A clean-room reconstruction of Ian C. Braid's B-rep solid modeler, presented at the PROLAMAT conference in Budapest, 1973. Developed at the Cambridge University Computer Laboratory CAD Group under Charles Lang.
BUILD was the first system to demonstrate that boundary representation — describing a solid by its closed surface of faces, edges, and vertices — was both mathematically sound and computationally tractable. Boolean operations (union, difference, intersection) on polyhedral solids were computed on Cambridge's Titan mainframe.
The commercial lineage runs directly through Shape Data (1974) → ROMULUS (1978) → Parasolid → SolidWorks, NX, Solid Edge. Every major commercial B-rep kernel in production CAD today traces to this thesis.
Four rooms in Classicery touch 3D: SP (1963, light-pen constraint sketch), SV (1972, CSG ray casting, the sibling on the other side of PROLAMAT 1973), BLD (1973, this room, B-rep solid modeling), ALYUS (1985, Cardinal-spline surfaces). Chapter 8 inside reads the four together.
HELP AT THE PROMPT · DRAG THE VIEWPORT TO ORBITThis room reconstructs BUILD — Ian C. Braid's boundary-representation solid modeler, submitted as a PhD thesis at the Cambridge University Computer Laboratory in 1973 and presented publicly at the PROLAMAT conference in Budapest that same year.
What is honest in this room: the wireframe display engine with back-face hidden-line removal; the VEF (Vertex-Edge-Face) B-rep data structure; the command vocabulary derived from Braid's thesis; the Boolean operations (union, difference, intersection) computed using face-plane half-space tests, accurate for convex solids. The boot text, the Titan mainframe framing, and the phosphor-green terminal aesthetic are period reconstruction.
What is polite forgery: intersection cap faces at Boolean boundaries are approximate — the true problem of computing intersection curves between faces was the central technical difficulty of the original system. The original ran in FORTRAN on Cambridge's Titan mainframe, not JavaScript on V8.
Cart 012 / 024. Type HELP at the prompt to begin, or DEMO for a guided sequence. Chapter 8 reads this room together with SP (Sketchpad, 1963), SV (SynthaVision, 1972), and ALYUS (Alias/1, 1985) — the other three rooms in Classicery that touch 3D.
In 1965, Professor Maurice Wilkes — already famous for the EDSAC, the first practical stored-program computer — and his doctoral student Charles Lang founded the Computer Aided Design Group at the Cambridge University Computer Laboratory. British government funding underwrote it.
The group worked on Cambridge's Titan mainframe — an Atlas 2 prototype jointly developed with Ferranti, running one of the earliest timesharing operating systems — with a Digital PDP-7 alongside for the interactive graphics work the Titan could not do directly. The research question was open and strange: what does it mean to represent a solid object inside a computer?
Initial experiments began in 1969. They were writing in assembly language. Then Ian Braid arrived as a doctoral student. Braid brought FORTRAN, mathematical rigor, and an insistence that the system handle the hard cases — curved surfaces, non-planar intersections — rather than faceting them away.
The fundamental insight of B-rep: a solid is completely determined by its bounding surface. A closed, orientable manifold of faces, connected by edges, joined at vertices, enclosing a finite volume — that is the solid. You do not need to store the interior; the boundary implies it.
BUILD stored this as a VEF list: Vertices, Edges, Faces. Each face is a planar polygon. Each edge connects exactly two vertices and borders exactly two faces. The structure satisfies the Euler-Poincaré formula:
V − E + F = 2(1 − G)
For a solid with no through-holes (genus G = 0): V − E + F = 2. This is Euler's formula for polyhedra, and it is the topological invariant BUILD used to verify validity. Try VEF name in the terminal to see Euler's formula checked for any defined object.
Braid's contribution was implementing Boolean operations — union, difference, intersection — that preserved topological validity. Other systems of the era avoided the hard cases. BUILD confronted them.
