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CAD Landscape

Paradigms, pipelines — how are parts designed and represented

Design → Manufactured Part

The path from a designer's intent to a physical part. At each stage some of the original information is compressed, translated, or thrown away — the friction badges mark lossy transitions.

Stage 01
Design Intent
  • Functional relationships
  • Constraints & tolerances
  • Material intent
  • Assembly dependencies
Friction
Stage 02
CAD Model
  • Geometry encoded
  • Params may survive
  • Constraints in solver
  • Native format (.f3d, .sldprt)
Fidelity loss
Stage 03
Exchange Format
  • STEP · geometry + some topo
  • IGES · older, lossy
  • STL · triangles only
  • 3MF · better than STL
Friction
Stage 04
CAM / Slicer
  • Toolpaths generated
  • Support structures
  • G-code / machine lang
  • Intent gone
Stage 05
Manufacture
  • FDM / SLA / SLS print
  • CNC mill / lathe
  • Sheet metal
  • Physical artifact
CAD Paradigms

How do you represent a shape?

Explicit
Boundary Representation (BRep)
You directly define geometry — vertices, edges, faces. The shape is the model. You draw it, extrude it, cut it. Most commercial CAD is here.
ToolsFusion 360, SolidWorks, FreeCAD, Rhino
Great forPrecision parts, manufacturing-ready geometry, GD&T
Weak atOrganic shapes, blending, algorithmic generation
Format outSTEP, IGES, STL
Implicit
Implicit / Field-Based
Shape is defined by a math function f(x,y,z). You're inside the shape where f < 0. The boundary is where f = 0. Blending, offsetting, morphing are trivial.
Toolslibfive, Curv, Hyperfun, Antimony
Great forOrganic forms, smooth blends, topology optimization, lattices
Weak atPerfect sharp corners, direct dimension control, standard CAM
Format outMesh (marching cubes), or direct to renderer
Parametric
Constraint-Driven Parametric
Geometry is defined by parameters and constraints. Change one value and the solver cascades updates through the model. Dependencies are explicit — the key answer to the assembly fragility problem.
ToolsFreeCAD, SolidWorks, Fusion 360, OpenSCAD (code-param)
Great forAssemblies, design families, part variants, manufacturing
Weak atComplex constraint graphs get brittle; solver failures
Format outSTEP, native, STL
Procedural / Code-First
Algorithmic / Script-Driven
Geometry is generated by a program. You write code, the CAD is output. Fully reproducible, diff-able, generative. Closest to what you'd want for algorithmic generation of complex geometry.
ToolsOpenSCAD, CadQuery, Build123d, Grasshopper (Rhino)
Great forAlgorithmic generation, automation, version control, generative design
Weak atInteractive design, freeform sculpting, fast iteration for non-coders
Format outSTL, STEP (via OCCT kernel)
Curve & Surface Primitives · The Spline Family

The mathematical objects every paradigm above uses to actually represent curved geometry — the things a CAD kernel knows how to compute booleans, offsets, and tangents against.

Bézier Curves
The building block
Defined by control points. The curve is "pulled toward" control points but doesn't pass through them (except endpoints). Cubic Béziers are most common.
Used in: SVG, font outlines, animation easing, early CAD
B-Splines
Basis splines
Generalization of Bézier. Local control — moving one control point only affects a local region. Pieced together from polynomial segments. Smooth, continuous.
Used in: CAD surfaces, animation rigs, path planning
NURBS
Non-Uniform Rational B-Splines
B-splines with weights and non-uniform knot vectors. Can represent conics (circles, ellipses) exactly — something polynomial splines cannot. The standard in precision CAD surfaces.
Used in: Rhino, SolidWorks, automotive/aerospace surfaces, STEP format
T-Splines
NURBS + T-junctions
Extension of NURBS that allows T-junctions in the control mesh — local refinement without propagating a whole row of control points. Great for organic modeling with precision output.
Used in: Fusion 360 sculpt workspace, formerly Autodesk T-Splines plugin
Subdivision Surfaces
Sub-D
Start with a coarse polygon mesh, apply recursive subdivision rules to get a smooth limit surface. Catmull-Clark is the standard scheme. Less common in precision engineering.
Used in: Blender, ZBrush, Maya, Pixar RenderMan
SDF
Signed Distance Field / Function
For every point in space, stores the signed distance to the nearest surface. Positive = outside, negative = inside, zero = on the surface. Enables trivial boolean ops and blending via smooth min.
Used in: Ray marching renderers, libfive, game collision, medical imaging
Constraint Propagation · The Assembly Problem

How an assembly responds when one part changes — the difference between a clean cascade update, hours of manual touch-up, and a solver explosion. Each card is one regime, in roughly increasing order of how well it scales.

×Dumb Explicit CAD
Parts have no knowledge of each other. Change a bolt hole diameter → manually find every mating part → update each one. In a 500-part assembly, this is weeks of work and a major source of manufacturing errors.
✓Parametric Assemblies
Parameters are linked across parts. "Bolt diameter" is a shared variable. Change it once → all mating features update. SolidWorks configurations, FreeCAD spreadsheets, Onshape variables all work this way.
!Brittle Constraint Graphs
Parametric solvers fail when changes create geometric impossibilities or circular dependencies. Deep assembly trees amplify this. Skilled CAD engineers design constraint graphs carefully to minimize fragility — it's an art.
◆Code-First Approach
In CadQuery / Build123d / OpenSCAD, constraints are just Python/code logic. No solver — you write the propagation yourself. More fragile to write, but fully transparent and version-controllable. Good fit for algorithmic generation.
Tool Comparison · When to Reach for What

The paradigm tags from above, applied to specific tools. Most commercial tools blend paradigms; some common tools and what each is good and bad at.

