“Discrete groups and visualization of three-dimensional manifolds” by Gunn

  • ©Charles Gunn




    Discrete groups and visualization of three-dimensional manifolds



    We describe a software implementation for interactive visualization
    of a wide class of discrete groups. In addition to familiar Euclidean
    space, these groups act on the curved geometries of hyperbolic
    and spherical space. We construct easily computable models of
    our geometric spaces based on projective geometry; and establish
    algorithms for visualization of three-dimensional manifolds based
    upon the close connection between discrete groups and manifolds.
    We describe an object-oriented implementation of these concepts,
    and several novel visualization applications. As a visualization
    tool, this software breaks new ground in two directions: interactive
    exploration of curved spaces, and of topological manifolds modeled
    on these spaces. It establishes a generalization of the application of
    projective geometry to computer graphics, and lays the groundwork
    for visualization of spaces of non-constant curvature.


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