Visualizing 3-Dimensional Manifolds

Dugan J. Hammock
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 551–552


Given a parametrized 3-dimensional manifold sitting in 4-dimensional space, we wish to visualize it by looking at its intersections with 3-dimensional hyperplanes. The intersections are 2-dimensional surfaces in 4-space which can then be projected into 3-space for visualization. In this paper I present an algorithm for displaying these surfaces of intersection using computer plotting applications (e.g. Mathematica, MATLAB, etc.).