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Cylinders Through Five Points: Computational Algebra and Geometry
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| Organization: | Wolfram Research, Inc. |
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ICMS 2006
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Castro Urdiales, Spain
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Presented at ICMS, Castro Urdiales, Spain, September 3, 2006.
Abstract:
We address the following question: Given five points in R3, determine a right circular cylinder containing those points. We obtain algebraic equations for the axial line and radius parameters and show that these give six solutions in the generic case. An even number (0, 2, 4, or 6) will be real valued and hence correspond to actual cylinders in R3. We will investigate computational and theoretical matters related to this problem. In particular we will show how exact and numeric Gröbner bases, equation solving, and related symbolic-numeric methods may be used to advantage. We will also discuss some applications.
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nonlinear computational geometry, enumerative geometry, algebraic systems of equations, Groebner bases
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http://www.icms2006.unican.es
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| ICMS2006_cylinders_talk.pdf (345 KB) - PDF Document | | cylinder_5_points_computation.pdf (2.8 MB) - PDF Document | | ICMS2006_cylinders_talk.nb (607.2 KB) - Mathematica Notebook | | cylinder_5_points_computation.nb (1.1 MB) - Mathematica Notebook |
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