Tool Paradigm Best for Not great for
Fusion 360 parametricexplicit Full product design, assemblies, CAM integration, manufacturing Organic forms, code-driven generation, open source workflows
SolidWorks parametricexplicit Industrial engineering, large assemblies, simulation, PDM Cost, accessibility, scripting workflows
Rhino + Grasshopper explicitprocedural Architecture, complex surfaces, algorithmic generation, NURBS Assembly management, standard mechanical engineering
OpenSCAD proceduralexplicit Code-driven geometry, 3D printing, version control, open source Curved surfaces, NURBS, interactive design
CadQuery / Build123d proceduralexplicit Python-driven precision CAD, STEP output, engineering-grade parts Visual/interactive design, non-programmer designers
libfive implicit Implicit modeling, SDFs, organic blending, research, algorithmic Manufacturing pipelines, sharp corners, standard CAM
Blender explicitprocedural Organic sculpting, animation, visualization, geometry nodes Precision engineering, tolerances, manufacturing output
Onshape parametricexplicit Collaborative design, cloud-native, parametric assemblies Offline workflows, scripting beyond FeatureScript
Exchange Formats · Representation cascade through tools

What's left of the model when it crosses a tool boundary. The bar shows roughly how much design intent is dropped on the way out; the text below names exactly what gets lost and what's preserved.

Native (.f3d, .sldprt)
Carries: everything — params, constraints, history, metadata
Loss: nothing — but locked to one tool
STEP (.step / .stp)
Carries: BRep geometry, NURBS surfaces, assembly structure, some metadata
Loses: parametric history, constraints, design intent
3MF
Carries: mesh + color + material + print settings
Loses: BRep, params, constraints, NURBS — but better than STL
STL
Carries: triangulated surface mesh only
Loses: everything except raw geometry. No params, no curves, no intent.
Synthesis Using procedural systems and baking in constraints into the logic/representation schem allows you to track and respond to downstream changes more effectively.

Procedural-on-Explicit: CadQuery and Build123d drive the OpenCascade BRep kernel and emit precision STEP for sketch-and-feature work.

Procedural-on-Implicit: nTop and libfive use field-based geometry for lattices, topology optimization, and blends.

Both keep design intent in code, not in a solver's hidden state, allowing for better constraint propagation.
References
Pipeline · exchange formats
  • STEP — ISO 10303 family, AP242 is the modern profile for mechanical CAD exchange. Carries BRep + NURBS + assembly structure; drops parametric history. iso.org/66654
  • STL — originated by 3D Systems for stereolithography; triangulated surface only, no topology or metadata. wiki: STL
  • 3MF — open spec maintained by the 3MF Consortium; mesh + color + material + print settings. 3mf.io/specification
  • IGES — NIST IGES 5.3 (1996); largely superseded by STEP. nist.gov
  • G-code — ISO 6983 / EIA RS-274; in practice every controller layers vendor dialects on top.
CAD paradigms
  • BRep — Mäntylä, An Introduction to Solid Modeling (Computer Science Press, 1988). The Parasolid and ACIS kernels are the production embodiments most commercial CAD ships on.
  • Implicit / field-based — Bloomenthal et al., Introduction to Implicit Surfaces (Morgan Kaufmann, 1997). Modern engineering implementations: libfive, nTop.
  • Parametric constraint solving — Hoffmann, Geometric and Solid Modeling (Morgan Kaufmann, 1989). Open implementations: SolveSpace, the FreeCAD sketcher.
  • Procedural / code-first — OpenSCAD; CadQuery and Build123d both sit on top of the OpenCascade BRep kernel, which is what lets them emit precision STEP.
Curve & surface primitives
  • Bézier curves — Pierre Bézier's original work at Renault in the 1960s. Modern treatment in Farin, Curves and Surfaces for CAGD (Morgan Kaufmann).
  • B-splines — de Boor, A Practical Guide to Splines (Springer).
  • NURBS — Piegl & Tiller, The NURBS Book, 2nd ed. (Springer, 1997). Underpins STEP surface entities and most commercial freeform CAD.
  • T-splines — Sederberg, Zheng, Bakenov, Nasri, "T-splines and T-NURCCs," ACM SIGGRAPH 2003.
  • Subdivision surfaces — Catmull & Clark, "Recursively generated B-spline surfaces on arbitrary topological meshes," Computer-Aided Design 10(6), 1978.
  • SDFs — Hart, "Sphere Tracing: a geometric method for the antialiased ray tracing of implicit surfaces," The Visual Computer (1996). Quílez's SDF primitive catalog is the most-used practical reference today.
Tools (capability claims sourced from vendor docs / product pages)
Synthesis · the implicit branch (nTop, libfive)
  • nTop — implicit-modeling-based engineering CAD; field-driven design, block-dataflow programming, STEP / CAD interop. ntop.com
  • Production case studies (aerospace, medical, defense): ntop.com/customers
  • Technical primer on the implicit-engineering approach: ntop.com/resources/blog