Solving systems of algebraic equations

• Autorzy: Kiciak P.
• Języki publikacji: EN

Abstrakty

EN

Numerical procedutes of solving a system for algebraic equations usually consist of a part that localizes the solutions and a part that computers their accurate approximations. The localization is often based on the convex hull property of the Bernstein-Bezier representation of the equations. In the procedure described in this paper, the convex hull test is complemented with another, which significantly improves the efficiency of the procedures.

Słowa kluczowe

EN

Bernstein polynomials; rational Bezier curves and patches; free-form deformation; de Castelijau algorithm; convex hull property

• Wydawca: Institute of Information Technology of the Warsaw University of Life Sciences – SGGW
• Czasopismo: Machine Graphics and Vision
• Rocznik: 2002
• Tom: Vol. 11, No. 4
• Strony: 455--473
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kiciak P.

• Institute of Applied Mathematics and Mechanics, Wasraw University, Banacha 2 st., 02-097 Warsaw, Poland

Bibliografia

• [1] Ortega J. M., Rheinboldt W. C.: Iterative Solution of Nonlinear Equations in Several Variables. AP. 1970.
• [2] Sederberg T. W., Parry S. R.: Free-form deformation of solid geometric models. CG, 20, 103-106. 1986.
• [3] Coquillart S.: Extended free-form deformation: a sculpting tool for 3D geometric modeling. CG, 24, 187-196. 1990.
• [4] Sherbroke E. C., Patrikalakis N. M.: Computation of the Real Solutions of Nonlinear Polynomial Systems. MIT Ocean Engineering Design Lab. Memorandum 91-12, MIT. 1991.
• [5] Farin G.: Curves and surfaces for Computer Aided Geometric Design. AP. 1993.
• [6] Manocha D., Krishnan S.: Algebraic pruning: a fast technique for curve and surface intersection. CAGD, l4, 823-845. 1997.
• [7] Kiciak P.: Computing intersections of rational patches. MG&V, 11(4), 431-454. 2002.