An improved condition for the convexity and positivity of Bernstein-Be´zier surfaces over triangles
Computer Aided Geometric Design
On the convexity of parametric Be´zier triangular surfaces
Computer Aided Geometric Design
On convexity of piecewise polynomial functions on triangulations
Computer Aided Geometric Design
Convexity and Bernstein-Be´zier polynomials
Curves and surfaces
The convexity of quadratic parametric triangular Bernstein-Be´zier surfaces
Computer Aided Geometric Design
Convexity of Be´zier nets on triangulations
Computer Aided Geometric Design
Convexity of Be´zier nets on sub-triangles
Computer Aided Geometric Design
Multivariate Bernstein polynomials and convexity
Computer Aided Geometric Design
An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
The convexity of parametric Be´zier triangular patches of degree 2
Computer Aided Geometric Design
Convexity preserving interpolation and Powell-Sabin elements
Computer Aided Geometric Design
Surface fitting using convex Powell-Sabin splines
Journal of Computational and Applied Mathematics
Be´zier nets, convexity and subdivision on higher-dimensional simplices
Computer Aided Geometric Design
A counterexample to a theorem about the convexity of Powell-Sabin elements
Computer Aided Geometric Design
Surface fitting using convex tensor-product splines
Journal of Computational and Applied Mathematics
Linear convexity conditions for rectangular and triangular Bernstein-Be´zier surfaces
Computer Aided Geometric Design
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Convex surface fitting with parametric Be´zier surfaces
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
C1 Convexity-Preserving Interpolation of Scattered Data
SIAM Journal on Scientific Computing
Convexity preserving interpolation
Computer Aided Geometric Design
On the convexity of Bézier nets of quadratic Powell—Sabin splines on 12-fold refined triangulations
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
Convexity preserving scattered data interpolation using Powell--Sabin elements
Computer Aided Geometric Design
The conditions of convexity for Bernstein--Bézier surfaces over triangles
Computer Aided Geometric Design
An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
Computer Aided Geometric Design
Convexity preserving C0 splines
Advances in Computational Mathematics
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A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein-Bezier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.