Abstract
The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate functions, from which we sample a univariate function at the mid-point. This refinement step is the basis to an extension of the 4-point subdivision scheme to our setting. The bivariate subdivision scheme can be reduced to a countable number of univariate, interpolatory, non-stationary subdivision schemes. Properties of the generated interpolant are derived, such as continuity, smoothness and approximation order.
Original language | English |
---|---|
Pages (from-to) | 709-730 |
Number of pages | 22 |
Journal | Journal of Approximation Theory |
Volume | 164 |
Issue number | 5 |
DOIs | |
State | Published - May 2012 |
Keywords
- Approximation order
- Bivariate interpolation
- Non-stationary subdivision scheme
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
- Numerical Analysis
- General Mathematics