A least squares method for estimation of Bezier curves and surfaces and its applicability to multivariate analysis |
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| Affiliation: | 1. School of Geosciences and Info-Physics, Central South University, Changsha, Hunan 410083, China;2. School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China;3. School of Civil Engineering, Central South University, Changsha, Hunan 410075, China;1. RIKEN–XJTU Joint Research Unit, RIKEN, Japan;2. Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, China;1. Government Polytechnic, Sambalpur, Odisha, India;2. Department of Civil Engineering, National Institute of Technology Rourkela, Odisha, India;1. PERCRO Laboratory, TeCIP Institute, Scuola Superiore Sant’Anna, L. Alamanni 13B, 56010 Ghezzano, San Giuliano Terme, Italy;2. Department of Electrical and Information Engineering (DEI), Polytechnic University of Bari (Italy), E. Orabona 4, 70126 Bari, Italy;1. Mechanical Engineering Department, École de technologie supérieure, Montreal, Canada;2. Mechanical Engineering Department, Faculty of Technology, University of M’sila, Algeria |
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| Abstract: | A new least squares estimation method for Bezier polynomial curves and surfaces is described and illustrated. The Cartesian coordinates of the vertices of polygons defining the curves separated well natural populations of Anodonta cygnea L. and human sagittal profiles of different sexes and age classes. Multivariate comparisons of the coordinates of Bezier polygon vertices and Euclidean distance measures showed that the polygon coordinates revealed shape differences better than distances between homologous points on the curves. Further, polygon coordinates separated groups for more than two variables as well as or better than the equivalent number distances. In addition, polygon coordinates permit construction of mean shapes and their variances. Possible applications in trend surface analyses and for illustration in computer-aided identification programs are suggested. |
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