CAD and 3D modelling

Mechanical Engineering (B.E./B.Tech) · Design tools and practice · free study notes for exams, placements and interviews

In short

Computer-aided design is the creation, modification and analysis of a product's geometry inside a computer, stored as a mathematical model rather than as lines on paper. A modern 3D model is a single master definition from which drawings, mass properties, FEA meshes, CNC toolpaths, 3D-print files and bills of material are all derived, so an error in the model propagates everywhere. It is examined in university CAD/CAM and CIM papers (curve and surface mathematics, transformations, B-rep versus CSG, Euler's formula, data exchange) and in the GATE Mechanical syllabus under Computer Integrated Manufacturing. Every design, tooling and R&D job in India — Tata Technologies, L&T Technology Services, Tata Elxsi, Cyient, KPIT, Quest Global, Maruti, Mahindra, Bosch, HAL, ISRO, BHEL — screens candidates on modelling discipline, not just on which software they can open.

Explained

What a CAD model actually contains

Geometry = the shapes and their equations (point coordinates, line, cylinder, spline surface). Topology = how they connect (which edge bounds which face, which faces meet at a vertex). Both are needed; geometry alone is a heap of surfaces.
Modelling kernel: the geometry engine underneath. Parasolid (NX, Solid Edge, SOLIDWORKS), CGM (CATIA, 3DEXPERIENCE), Granite (Creo), ACIS and its Autodesk Shape Manager fork (Inventor, Fusion), Open CASCADE (FreeCAD, CollabCAD-class open tools).
Model tree (history): the ordered list of features; each feature stores its sketch, dimensions and references. Rebuilding replays the tree, so a change at the top regenerates everything below it.
Associativity: drawings, assemblies and CAM programs point back at the model, so they update when it changes. This is the central benefit of 3D CAD over 2D drafting.
Non-geometric data: material, density, mass properties, custom properties (part number, revision, finish), PMI (product and manufacturing information) annotations.

Types of geometric modelling

Wireframe: only edges and vertices. Light, but ambiguous (the same wireframe can be read as several solids), no surface or volume data, cannot compute mass or hide lines reliably.
Surface modelling: defines bounding faces with no notion of inside/outside. Needed for styled, free-form shapes — car panels, turbine blades, mobile housings. A set of surfaces that is closed and gap-free ("watertight") can be knitted into a solid.
Solid modelling: unambiguous, closed volume with material defined. Gives volume, mass, centre of gravity, moments of inertia, section properties, interference checking.
Two classical solid representations:
- CSG (constructive solid geometry): the part is a binary tree of primitives (block, cylinder, sphere, cone, torus) combined by Boolean union, difference and intersection. Compact, always valid, but no explicit faces, so display and manufacturing data must be evaluated each time; blends and fillets are awkward.
- B-rep (boundary representation): the part is stored as its boundary — shells → faces → loops → edges → vertices — with geometry attached to each. Fast display, easy local operations (fillet one edge), supports free-form faces; larger files and validity must be enforced.
- Commercial kernels are hybrid: a B-rep body built by a CSG-like feature history. Other schemes: cell decomposition, octree/voxel, sweep representation.
Validity of a B-rep solid is checked by the Euler–Poincaré relation (see Formulas) — manifold, no self-intersection, every edge shared by exactly two faces.

Parametric, feature-based modelling and sketching

Feature: a shape with engineering meaning — extrude (pad), revolve, sweep, loft, hole, fillet, chamfer, shell, rib, draft, pattern, mirror, thread. Sketched features come from a 2D profile; applied features act on existing faces and edges.
Parametric means driven by dimensions and relations, not drawn to size: change 50 to 60 and the model rebuilds. Dimensions can be linked by equations (e.g. boss_dia = 2*shaft_dia), design tables or configurations/variants for a family of sizes.
Sketch constraints (geometric, remove degrees of freedom without a number): coincident, collinear, parallel, perpendicular, horizontal, vertical, tangent, concentric, equal, symmetric, midpoint, fix. Dimensions (driving) remove the rest. A sketch should end fully constrained — no free DOF, no redundancy.
Design intent: build so the model fails safely and updates predictably — sketch from the origin, constrain to planes and axes rather than to fillet edges, use one feature per manufacturing operation, keep fillets and drafts last.
Parent–child dependency: deleting or moving a parent face breaks the children (the classic "dangling reference" rebuild error). Rollback, reorder and suppression manage the tree.
History-based versus direct/synchronous modelling: direct editing (Siemens Synchronous Technology, SOLIDWORKS Direct Editing, Creo Flexible Modeling) pushes faces on dumb imported geometry with no feature tree — essential for working on STEP files from a customer.
Top-down versus bottom-up design: top-down drives part geometry from a skeleton/layout sketch or master model in the assembly; bottom-up models parts independently and then mates them.

