This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Random Constructions ====== ===== Random points on the unit sphere ===== The easiest way to randomly construct a polytope is by sampling points on the unit sphere. The following chooses 100 points on the unit sphere in 3-space. <code perl> > $p1=rand_sphere(3,100); > print $p1->SIMPLICIAL; true </code> ===== Random points sampled from a normal distribution ===== A second way to randomly construct a polytope is by sampling points by a standard normal distribution. The following chooses 100 points sampled from the standard normal distribution in 3-space. <code perl> > $p2 = rand_normal(3, 100); > print $p2 -> SIMPLICIAL, "\n", $p2 -> F_VECTOR; true 24 66 44 </code> With probability one such polytopes under either distribution are simplicial. ===== Random polytopes with are neither simplicial nor simple ===== <code perl> > ($d,$m,$n) = (4,50,30); > $p1=rand_sphere($d,$m); > $p2=polarize($p1); > $p3=new Polytope(POINTS=>rand_vert($p2->VERTICES,$n)); > print $p3->SIMPLICIAL, " ", $p3->SIMPLE, "\n", $p3->F_VECTOR; false false 30 162 251 119 </code> user_guide/tutorials/latest/random.txt Last modified: 2023/11/06 10:57by 127.0.0.1