A Muntz Type Theorem for a Family of Corner Cutting Schemes
It establishes a theoretical connection between Muntz conditions and convergence of corner cutting schemes, which is a specific incremental result for geometric modeling.
The paper identifies a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves and provides a Muntz type condition for the convergence of control polygons to the underlying curve.
By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.