Frequency domain analysis of B-spline interpolation

This paper describes B-spline interpolation and compares it with other reconstruction methods, especially in three-dimensional space. We first consider the B-spline bases in the terms of convolution in signal processing. The presented analysis requires careful usage of continuous and discrete representation of B-spline. Emphasis is given to the important difference between B-spline interpolation and approximation. The difference is shown through frequency domain analysis, so we derive frequency responses of the B-spline interpolation and approximation. We conclude by demonstrating the use of several reconstruction filters and appropriate gradient estimators in volume rendering. Exact reconstruction in volume visualization is very important in many industrial applications, such as material cavity control.