Projective transformations of the parameter of a Bernstein-Bézier curve
ACM Transactions on Graphics (TOG)
Improperly parametrized rational curves
Computer Aided Geometric Design
Generalizing rational degree elevation
Computer Aided Geometric Design
The uniqueness of Be´zier control points
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
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In a recent article, Wang et al. [2] derive a necessary and sufficient condition for the coincidence of two cubic Bezier curves with non-collinear control points. The condition reads that their control points must be either coincident or in reverse order. We point out that this uniqueness of the control points for polynomial cubics is a straightforward consequence of a previous and more general result of Barry and Patterson, namely the uniqueness of the control points for rational Bezier curves. Moreover, this uniqueness applies to properly parameterized polynomial curves of arbitrary degree.