The method of finding points of intersection of two cubic Bezier curves using the Sylvester matrix

• Autorzy: Biły B.
• Języki publikacji: EN

Abstrakty

EN

Sylvester matrix is used to create a 9th degree polynomial from coefficients of two cubic Bezier curves. The real roots of this polynomial allow to compute points of intersection of aforementioned curves. An additional constraint is used to indicate valid points. The “reverseinverse law” is presented in order to reduce the cost of calculation in this particular case. Also some limitations of the method as well as the ways to avoid them, if possible, are pointed out.

Słowa kluczowe

EN

Sylvester matrix; Bezier curve; reverse-inverse law

PL

macierz Sylvestera; krzywa Beziera

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2016
• Tom: Vol. 6, iss. 1
• Strony: 155--176
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Biły B.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

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• 4. Klockiewicz B.: Resultant theory... Online: https://gajda.faculty.wmi.amu. edu.pl/Pliki/Klockiewicz Teoria rugownika.pdf (in Polish).
• 5. Manocha D., Demmel J.W.: Algorithms for intersecting parametric and algebraic curves. Online: https://www2.eecs.berkeley.edu/Pubs/TechRpts/1992/ CSD-92-698.pdf
• 6. Mostowski A., Stark M.: Elements of Higher Algebra. PWN, Warszawa 1977 (in Polish).
• 7. Stoer J.: Introduction to Numerical Methods, vol. 1. PWN, Warszawa 1979 (in Polish).
• 8. Weisstein E.W.: Sylvester matrix. From MathWorld – A Wolfram Web Resource.
• 9. Wikipedia contributors: James Joseph Sylvester. Online: https://en.wikipedia.org/wiki/James Joseph Sylvester.
• 10. Zorin D.: Operations on parametric curves and surfaces: intersection and trimming. Online: www.mrl.nyu.edu/~dzorin/geom02/lectures/lect06.pdf.