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d4

Higher dimensional geometry

  • How to define it? (Mathematical description of spheres, cylinders, cubes, ...)
    • Boolean operations
    • Simple Mathematical bodies
    • f(x, y, z, w) = 0
  • How to save it? (Triangle based format after surface triangulation, higher dimensional generalization of STL)
    • In n dimensions: boundary n-1 dimensional; This means from 3-dim boundary generation of 4-dim mesh
  • How to draw it?
    • Projection based: local coordinate system defines a w = 0 plane
    • which slices the higher dimensional geometry
    • these cutted higher dimensional geometry is 3D but maybe not simply connected anymore
    • mesh of 4d tets: slicing of 4d tet sub problem but solvable

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