Reflectance fields have a limited number of discrete lighting directions that can be used for lighting design. Multiple methods for interpolating these reflectance fields have been proposed to get an approximation of the missing lighting directions. However, these methods can struggle with specular highlights, because they are more sensitive to changes in lighting direction. We propose a method that solves this problem by representing the specular highlights as Gaussians and interpolating them, framing the problem as a Lagrangian formulation. We interpolate these Gaussians by optimizing their parameters twice: first for each lighting direction, then for every neighboring lighting direction. By doing this, we can efficiently interpolate specular highlights in real-time. This enables the designer to design the specular highlights and their movements with immediate feedback.

In the multi-agent pathfinding (MAPF) problem, agents have to traverse a graph to a goal location without running into each other. Currently, the Branch-and-Cut-and-Price-MAPF (BCP-MAPF) algorithm is the state-of-the-art algorithm for solving MAPF problems, which uses Branch-Price-and-Cut (BPC) to solve a linear minimization problem. The multi-agent pathfinding with waypoints (MAPFW) problem is a variation on the classical MAPF problem. MAPFW can be useful for e.g. navigating warehouses and scheduling trains. However, little to no research exists on MAPFW. This research proposes two extensions to the BCP-MAPF algorithm to incorporate waypoints and reviews their performance.