Hypersliceplorer: Interactive Visualization of Shapes in Multiple Dimensions

Authors. Thomas Torsney-Weir, Torsten Möller, Michael Sedlmair, Mike Kirby

Venue. CGF (2018)

Materials. DOI PDF video

Abstract. In this paper we present Hypersliceplorer, an algorithm for generating 2D slices of multi-dimensional shapes defined by a simplical mesh. Often, slices are generated by using a parametric form and then constraining parameters to view the slice. In our case, we developed an algorithm to slice a simplical mesh of any number of dimensions with a two-dimensional slice. In order to get a global appreciation of the multi-dimensional object, we show multiple slices by sampling a number of different slicing points and projecting the slices into a single view per dimension pair. These slices are shown in an interactive viewer which can switch between a global view (all slices) and a local view (single slice). We show how this method can be used to study regular polytopes, differences between spaces of polynomials, and multi-objective optimization surfaces.

@article{https://doi.org/10.1111/cgf.13415,
    title        = {Hypersliceplorer: Interactive visualization of shapes in multiple dimensions},
    author       = {Torsney-Weir, T. and M\"{o}ller, T. and Sedlmair, M. and Kirby, R. M.},
    year         = {2018},
    journal      = {Computer Graphics Forum},
    volume       = {37},
    number       = {3},
    pages        = {229--240},
    doi          = {https://doi.org/10.1111/cgf.13415},
    url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13415},
    keywords     = {Categories and Subject Descriptors (according to ACM CCS), I.3.3 Computer Graphics: Picture/Image Generation--Line and curve generation},
    eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13415},
    abstract     = {Abstract In this paper we present Hypersliceplorer, an algorithm for generating 2D slices of multi-dimensional shapes defined by a simplical mesh. Often, slices are generated by using a parametric form and then constraining parameters to view the slice. In our case, we developed an algorithm to slice a simplical mesh of any number of dimensions with a two-dimensional slice. In order to get a global appreciation of the multi-dimensional object, we show multiple slices by sampling a number of different slicing points and projecting the slices into a single view per dimension pair. These slices are shown in an interactive viewer which can switch between a global view (all slices) and a local view (single slice). We show how this method can be used to study regular polytopes, differences between spaces of polynomials, and multi-objective optimization surfaces.}
}