452 |
| Yayımlanma Tarihi | 31 Aralık 2021 |
| Gönderilme Tarihi | 23 Kasım 2021 |
| Yayımlandığı Sayı | Yıl 2021 Sayı: 37 |
Kaynak Göster
- Makale Dosyaları
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