topology preserving simplification with quantization in OpenLayers3
via boundlessgeo
roomthily: spatially, with respect to space (save the words)
Klein Bottle Opener
The problem of beer That it is within a ‘bottle’, i.e. a boundaryless compact 2-manifold homeomorphic to the sphere. Since beer bottles are not (usually) pathological or “wild" spheres, but smooth manifolds, they separate 3-space into two non-communicating regions: inside, containing beer, andoutside, containing you. This state must not remain.
A proposed solution Clearly the elegant course is to introduce a non-orientable manifold, which has one side and does not divide 3-space. When juxtaposed with the beer-bounding manifold described above, it acts to disrupt the continuity thereof, canceling the outdated paradigm of distinction between interior and exterior. This enables the desired interaction between beer and self.
Q E D You need one.
Icosahedron (via Richard Sweeney)
Tetrahedron (via Richard Sweeney)