We examine visual representations of data that make use of combinations of both 2D and
3D data mappings. Combining 2D and 3D representations is a common technique that …

While the interpretation of high‐dimensional datasets has become a necessity in most
industries, the spatial visualization of higher‐dimensional geometry has mostly remained a …

In this paper we present a user-friendly sketching-based suggestive interface for untangling
mathematical knots with complicated structures. Rather than treating mathematical knots as …

Just as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections
of smooth 4D topological surfaces are interrupted where one surface intersects itself. They …

We present a computer interface to visualize and interact with mathematical knots, ie, the
embeddings of closed circles in 3-dimensional Euclidean space. Mathematical knots are …

Mathematical knots are different from everyday ropes, in that they are infinitely stretchy and
flexible when being deformed into their ambient isotopic. For this reason, challenges of …

Just as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections
of smooth 4D topological surfaces are interrupted where one surface intersects itself. They …

Smooth topological surfaces embedded in 4D create complex internal structures in their
projected 3D figures. Often these 3D figures twist, turn, and fold back on themselves, leaving …

Smooth topological surfaces embedded in 4D create complex internal structures in their
projected 3D figures. Often these 3D figures twist, turn, and fold back on themselves, leaving …

Mathematical knots are different from everyday ropes in that they are infinitely stretchy and
flexible when being deformed into their ambient isotopic. For this reason, a number of …