{
 "title": "Constrained Delaunay mesh of a cylinder: volume within the chordal bound, valid elements",
 "kind": "theory",
 "source": "mesh invariants: an inscribed polygon of sagitta s loses at most 2s/R of a circle's area (elementary geometry); constrained Delaunay tetrahedralization after Diazzi et al., ACM TOG 42(6) 2023",
 "quantities": [
  {
   "id": "volume",
   "quantity": "volume of the tetrahedra",
   "measure": {
    "from": "tet",
    "pointer": "/volume"
   },
   "value": 6267.477343911638,
   "tolerance": {
    "relative": 0.0025
   },
   "reason": "the tessellation inscribes the cylinder within the chordal tolerance s = 0.05: the polygon section loses between 0 and 2s/R = 0.5% of the area; the reference is the middle of that band"
  },
  {
   "id": "invalid",
   "quantity": "elements that fail the certified Jacobian check",
   "measure": {
    "command": "mesh.quality",
    "pointer": "/invalid/count"
   },
   "value": 0.0,
   "tolerance": {
    "exact": true
   },
   "reason": "every element of a valid mesh has positive volume"
  }
 ]
}