Multivariate volumetric datasets, which are volumetric datasets that contain more than one variable per voxel, are becoming increasingly prevalent, such as transcriptomic datasets, which can contain up to hundreds of dimensions. This high dimensionality has proven to be a difficult obstacle to overcome when trying to visualize such datasets, especially in creating user-friendly transfer functions, which are needed to guide the direct volume rendering pipeline into visualizing information relevant to the user.
This work proposes the use of neighborhood-preserving dimensionality reduction, such as t-SNE and UMAP, to define a transfer function that simplifies highlighting highly similar points in data with an arbitrarily high number of dimensions.
However, since direct interpolation between points in the resulting non-linear embedded space does not provide correct results, we propose and evaluate several interpolation methods to address this limitation. The most accurate of which is the use of approximate nearest neighbor algorithms to approximate the position an interpolated high-dimensional point would have in the embedded space. We also propose an adaptation of a two-step TF that can simulate some of the surface-based effects whose scalar-based implementations cannot be directly applied to multivariate data, such as gradient-based opacity and surface shading.
Finally, we implement a plugin in the ManiVault framework, which is an existing framework made to analyze multivariate data, to test and analyze our method.

It is possible to use a different representation of space in a Virtual Reality (VR) game, instead of using the euclidean representation we are used to. The reason why that is interesting is that it opens up the possibility of traversing infinitely far in the virtual space while being confined to a relatively limited space in the real world. But for this to be a useful use case, people will need the ability to traverse this new space in an intuitive or at least competent way. One way to help people with navigation in such a space would be to show the person what the fastest path from point A to point B is. This paper researches the possible ways to calculate this path so it can be used to help people while they are traversing this different type of space. Concluding that a trade-off needs to be made between the speed and accuracy of the result depending on the situation, and that no algorithm exists which is the best in both speed and accuracy. Meaning that the context determines what algorithm should be used.