Author : Kawa M. A. Manmi1
1Department of Mathematics, College of Science, University of Salahaddin, Erbil, Iraq
Abstract: The normal vector at a node on the discrete surface is not unique, when a surface discretized by triangular elements. A widely used technique to estimate the normal vector at a giving node is a weighted average of the exact normal of the surrounding triangular elements. In this paper, two weight factors proposed to estimate the normal vector at a node in the triangular mesh. The numerical comparisons are performed between the new weights and with some existing weights for the two knowing geometrical surface.
Keywords: Averaging Normal Vector, Triangular Mesh, Weight Factors, Toroidal Surface
Download the PDF Document from here.
Chen, S. G. & Wu, J. Y. (2004). Estimating normal vectors and curvatures by centroid weights.
Computer Aided Geometric Design, 21(5), 447-458.
Gouraud, H. (1971). Continuous shading of curved surfaces. IEEE Transactions on Computers,
Hoffman, R., & Jain, A. K. (1987). Segmentation and classification of range images. IEEE
Transactions on Pattern Analysis and Machine Intelligence, (5), 608-620.
Huang, J., & Menq, C.H. (2001). Automatic data segmentation for geometric feature extraction from
unorganized 3-D coordinate points. IEEE Transactions on Robotics and Automation, 17(3),
Meek, D. S., & Walton, D. J. (2000). On surface normal and Gaussian curvature approximations
given data sampled from a smooth surface. Computer Aided Geometric Design, 17(6), 521-
Milroy, M. J., Bradley, C., & Vickers, G. W. (1997). Segmentation of a wrap-around model using an
active contour. Computer-Aided Design, 29(4), 299-320.
Phong, B. T. (1975). Illumination for computer generated pictures. Communications of the ACM,
Schaufler, G., & Jensen, H.W. (2000). Ray tracing point sampled geometry. Rendering Techniques
2000: 11th Eurographics Workshop on Rendering ( 319-328).
Taubin, G. (1995). Estimating the tensor of curvature of a surface from a polyhedral approximation.
In Computer Vision, 1995. Proceedings., Fifth International Conference on (902-907). IEEE.
Ubach, P.A., Estruch, C., & Garcia‐Espinosa, J. (2013). On the interpolation of normal vectors for
triangle meshes. International Journal for Numerical Methods in Engineering, 96(4), p.247-
Woo, H., Kang, E., Wang, S., & Lee, K.H. 2002. A new segmentation method for point cloud data.
International Journal of Machine Tools and Manufacture, 42(2), 167-178.
Yang, M., & Lee, E., (1999). Segmentation of measured point data using a parametric quadric
surface approximation. Computer-Aided Design, 31(7), 449-457.
Zhang, Y.L., Yeo, K.S., Khoo, B.C., & Wang, C. (2001). 3D jet impact and toroidal bubbles.
Journal of Computational Physics, 166(2), 336-360.