Box spline reconstruction on the face-centered cubic lattice

Area of Science:

• Computer Graphics
• Geometric Modeling
• Numerical Analysis

Background:

• Face-centered cubic (FCC) lattices are common in various scientific domains.
• Efficient reconstruction of FCC-sampled data is crucial for accurate analysis and visualization.
• Existing methods may suffer from aliasing and lower computational efficiency.

Purpose of the Study:

• To introduce and analyze an efficient reconstruction algorithm for FCC-sampled data.
• To leverage the properties of 6-direction box splines for improved reconstruction.
• To achieve higher evaluation efficiency and reduced aliasing.

Main Methods:

• Developing a reconstruction algorithm based on the 6-direction box spline.
• Associating the spline with the FCC lattice structure.
• Analyzing continuity and approximation order, comparing it to triquadratic B-splines.
• Deriving techniques for enhanced evaluation efficiency.

Main Results:

• The 6-direction box spline shares continuity and approximation order with triquadratic B-splines.
• The algorithm demonstrates reduced aliasing for generic level sets.
• Special techniques were derived to exploit the spline's lower degree and smaller stencil size.
• Higher evaluation efficiency is achieved compared to triquadratic B-splines.

Conclusions:

• The proposed algorithm offers an efficient and effective method for reconstructing FCC-sampled data.
• The 6-direction box spline provides advantages in terms of aliasing reduction and computational speed.
• This work contributes to improved data processing in fields utilizing FCC lattices.