Araştırma Makalesi
BibTex RIS Kaynak Göster

Reconstruction of a Ruled Surface in 3-dimensional Euclidean Space

Yıl 2024, Cilt: 17 Sayı: 1, 259 - 267, 28.03.2024

Mustafa Dede Cumali Ekici Mahmut Koçak

https://doi.org/10.18185/erzifbed.1362369

Öz

In this paper, we first provide a summary of certain results related to the differential geometry of ruled surfaces. Next, we introduce the signature curve for ruled surfaces in Euclidean three-space. Additionally, we present a straightforward algorithm for the reconstruction of a ruled surface, which is both efficient and entirely local, requiring only the initial motion direction and starting point. Finally, we illustrate the efficiency and accuracy of the algorithm through several examples.
Bu makalede, öncelikle regle yüzeylerin diferesiyel geometrisi ile ilgili bazı sonuçların bir özetini sunuyoruz. Daha sonra, Öklid üç uzayında regle yüzeyler için işaret eğrisini tanıtıyoruz. Ek olarak, bir regle yüzeyin yeniden yapılandırılması için hem verimli hem de tamamen yerel olan, yalnızca ilk hareket yönü ve başlangıç noktası gerektiren basit bir algoritma sunuyoruz. Son olarak, algoritmanın verimliliğini ve doğruluğunu birkaç örnekle gösteriyoruz.

Anahtar Kelimeler

Ruled surface Signature curve Curvature Reconstruction

Kaynakça

  • [1] Calabi, E., Olver, P. J., Shakiban, C., Tannenbaum, A., Haker, S. (1998). Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision, 26, 107-135.
  • [2] Calabi, E., Olver, P. J., Tannenbaum, A. (1996). Affine geometry, curve flows, and invariant numerical approximations, Adv. Math., 124, 154-196.
  • [3] Surazhsky, T., Elber, G. (2002). Metamorphosis of planar parametric curves via curvature interpolation, International Journal of Shape Modeling, 8, 201-216.
  • [4] Hickman, M. S. (2012). Euclidean signature curves, J. Math. Imaging. Vis., 43, 206-213.
  • [5] Boutin, M. (2000). Numerically invarint signature curves , Int. J. Comput. Vision, 40(3), 235-248.
  • [6] Wu, S., Li, Y. F., Zhang, J.W. (2007). Signature descriptor for free form trajectory modeling, in Proc. IEEE International Conference on Integration Technology, Shenzhen, China, 167-172.
  • [7] Wu, S., Li, Y. F. (2010). Motion trajectory reproduction from generalizedsignature description, Pattern Recognition, 43, 204-221.
  • [8] Wu, S., Li, Y. F. (2008). On signature invariants for effective motion trajectory recognition, The International Journal of Robotics Research, 27, 895-917.
  • [9] Chen, H. Y., Pottmann H. (1974). Approximation by ruled surfaces. J. Comput. Appl. Math. 102, 143-156.
  • [10] Ryuh, B. S., Pennock, G.R. (1988). Accurate motion of a robot end-effector using the curvature theory of ruled surfaces, Journal of Mechanisms, Transmissions, and Automation in Design, 110, 383-388.
  • [11] Peternell, M. (2004). Developable surface fitting to point clouds. Comp. Aided Geom. Design, 21, 785-803.
  • [12] Pottmann, H., Lüa, W., Ravani, B. (1996). Rational ruled surfaces and their Offsets, Graphical Models and Image Processing, 58, 544-552.
  • [13] Kühnel, W. (1994). Ruled W-surfaces, Arch. Math., 62, 475-480.
  • [14] Ekici, C., Çöken, A. C. (2012). The integral invariants of parallel timelike ruled surfaces, J. Math. Anal. Appl. 393, 97-107.
  • [15] Zhang, X.M., Zhu, L.M., Ding, H., Xiong, Y.L. (2012). Kinematic generation of ruled surface based on rational motion of point-line, Science China Technological Sciences, 55, 62- 71.
  • [16] Abdel Baky, R. A. (2003). On the Blaschke approach of ruled surfaces, Tamkang J. Math., 34, 107-116.
  • [17] Ünlütürk, Y., Çimdiker, M., Ekici, C. (2016). Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3-space, Communication in Mathematical Modeling and Applications. 1(1), 26-43.
  • [18] Ekici, C., Kaymanlı U.,G., Okur, S. (2021). A new characterization of ruled surfaces according to q-frame vectors in Euclidean 3-space, International Journal of Mathematical Combinatorics, 3, 20-31.

