Glossary

Every domain term is defined once, here, and linked to rather than redefined inline (PRD 15.5). The definitions match PRD section 4.

Host face

The face being unrolled — the outer surface of the tube being cut. Resolving it is ambiguous when a severing cut produces two faces of identical radius and near-identical area, which is why the add-in asks rather than picking the larger one.

Miter curve

The ordered 3D polyline of the cut edge or edge chain lying on the host face. Closed for a full cope, open for a partial one; both are in scope.

Datum

The reference defining circumferential zero, and optionally axial zero. Everything about a template’s rotational position is measured from it.

Unrolling map

A map from points on the host face to 2D template coordinates. Isometric — length-preserving — where the surface allows it.

Template coordinates

The 2D frame a template is drawn in. x is arc length around the tube from the datum, increasing counter-clockwise viewed along the tube axis in the direction of the outward-pointing end. y is axial distance, increasing away from the cut end. The origin is the datum position at the axial reference. This convention is fixed: getting the handedness wrong produces a template that looks correct and fits nothing.

Strain

Relative length distortion introduced by the unrolling map. Zero for a developable surface. Reported as a measured field, never as a whole-face average, because a real tube face can vary from near-circular to strongly oval along its own length.

Developable surface

A surface with zero Gaussian curvature everywhere, which can therefore be flattened into the plane without stretching. Cylinders, cones and generalized cylinders are developable; a bent tube is not.

First fundamental form

The three quantities E, F, G that govern every length measured on a parametric surface. Every unrolling tier is an answer to “integrate this metric”, which is what makes the tiers mutually testable.

Template

A named 2D artifact: the miter curve, datum marks, annotations and calibration geometry, drawn at 1:1.

Template set

A named, ordered collection of templates exported together, sharing print settings.

Tier

One of five unrolling algorithms, A through E, chosen by numerical classification of the measured metric — never by the type name the CAD kernel reports.

Channel surface

The surface swept by a sphere of varying radius moving along a spine curve. A bent tube of constant section is the case that matters here, and it is what Tier D unrolls.

Rotation-minimizing frame

A frame carried along a curve that does not twist about the tangent. Also called a Bishop frame. Used instead of the Frenet frame, which flips at an inflection point and would put a visible discontinuity in a template of an S-bend.

Calibration geometry

A rectangle of known size printed on every template, so a user can measure it and confirm the print came out at 1:1 before cutting anything.