Compare with SP (Sketchpad, cart 009): Sutherland's ring structure stored topological relationships among 2D entities and constraints. Braid's VEF stored topological relationships among 3D faces. Same intuition — geometry is just one face of the object; topology is the other — taken from the plane into the solid.
Cambridge's Titan (officially the Atlas 2) was a second-generation transistor mainframe derived from the Manchester Atlas. It ran the Cambridge Multiple Access System — one of the earliest timesharing operating systems. Designed from 1963, operational from 1964, fully timeshared by 1967, it served as the sole large-scale computing resource for the entire university until October 1973.
BUILD ran on Titan as batch FORTRAN jobs. The operator would mount a fresh Calcomp paper roll, submit the job, wait for the queue, and collect the wireframe output on the plotter. Interactive graphics — where you drag a control point and watch the solid rebuild in real time — was impossible on shared mainframe time. That required dedicated workstations, which arrived later in the decade.
The display output would have been a vector scope or Calcomp plotter. The wireframe hidden-line images that came out of Braid's system — polyhedral solids rendered from arbitrary viewpoints with occluded edges suppressed — were, in 1973, technically remarkable.
Braid's PhD thesis, submitted and awarded in 1973, was titled Designing with Volumes. It described the BUILD1 system in full: the data structures, the geometric algorithms, the Boolean operations, and the display pipeline.
Several ideas from the thesis are now standard practice: the explicit separation of geometry (metric coordinates) from topology (how faces connect); the use of outward face normals to determine inside and outside; regularized Boolean operations that close under the solid validity condition.
Braid also tackled non-planar surfaces and curved edges — a degree of generality that set the thesis apart from contemporaneous work. The system was implemented entirely in FORTRAN on Titan and could handle genuinely complex polyhedral solids.
The thesis was commercially republished by Cantab Press, Cambridge, in 1974. It is cited in virtually every paper on solid modeling published in the following decade.
PROLAMAT (Programming Languages for Machine Tools) was a conference series focused on numerical control and CAD/CAM. The 1973 edition, held in Budapest, became the unlikely venue where the field of solid modeling coalesced. Groups that had been working in geographic isolation met and compared notes for the first time.
Three systems were presented that year that would define the architecture of the field:
BUILD — Ian Braid, Cambridge University, England. Boundary representation, VEF data structure, Boolean operations on general polyhedra.
TIPS-1 — Professor N. Okino, Hokkaido University, Japan. Constructive Solid Geometry: primitives combined with Boolean operations and stored as an operation tree.
PADL — Herb Voelcker and Ari Requicha, University of Rochester, USA. CSG with a formal set-theoretic mathematical foundation; the regularized Boolean operations framework.
The field immediately diverged into two camps. The division was not merely technical — it reflected deep differences in modeling philosophy.
B-rep (Braid, Cambridge) stores the result of operations: a list of faces, edges, and vertices. Evaluation is immediate because the solid is already computed. Rendering is direct — draw the faces. Boolean operations require computing geometric intersections between faces — the hard part, which is why most contemporary systems avoided it.
CSG (Voelcker/Requicha, Rochester; Okino, Hokkaido) stores the operations themselves: a binary tree of primitives combined with union/difference/intersection. Compact to store, natural to parameterize. But rendering requires either ray-casting or conversion to B-rep at display time.
Today, the B-rep kernel is always present at the base. The CSG history lives above it as the user-facing feature tree. PROLAMAT 1973 in Budapest was the academic convergence (Braid/Voelcker/Okino); Classicery's SV room (cart 013) recreates the commercial CSG lineage that ran alongside it — MAGI in Elmsford, NY, a year earlier.
Classicery has thirteen carts. Four of them touch three-dimensional geometry, each from a different starting point. It is worth saying clearly how this one differs from its siblings.
SP · Sketchpad, 1963 (cart 009). Ivan Sutherland on the TX-2. Constraint sketching in 2D. Draw rough lines with a light pen, declare relationships — parallel, perpendicular, equal-length — and the program solves the system to enforce them. This is the parametric ancestor: every modern CAD sketch that snaps and constrains traces here. SP is in the plane. There is no notion of volume.
