Is there a geometric variation diminishing property for B-spline or Be´zier surfaces?
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Totally positive bases for shape preserving curve design and optimality of B-splines
Computer Aided Geometric Design
The NURBS book
Shape preserving representations for trigonometric polynomial curves
Computer Aided Geometric Design
Shape preserving alternatives to the rational Bézier model
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Computer Aided Geometric Design
Representing circles with five control points
Computer Aided Geometric Design
On a class of weak Tchebycheff systems
Numerische Mathematik
Are rational Bézier surfaces monotonicity preserving?
Computer Aided Geometric Design
A general class of Bernstein-like bases
Computers & Mathematics with Applications
C-curves: An extension of cubic curves
Computer Aided Geometric Design
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We prove that, in contrast to the case for rational surfaces, some tensor product representations through spaces containing algebraic, trigonometric and hyperbolic polynomials are monotonicity preserving. The surface representations provided in this paper are the only known monotonicity preserving surfaces in addition to the tensor product Bezier and tensor product B-spline surfaces.