ENGINEERING GEOMETRY / 2026.08.31

One set of eight morphisms produces both solids and drawings.

Without adding part-specific commands, a typed construction now derives exact 3D solids, third-angle views, hidden lines, sections, dimensions and exchange files.

8generic morphisms

11 / 11valid B-reps

0new holdout operations

44drawing and exchange artifacts

Third-angle mechanical drawing of a spoked wheel generated by MORTRA — SPK-001Topology holdout / third-angle projection, section A-A and principal dimensions

01 / GENERATIVE BASIS

Describe operations, not parts.

Extrusion, revolution and lofting are not separate primitives. They are parameterizations of sweep: transporting a section along a path. MORTRA stores compositions, not part names.

01transform

Change position, orientation or symmetry

02sweep

Transport a section along a trajectory

03combine

Take union, difference or intersection

04select

Select faces, edges or boundaries

05slice

Intersect a shape with a cutting flat

06project

Map a solid to orthographic or isometric views

07constrain

Check dimensions and validity conditions

08annotate

Attach dimensions, centrelines and notes

ONE TYPE RULEsweep_d : Cell(k, Rⁿ) → Cell(min(k+d,n), Rⁿ)

The vocabulary is unchanged when a plane section becomes a 3D solid or a 3D cell is swept in 4D. The exact OpenCascade execution backend currently stops at three dimensions.

02 / ONE CONSTRUCTION DAG

The solid and drawing are never authored separately.

No display outline is hand-authored. Projection lines, hidden lines, sections and hatching are all derived from the same B-rep, so a geometry change propagates to the drawing.

01Typed program

Record the construction with Cell(k, R^n) and eight morphisms

02Exact B-rep

Execute solid geometry and topology in OpenCascade

03Derived views

Derive projection, hidden lines and sections from the B-rep

04Drawing

Attach centrelines, dimensions and notes to semantic entities

05Artifacts

Persist STEP, STL, SVG, DXF and replay JSON

03 / TOPOLOGY HOLDOUTS

Test shapes absent from the basis set.

These are not dimension-only variants. Repeated spokes, paired lugs and three-axis intersecting passages were held out from the five-family basis and generated without changing the operator set.

Mechanical drawing of Spoked wheel — SPK-001Spoked wheel
Repeated transforms, swept profiles and Boolean union.

Mechanical drawing of Clevis bracket — CLV-001Clevis bracket
Paired lugs, cross bore and an exact section from one B-rep.

Mechanical drawing of Cross-drilled manifold — MNF-001Cross-drilled manifold
Three orthogonal passages, hidden lines and clipped hatching.

04 / MEASURED RESULT

Verify geometry and artifacts, not screenshots alone.

Each case independently checks B-rep validity, single-solid topology, positive and closed-form volume, sections, view bounds and exported files.

Basis families5 / 5

Flange, stepped shaft, bracket, transition duct and lattice

Parameter holdouts3 / 3

Unseen dimensions and hole counts

Topology holdouts3 / 3

Spoked wheel, clevis and cross-drilled manifold

Exact solids11 / 11

Replayed as valid single solids

Projected views44 / 44

TOP, FRONT, RIGHT and ISOMETRIC fit their view regions

Added operator families0

No part-specific command was added for the six holdouts

STEPexact 3D solid DXFtechnical drawing JSONresults for all 11 cases Research recordprinciple, method, result and limits

05 / CURRENT BOUNDARY

The next additions are not part names.

This experiment covers geometry and drawing. Material, loads, fatigue, heat, manufacturing tolerance, surface finish, GD&T, assembly sequence and BOM are not executable yet. The next engineering task is to connect them to constrain and annotate with explicit types.

The drawings include third-angle projection, hidden lines, centrelines, sections and principal dimensions, but have not been certified against ASME or ISO. Four-dimensional use is type-checked only; the exact geometry backend is three-dimensional.