The t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm is a tool for analyzing high-dimensional data, such as RNA sequencing data from brain cells. However, its applicability to large datasets is limited by the quadratic complexity of its gradient computation, which arises from all-to-all interactions between points. This computation can be interpreted as an N-body problem, enabling the use of approximation methods to accelerate evaluation.This work investigates the fast multipole method (FMM), a hierarchical N-body solver based on multipole expansions, as an acceleration strategy for t-SNE. To further optimize performance, a time-varying theta parameter is introduced to adapt the approximation accuracy during optimization. FMM is integrated into the t-SNE framework and evaluated against existing approaches, including the Barnes-Hut (BH) method and the particle-mesh method (PM). Results show that FMM outperforms other BH-like methods in terms of the error–time trade-off, but does not match the performance of PM. The proposed time-varying theta parameter enables FMM to achieve a lower embedding cost within the same runtime as PM, improving the cost–time trade-off despite not surpassing its error–time efficiency.

The micro detail on surfaces can have a profound effect on how rays bounce of it. In ray tracing, this micro-surface is normally approximated with statistical models. We wish to figure out what the effect of normal interpolation and Phong tessellation is on how rays reflect on the surface. This has been Done by creating a ray tracers from scratch, that uses height fields, with normal interpolation and Phong tessellation. This ray tracer has then been used to render 3 different micro-surfaces, which were compared in order to understand the difference. The conclusion of this research was that both smoothing techniques had little to no effect on the reflection of rays on micro-surfaces with a high triangle density. However on micro-surfaces with a low triangle density, there was a much more pronounced difference with the smoothing techniques. A second conclusion was made which was that rougher surfaces have a more spread out distribution of rays than smoother surfaces.