Mixed product surfaces in euclidean 3-space E3

Year 2016, Volume: 4 Issue: 2, 203 - 210, 01.03.2016

Betul Bulca , Kadri Arslan

Abstract

In the present study we define a
new kind of product surfaces namely mixed product which are product of plane
curve and space curve in 3-dimensional
Euclidean space. We give the original results of mixed product surface patches
of flat or minimal type in E³. Further, we give some examples of
these kind of surfaces and plot their graphics.

Keywords

Spherical product, mixed product, surfaces

References

• Arslan, K., Bulca, B., Bayram, B., Ozturk and Ugail, H., On Spherical Product Surfaces in E3, IEEE Computer Society, International Conference on Cyberworlds, 2009, 132–137.
• Chen, B.Y., Geometry of Submanifolds, Dekker, New York, 1973.
• Gielis, J., Beirinchx, J. and Bastianens, Superquadrics with rational and irrational symmetry, Symposium on solid modelling and Applications, 2003.
• Gupta, A. and Bajcsy, R., Surface and volumetric segmentation of range images using biquadrics and superquadrics. In Int. Conf. Pattern Recognition, 1(1992), 158–162.
• Hager, G., Task-directed computation of qualitative decisions from sensor data, IEEE Transactions of Robotics and Automations, 10(1994), 415–429.
• Jaklic, A., Leonardis, A. and Solina, F., Segmentation and Recovery of Superquadrics, Kluwer Academic Publishers, 20, 2000.
• Leonardis, A., Jaklic, A. and Solina, F., Superquadrics for segmenting and modelling data. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 1997, 19(11): 1289–1295.
• O’ Neill, B., Elementary Differential Geometry, Academic Press, USA, 1997.
• Pentland, A.P., Percettual Organization and the Representation of Natural Form, Artificial Intelligence, 28(1986), 293–331.
• Pentland, A.P., Automatic Extraction of Deformable Part Models, Int. J. Com. Vision, 4(1990), 107–126.