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De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two
important techniques in computer aided geometric design. This paper presents the de …

We propose a new isogeometric method using Toric surface patches for trimmed CAD
planar surfaces. This method converts each trimmed spline element into a Toric surface …

Toric surface patches are a class of multi-sided surface patches that can represent multi-
sided domains without mesh degeneration. In this paper, we propose an improved …

Generalized Bézier surfaces are a multi-sided generalization of classical tensor product
Bézier surfaces with a simple control structure and inherit most of the appealing properties …

Abstract The Geometry-Independent Field approximaTion (GIFT) technique, an extension of
isogeometric analysis (IGA), allows for separate spaces to parameterize the computational …

Rational Bézier curves provide a curve fitting tool and are widely used in Computer Aided
Geometric Design, Computer Aided Design and Geometric Modeling. The injectivity (one-to …

The injectivity of NURBS curve implies the curve has no self-intersection. In this paper, we
propose a geometric condition on the control polygon which guarantees the NURBS curve …

Toric Bezier patches generalize the classical tensor-product triangular and rectangular
Bezier surfaces, extensively used in CAGD. The construction of toric Bezier surfaces …

Degenerations of toric ideals and toric varieties Page 1 J. Math. Anal. Appl. 386 (2012) 613–618
Contents lists available at ScienceDirect Journal of Mathematical Analysis and Applications …