Ternary and Three-point Univariate Subdivision Schemes
Abstract:
Abstract. A family of interpolating 3-point ternary subdivision schemes is shown to exist and have C 1-continuity. A family of interpolating 4-point ternary subdivision schemes is shown to exist and have C 2-continuity. An approximating 3-point ternary scheme has been found and shown to have C 2 continuity. An approximating 3-point binary scheme is derived and shown to have C 3 continuity. The generating function formalism is used to analyze the continuity properties of these schemes. These are compared with the established schemes. Most work in the area of subdivision schemes has considered binary schemes with an even number of control points. Following a similar argument to that used in [2], we decided to investigate schemes with an odd number of control points, specifically 3-point schemes. This led to a more general
Citations
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