III.3 - Tricubic Interpolation

Abstract

This chapter analyzes the method of tricubic interpolation. In many cases, linear interpolation provides a very good compromise between speed and accuracy. However, when the data volume is non-isotropic, linear interpolation may introduce objectionable artifacts. In these cases cubic interpolation may be substituted. This chapter reviews tricubic interpolation and provides a C-code implementation. This implementation uses Catmull–Rom interpolating curves. For the one-dimensional case, these curves can be expressed by a matrix formula. Tricubic interpolation is done by cascading the one-dimensional operations in the X, Y, then Z directions. Sixteen interpolations using sixty-four original data values are performed in the X direction (in the inner loop of the code). Four interpolations using the prior sixteen values are then done in the Y direction. Finally, the data from the previous four interpolations are combined in the Z direction for the final value. As with trilinear interpolation, the order of combination is not important; the interpolated value is unique.