Direct manipulations of B-spline and NURBS curves |
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| Affiliation: | 1. Health Science University, Antalya Educational and Research Hospital, Clinical of Infectious Diseases, Antalya, Turkey;2. Medical Faculty, Department of Gastroenterology, Kocaeli University, Izmit, Kocaeli, Turkey;4. DESAM Institute, Near East University, Turkish Republic of Northern Cyprus, Nicosia, Turkey;5. Medical Diagnostic Imaging Department, College of Health Sciences, University of Sharjah, Sharjah, United Arab Emirates;1. Department of Marine Technology, Amirkabir University of Technology, Hafez Ave. No. 424, Tehran, Iran;2. Department of Civil Engineering, Pardis Branch, Islamic Azad University, Tehran, Iran;1. College of Sciences, PLA University of Science and Technology, Nanjing 211101, China;2. Business School, Sichuan University, Chengdu, Sichuan 610064, China;3. Departamento de Automatica y Computacion, Universidad Publica de Navarra, Pamplona 31006, Spain |
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| Abstract: | This paper presents a method for the direct manipulations of B-spline and non-uniform rational B-splines (NURBS) curves using geometric constraints. A deformable model is developed to define the deformation energy functional of B-spline and NURBS curves. The finite element method is used to minimize the deformation energy functional and solve for the deformed shape of curves subjected to constraints. This approach results in a set of linear equations for a B-spline curve and a set of non-linear equations for a NURBS curve. A perspective mapping is used to linearize the NURBS formulations. NURBS curves are first mapped from the 3D Cartesian coordinate space to the 4D homogeneous coordinate space, and transformed to 4D B-spline curves. After the manipulation in the 4D homogeneous coordinate space, the modified NURBS curves are then mapped back to the 3D Cartesian coordinate space. The approach is implemented by a prototype program, which is written in C, and runs under WINDOWS. Several examples are presented to demonstrate the capabilities of this approach. |
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