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