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Journal of Graphics ›› 2021, Vol. 42 ›› Issue (4): 651-658.DOI: 10.11996/JG.j.2095-302X.2021040651

• Computer Graphics and Virtual Reality • Previous Articles     Next Articles

Geometric evaluation algorithms for Lupaş q-Bézier curve and its applications

  

  1. 1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang Hebei 050024, China;
    2. Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang Hebei 050024, China
  • Online:2021-08-31 Published:2021-08-05
  • Supported by:
    National Natural Science Foundation of China (61573127); National Natural Science Foundation of Hebei Porvince (A2018205103);
    Research Fund of Hebei Normal University (L2020Z02, L2020K09); Hebei Normal University Graduate Project (CXZZSS202053)

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Abstract: The Lupaş q-Bézier curve is a generalized Bézier curve with q-integer as the shape parameter. A new
geometric evaluation algorithm for Lupaş q-Bézier curve was constructed in this paper, in which the affine
combination of two nodes in the penultimate layer of the algorithm is tangent to the curve. A new representation of the
derivative of the Lupaş q-Bézier curve was obtained using the property of algorithm, and the subdivision of curve was
realized. Particularly, a product of the shape parameters of the two subcurves produced by the subdivision of the Lupaş
q-Béziercurves was equal to the shape parameter of the original curve. Furthermore, a new geometric evaluation
algorithm of weighted Lupaş q-Bézier with an explicit matrix representation was gained.

Key words: Lupa? q-Bézier curve, de Casteljau algorithm, explicit matrix representation, subdivision, computational
complexity

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