Yıl 2024, Cilt: 17 Sayı: 1, 259 - 267, 28.03.2024

Mustafa Dede Cumali Ekici Mahmut Koçak

https://doi.org/10.18185/erzifbed.1362369

Öz

Kaynakça

  • [1] Calabi, E., Olver, P. J., Shakiban, C., Tannenbaum, A., Haker, S. (1998). Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision, 26, 107-135.
  • [2] Calabi, E., Olver, P. J., Tannenbaum, A. (1996). Affine geometry, curve flows, and invariant numerical approximations, Adv. Math., 124, 154-196.
  • [3] Surazhsky, T., Elber, G. (2002). Metamorphosis of planar parametric curves via curvature interpolation, International Journal of Shape Modeling, 8, 201-216.
  • [4] Hickman, M. S. (2012). Euclidean signature curves, J. Math. Imaging. Vis., 43, 206-213.
  • [5] Boutin, M. (2000). Numerically invarint signature curves , Int. J. Comput. Vision, 40(3), 235-248.
  • [6] Wu, S., Li, Y. F., Zhang, J.W. (2007). Signature descriptor for free form trajectory modeling, in Proc. IEEE International Conference on Integration Technology, Shenzhen, China, 167-172.
  • [7] Wu, S., Li, Y. F. (2010). Motion trajectory reproduction from generalizedsignature description, Pattern Recognition, 43, 204-221.
  • [8] Wu, S., Li, Y. F. (2008). On signature invariants for effective motion trajectory recognition, The International Journal of Robotics Research, 27, 895-917.
  • [9] Chen, H. Y., Pottmann H. (1974). Approximation by ruled surfaces. J. Comput. Appl. Math. 102, 143-156.
  • [10] Ryuh, B. S., Pennock, G.R. (1988). Accurate motion of a robot end-effector using the curvature theory of ruled surfaces, Journal of Mechanisms, Transmissions, and Automation in Design, 110, 383-388.
  • [11] Peternell, M. (2004). Developable surface fitting to point clouds. Comp. Aided Geom. Design, 21, 785-803.
  • [12] Pottmann, H., Lüa, W., Ravani, B. (1996). Rational ruled surfaces and their Offsets, Graphical Models and Image Processing, 58, 544-552.
  • [13] Kühnel, W. (1994). Ruled W-surfaces, Arch. Math., 62, 475-480.
  • [14] Ekici, C., Çöken, A. C. (2012). The integral invariants of parallel timelike ruled surfaces, J. Math. Anal. Appl. 393, 97-107.
  • [15] Zhang, X.M., Zhu, L.M., Ding, H., Xiong, Y.L. (2012). Kinematic generation of ruled surface based on rational motion of point-line, Science China Technological Sciences, 55, 62- 71.
  • [16] Abdel Baky, R. A. (2003). On the Blaschke approach of ruled surfaces, Tamkang J. Math., 34, 107-116.
  • [17] Ünlütürk, Y., Çimdiker, M., Ekici, C. (2016). Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3-space, Communication in Mathematical Modeling and Applications. 1(1), 26-43.
  • [18] Ekici, C., Kaymanlı U.,G., Okur, S. (2021). A new characterization of ruled surfaces according to q-frame vectors in Euclidean 3-space, International Journal of Mathematical Combinatorics, 3, 20-31.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliğinde Sayısal Yöntemler
Bölüm Makaleler
Yazarlar

Mustafa Dede 0000-0003-2652-637X

Cumali Ekici 0000-0002-3247-5727

Mahmut Koçak 0000-0001-7774-0144

Erken Görünüm Tarihi 27 Mart 2024
Yayımlanma Tarihi 28 Mart 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 17 Sayı: 1

Kaynak Göster

APA Dede, M., Ekici, C., & Koçak, M. (2024). Reconstruction of a Ruled Surface in 3-dimensional Euclidean Space. Erzincan University Journal of Science and Technology, 17(1), 259-267. https://doi.org/10.18185/erzifbed.1362369
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