{
 "title": "Constrained Delaunay mesh of a stepped block: exact volume, valid elements",
 "kind": "theory",
 "source": "mesh invariants: a tetrahedralization of a polyhedron fills its volume exactly (Si, TetGen paper ACM TOMS 41(2) 2015 for the definition of a CDT; Diazzi et al., ACM TOG 42(6) 2023); the volume is 60·40·10 + 40·40·10 + 20·40·10 − 10·10·10",
 "quantities": [
  {
   "id": "volume",
   "quantity": "volume of the tetrahedra",
   "measure": {
    "from": "tet",
    "pointer": "/volume"
   },
   "value": 47000.0,
   "tolerance": {
    "relative": 1e-12
   },
   "reason": "a planar boundary is tessellated exactly and the constrained Delaunay mesh fills it exactly: only rounding"
  },
  {
   "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"
  },
  {
   "id": "undetermined",
   "quantity": "elements the Jacobian check could not decide",
   "measure": {
    "command": "mesh.quality",
    "pointer": "/undetermined/count"
   },
   "value": 0.0,
   "tolerance": {
    "exact": true
   },
   "reason": "a linear tetrahedron's sign is exact"
  }
 ]
}