Spline Curve Distance Minimization: Robust and performant computation of distance queries for spline curves on B-spline form

This thesis investigates the problem of efficiently determining the shortest distance from a point to a spline curve, and the location of the nearest point on the spline. Splines are versatile and popular approximation functions used in a plethora of applications, including geometric modeling software, physical simulations and differential equation solvers, computer graphics, image analysis, statistical tools, and more. Distance queries are an important part of the basic operations on which many other operations are dependent. It is therefore essential that these operations are robust and highly performant. A robust and efficient algorithm for solving this problem is presented, which combines established methods with recent techniques developed for spline curves and functions. The algorithmis conceptually simple with clearly separated constituent parts. It can therefore be easily adapted to more specialized applications. The approach can also be extended to related, more general, problems