The geometrical construction of pointwise distributions on curves |
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| Institution: | 1. School of Pharmacy, Faculty of Science, University of Nottingham Malaysia Campus, 43500 Semenyih, Malaysia;2. School of Allied Health Sciences and Research Excellence Center for Innovation and Health Products (RECIHP), Walailak University, 80161 Nakhon Si Thammarat, Thailand;3. National Center for Genetic Engineering and Biotechnology (BIOTEC), 113 Thailand Science Park, Khlong Luang, 12120, Pathum Thani, Thailand;4. Department of Pharmacy, Faculty of Life Science, University of Development Alternative, 1207 Dhaka, Bangladesh;5. Department of Parasitology, Faculty of Medicine, University of Malaya, 50603, Kuala Lumpur, Malaysia;6. Department of Medical Microbiology, Faculty of Medicine, University of Malaya, 50603, Kuala Lumpur, Malaysia;7. Department of Pharmaceutical Technology, Jadavpur University, 70032, Kolkata, India;8. Herbal Medicine Research Center, Institute for Medical Research, 50588, Kuala Lumpur, Malaysia;9. Department of Biochemistry, School of Life Sciences, Central University of Rajasthan, 305817 Rajasthan, India;10. Institute of Biological Sciences, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia;11. Laboratory of Natural Products, Institute of Bioscience, University Putra Malaysia, 43400, Serdang, Malaysia;12. Atta-ur-Rahman Institute for Natural Products Discovery, Universiti Teknologi MARA Puncak Alam, 42300 Kuala Selangor, Malaysia;13. Institute for Molecular Bioscience, University of Queensland, QLD 4072, St Lucia, Australia;14. Pasteur Institute of Epidemiology and Microbiology, 14 Mira str., 197101, St. Petersburg, Russia |
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| Abstract: | A method is developed to generate desirable pointwise distributions along curves. This is accomplished with a simple geometrical construction which provides a global parameter for curvature clustering together with other parameters for arbitrary local clustering specifications. The level of available precision is considerable in that exact numbers of points can be assigned to both local clusters and to curvature simultaneously with specified spacing from the endpoints. The basic construction simply involves the generation of an auxiliary curve along outward normal directions from the given one. The distribution results when uniform arc-length increments are taken along the auxiliary curve and are projected back along the normals to our given curve. This construction can be applied either directly or in the form of equivalent weight functions. Moreover, it is valid regardless of whether the curve lies in Euclidian space or in surfaces and regardless of the dimensionality of the space in which the curve lies. |
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