id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
30015 Schlegel projection breaks convexity jipilab "The documentation string of `.schlegel_projection` reads:
{{{
Return the Schlegel projection.
* The polyhedron is translated such that its ""center()"" is at the
origin.
* The vertices are then normalized to the unit sphere
* The normalized points are stereographically projected from a
point slightly outside of the sphere.
}}}
When normalizing to the unit sphere this (potentially) completely breaks the convexity of the object.
Minimal example:
{{{
sage: fcube = polytopes.hypercube(4)
sage: tfcube = fcube.face_truncation(fcube.faces(0)[0])
sage: sp = tfcube.schlegel_projection()
sage: sp.plot()
Launched html viewer for Graphics3d Object
}}}
The pentagons are not planar although they should in a schlegel diagram.
The scaling to the unit sphere should be removed to preserve convexity.
This ticket fixes the projection while de-duplicating some code.
FOLLOW-UP: Fix .plot() and .show() to have a better behaviour of smaller dimensional objects." defect closed major sage-9.3 geometry fixed polytope, schlegel gh-kliem gh-LaisRast Jean-Philippe Labbé Jonathan Kliem N/A f10d5714bc757db8ec8910359931fb1bcb0dbb29 f10d5714bc757db8ec8910359931fb1bcb0dbb29