Öz
In the present paper we study with the convolution surface $C=M\star N$ of a paraboloid $M\subset \mathbb{E}^{3}$ and a parametric surface $N\subset \mathbb{E}^{3}$. We take some spacial surfaces for $N$ such as, surface of revolution, Monge patch and ruled surface and calculate the Gaussian curvature of the convolution surface $C$. Further, we give necessary and sufficient conditions for a convolution surface $C$ to become flat.
Anahtar Kelimeler
Minkowski sum Convolution of surfaces Flat surfaces Gaussian curvature Second fundamental form
Kaynakça
- [1] J. Bloomenthal, K. Shoemake, Convolution surfaces, Computer Graphics 25(4) (1991), 251–256.
- [2] M. Lavicka, B. Bastl, Z. Sir, Reparameterization of curves and surfaces with respect to convolutions, in: Dæhlen, M., et al.(Eds.), MMCS 2008. In: Lecture Notes in Computer Science, 5862, 2010, 285-298.
- [3] M. Peternell, T. Steiner, Minkowski sum boundary surfaces of 3D-objects, Graphical Models 69 (2007), 180–190.
- [4] M. Peternell, F. Manhart, The Convolution of a Paraboloid and a Parametrized Surface, www.dmg.tuwien.ac.at/geom/peternell/parsurf article.pdf
- [5] Z. Sir, J. Gravesen, B. J¨uttler, Computing Convolutions and Minkowski sums via Support Functions, Industrial Geometry, FSP Report 29, 2006.
- [6] J. Vrsek, M. Lavicka, On convolutions of algebraic curves, J. Sym. Comp. 45 (2010), 657–676.
Öz
Kaynakça
- [1] J. Bloomenthal, K. Shoemake, Convolution surfaces, Computer Graphics 25(4) (1991), 251–256.
- [2] M. Lavicka, B. Bastl, Z. Sir, Reparameterization of curves and surfaces with respect to convolutions, in: Dæhlen, M., et al.(Eds.), MMCS 2008. In: Lecture Notes in Computer Science, 5862, 2010, 285-298.
- [3] M. Peternell, T. Steiner, Minkowski sum boundary surfaces of 3D-objects, Graphical Models 69 (2007), 180–190.
- [4] M. Peternell, F. Manhart, The Convolution of a Paraboloid and a Parametrized Surface, www.dmg.tuwien.ac.at/geom/peternell/parsurf article.pdf
- [5] Z. Sir, J. Gravesen, B. J¨uttler, Computing Convolutions and Minkowski sums via Support Functions, Industrial Geometry, FSP Report 29, 2006.
- [6] J. Vrsek, M. Lavicka, On convolutions of algebraic curves, J. Sym. Comp. 45 (2010), 657–676.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2018 |
| Gönderilme Tarihi | 18 Mayıs 2018 |
| Kabul Tarihi | 24 Eylül 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 1 Sayı: 2 |
Kaynak Göster
Cited By
Erratum to ”On Convolution surfaces in Euclidean spaces”
Journal of Mathematical Sciences and Modelling
https://doi.org/10.33187/jmsm.539731
Journal of Mathematical Sciences and Modelling
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