SV · SynthaVision, 1972 (cart 013). MAGI in Elmsford, NY, on an IBM 360/65. Constructive Solid Geometry by ray casting. A shape is a boolean expression — sphere ∩ sphere is a flying saucer. The renderer fires rays into the scene and resolves the boolean tree per pixel. The CSG kernel side of CAD: feature trees, history, manufacturing parts that are literally written as union/diff/intersect expressions. Goldstein & Nagel published the method in 1971; the commercial system shipped in 1972.
BUILD · 1973 (this room, cart 012). Ian Braid at Cambridge. Boundary representation solid modeling. Closed orientable surfaces of polygonal faces enclosing finite volume. Boolean operations (union, difference, intersection) that close under solid validity. The B-rep kernel side of CAD. Every solid you have ever made in SolidWorks, NX, CATIA, or OnShape is stored in a descendant of the VEF list this thesis defined.
ALYUS · Alias/1, 1985 (cart 004). Toronto four-founder studio on an SGI IRIS 2400. Spline-surface modeling. Cardinal splines (NURBS came later, in the PowerAnimator era) pulled toward control points; revolve, sweep, loft to build smooth skins; paint directly onto the surface. The curve-and-skin side of CAD: the lineage that finished every automobile body and rendered every Jurassic Park dinosaur. Surfaces, not volumes.
Practical guide: if you want to drill a hole through a block as stored history you can re-edit, SV's lineage. If you want the evaluated solid as a closed surface you can mesh and ship, BUILD's. If you want a Class-A car body, ALYUS's. If you want a hinged mechanism that re-solves when you change one dimension, SP's.
In 1974, Charles Lang, Ian Braid, Alan Grayer, and Peter Veenman left Cambridge and founded Shape Data Limited in Cambridge — one of the first CAD software companies in the world. The company's explicit mission was to commercialize B-rep solid modeling.
In 1978, Shape Data released ROMULUS: the first commercial B-rep solid modeling kernel, designed from the start to be embedded in other CAD systems. The architecture was novel — not a finished product but a geometry engine you licensed and integrated.
Evans & Sutherland acquired Shape Data in 1981 (the Romulus and Romulus-D era). Work on the next-generation kernel, Parasolid, began at Shape Data in 1985; v1.0 shipped in 1988. McDonnell Douglas absorbed the operation in 1988, then EDS in 1991, then UGS — and finally Siemens AG bought UGS in January 2007. Parasolid is now owned by Siemens Digital Industries Software and underlies SolidWorks, Solid Edge, NX, and over 350 other applications.
ACIS, the parallel B-rep kernel founded in 1985 by Lang, Braid, and Grayer through Three-Space Ltd, powers CATIA, AutoCAD's 3D solids, and many others.
Every solid model you have ever created in SolidWorks, CATIA, Fusion 360, Rhino, or OnShape is stored as a B-rep: a closed surface of faces, connected by edges, joined at vertices. The data structure is a direct descendant of Braid's VEF list. The winged-edge / half-edge structures that make B-rep traversal efficient came soon after — Bruce Baumgart's Stanford thesis in 1972 — and converged with Cambridge's work through the seventies. The concept of regularized Boolean operations is from the 1973 thesis.
Ian Braid went on to build BUILD2 (a clean rewrite separating geometry from topology), ROMULUS, and then led development at Shape Data through the Parasolid era. In 2008 he, Alan Grayer, and Charles Lang jointly received the Pierre Bézier Award from the Solid Modeling Association for foundational contributions to solid modeling.
This room is cart 012 of the Classicery suite. Type DEMO at the prompt for a scripted demonstration of primitives and Boolean operations.
If you want to work in the contemporary B-rep / NURBS register today, the next-door room is the Plug Innery — a small suite of plugins for Rhino. Different generation, same lineage.
From THE LITERATURE · CANON / 001B · the theory wing of CLASSICERY. Hear Edwin Catmull and Jim Clark on Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes read aloud — → track 09 →