# Multilevel B-Spline Interpolation (from Grid)

(c) 2006 by O.Conrad
Multilevel B-spline algorithm for spatial interpolation of scattered data as proposed by Lee, Wolberg and Shin (1997). The algorithm makes use of a coarse-to-fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions, whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function.
The 'Maximum Level' determines the maximum size of the final B-spline matrix and increases exponential with each level. Where level=10 requires about 1mb level=12 needs about 16mb and level=14 about 256mb(!) of additional memory.
Reference:
- Lee, S., Wolberg, G., Shin, S.Y. (1997): 'Scattered Data Interpolation with Multilevel B-Splines', IEEE Transactions On Visualisation And Computer Graphics, Vol.3, No.3

## Parameters

Grid system
Grid system
Grid
Input Grid
Target Grid
Choice
  Available choices: user defined, grid
Method
Choice
  Available choices: without B-spline refinement, with B-spline refinement
Threshold Error
Floating point
Maximum Level
Integer
  Minimum: 1.0; Maximum: 14.0
Update View
Boolean
Data Type
Choice
  Available choices: same as input grid, floating point
Left
Floating point
Right
Floating point
Bottom
Floating point
Top
Floating point
Cellsize
Floating point
Columns
Integer
Rows
Integer
Grid
Output Data Object
Grid system
Grid system
Grid
Output Grid