Fast Line Integration of B-Spline Data Models

B-spline data models are a powerful way to represent scientific data sets with a functional approximation that admit analytical formulas for computing function values, derivatives, and box-aligned integrals. However, computing line integrals of these models is only efficient when the path of integration is aligned with a Cartesian direction. In many scientific disciplines, it is necessary to quickly and repeatedly compute line integrals along rays with high accuracy. Here, we demonstrate a new method for quickly integrating B-spline models along straight-line (but not axis-aligned) paths. We show that our method operates roughly an order of magnitude more efficiently than standard approximations with the trapezoidal rule for two dimensional data. The efficiency of the method is also studied in three dimensions. In three dimensions, we find the method is less efficient, yet still comparable with traditional approaches.