Resources Numerical accuracy Calculation policy
The tolerances and the volume used when a Form cage is converted to exact B-rep geometry.
Each bicubic patch becomes a B-spline surface with the patch's 64-bit control points, and the faces are sewn within a tolerance scaled to the model size. The reported volume comes from OpenCascade's volume properties of the solid.
2 calculations in 1 source file. The code is read from the released app when this page loads. It is the calculation people run, not a copy kept for this page.
Tests None found by the review
The tolerance with which patch edges are joined.
tol = max(1e-7, 1e-7 × max |coordinate|)
Scaled to the largest absolute coordinate of the cage, with a floor of 1e-7. The face tolerance 1e-9 is absolute.
let size = 0;
for (const p of form.verts) size = Math.max(size, Math.abs(p[0]), Math.abs(p[1]), Math.abs(p[2]));
const sewTol = tol || Math.max(1e-7, 1e-7 * size);Sews the faces, makes a solid, and measures its volume.
A closed shell becomes a solid, and a negative mass from OpenCascade flips its orientation. The volume in the report is OpenCascade's own double result.
/**
* Sew faces into one shape: { shape, closed, free, shells, sew (for Modified) }. `closed`: no free edges → a solid (outward,
* valid) is returned; otherwise the sewn shell(s).
*/
export function sewFaces(oc, T, faces, tol) {
const sew = T(new oc.BRepBuilderAPI_Sewing(tol, true, true, true, false));
for (const f of faces) sew.Add(f);
sew.Perform(T(new oc.Message_ProgressRange()));
const sewn = T(sew.SewedShape());
const free = sew.NbFreeEdges();
const shells = [];
const ex = T(new oc.TopExp_Explorer(sewn, oc.TopAbs_ShapeEnum.TopAbs_SHELL, oc.TopAbs_ShapeEnum.TopAbs_SHAPE));
for (; ex.More(); ex.Next()) shells.push(T(oc.TopoDS.Shell(T(ex.Current()))));
if (free === 0 && shells.length === 1) {
const ms = T(new oc.BRepBuilderAPI_MakeSolid(shells[0]));
if (!ms.IsDone()) fail(t('form.brep.no_solid'));
const solid = T(ms.Solid());
oc.BRepLib.OrientClosedSolid(solid);
const gp = T(new oc.GProp_GProps());
oc.BRepGProp.VolumeProperties(solid, gp, false, false, false);
let s = solid;
if (gp.Mass() < 0) s = T(solid.Reversed());
return { shape: s, closed: true, free, shells: 1, sew };
}
return { shape: sewn, closed: false, free, shells: shells.length, sew };
}The arithmetic is 64-bit, but the method or the data sets the accuracy: a solver tolerance, a mesh, a step size, a datum shift, a table. The limit is stated where the result is shown.