Curves and surfaces (the mathematics that is examined)

Analytic entities: line, arc, circle, ellipse, parabola, hyperbola — exact, defined by a few parameters. Also stored parametrically, e.g. a circle as x = x_c + R cos u, y = y_c + R sin u.
Synthetic (free-form) curves, needed when the shape is given by points, not an equation:
- Hermite (cubic spline): defined by two end points and two end tangents; interpolates the points.
- Bezier: defined by n+1 control points, degree n; passes through only the first and last point; lies inside the convex hull of the control polygon; affine invariant; variation-diminishing. No local control — moving one control point changes the whole curve — and degree rises with point count.
- B-spline: piecewise polynomial of chosen degree p with a knot vector; gives local control (a control point affects only p+1 spans) and C^p−1 continuity at knots; degree is independent of the number of control points.
- NURBS (non-uniform rational B-spline): B-spline with a weight per control point. Rational form represents circles, ellipses and all conics exactly, so one entity type covers analytic and free-form geometry — which is why every modern kernel is NURBS-based.
Surfaces: plane, ruled, revolved, tabulated cylinder, swept, Coons patch (from four boundary curves), bicubic patch, Bezier/B-spline/NURBS patch, offset, fill, blend. Trimmed surfaces carry a parametric-space boundary.
Continuity between patches: G0 position (a visible crease), G1 tangent (no crease, a highlight break), G2 curvature (smooth reflections — "class-A" styling surfaces), G3 curvature-rate.

Transformations, viewing and display

Geometry is moved by homogeneous transformation matrices — 3×3 in 2D, 4×4 in 3D — so that translation, rotation, scaling, shear, mirror and projection are all matrix multiplications and can be concatenated into one composite matrix.
Order matters: rotation then translation ≠ translation then rotation. Rotation about an arbitrary point or axis = translate the point to the origin, rotate, translate back.
Projections: multiview orthographic (the drawing views), axonometric (isometric, foreshortening ratio 0.816, usually drawn full size), oblique, and perspective with one, two or three vanishing points for renderings.
Display pipeline: model → world → view transformation → clipping → projection → hidden-line/hidden-surface removal (z-buffer) → shading. Curved faces are tessellated into triangles for display only; the stored model remains exact. Level-of-detail and lightweight graphics (JT, 3D XML) make 10,000-part assemblies usable.

Assemblies, drawings and model-based definition

A free rigid part has 6 DOF (3 translations, 3 rotations). Mates/constraints remove DOF: coincident planar faces −3, concentric/cylindrical axes −4, distance or angle −1, fix −6. A revolute joint (shaft in a bore, located axially) leaves 1 DOF.
Over-constraining creates conflicting or redundant mates; CAD will flag them. Keep one part fixed/grounded as the datum.
Assembly tools: sub-assemblies, patterns, exploded views, interference and clearance detection, static and dynamic collision checks, envelope and section views, BOM (structured, flat, indented) that feeds ERP.
Drawing generation from the model: associative orthographic, section, detail, auxiliary, broken and isometric views, with dimensions and tolerances annotated per the drawing standards (BIS SP 46 practice in Indian colleges and industry).
Model-based definition (MBD): the 3D model with embedded PMI is the released authority, with no 2D sheet — governed by ISO 16792 (ASME Y14.41 in US practice) and carried by STEP AP242 or 3D PDF. Growing in Indian aerospace and automotive tier-1 work.
PDM/PLM: vaulting, check-in/check-out, version versus revision, where-used and where-referenced, release workflow, ECR/ECO change control. Common systems: Teamcenter, Windchill, 3DEXPERIENCE/ENOVIA, Autodesk Vault.

Data exchange, interoperability and downstream use

Neutral formats: STEP (ISO 10303 — AP203 configuration-controlled 3D design, AP214 automotive, AP242 the merged current standard supporting PMI and assemblies) is the default for solid exchange; IGES (older, surfaces and wireframe, often produces gaps needing healing); DXF/DWG for 2D; STL and 3MF/AMF for additive manufacturing; JT (ISO 14306) and 3D PDF for visualisation; Parasolid x_t, ACIS sat, native formats for fuller fidelity.
STL stores only unordered triangles with normals — no units, no topology, no colour, no tolerances. Facet size is set by chord height and angle tolerance: tighter tolerance means far more triangles.
Common import problems: lost feature tree ("dumb solid"), tiny gaps and slivers, failed sew, inverted normals, duplicate faces, wrong unit scale (inch/mm). Healing and direct editing tools fix these.
Downstream: CAE meshing, CAM toolpaths and post-processed G-code, CMM inspection programs, mould flow, tool and fixture design, additive slicing, technical publications, AR/VR and digital twins.
Reverse engineering: laser/structured-light scanning or industrial CT → point cloud → aligned and decimated mesh → fitted analytic surfaces or NURBS → parametric solid. Used for legacy spares, castings and competitor benchmarking.
Licensing reality in India: commercial seats are typically an annual subscription running into lakhs of rupees for high-end PLM-grade suites; free or low-cost options include FreeCAD, Onshape's free plan, and CollabCAD (developed by NIC with ISRO, distributed free to Indian schools under the Atal Innovation Mission). Prices change — verify current quotations before relying on a figure.

Key points

CAD model - a mathematical geometry definition plus topology plus non-geometric attributes, not a picture.
Wireframe/surface/solid - edges only (ambiguous) / bounding faces (no inside) / closed volume (mass properties possible).
CSG - Boolean tree of primitives; compact, always valid, no explicit faces.
B-rep - shell–face–loop–edge–vertex boundary; fast display and local edits; validity checked by Euler–Poincaré.
Euler–Poincaré relation - V − E + F − R = 2(S − G); the integrity test for a solid model.
Parametric/feature-based - geometry driven by dimensions, constraints and an ordered feature tree, so edits regenerate the model.
Fully constrained sketch - zero remaining DOF and no redundant constraints; the mark of a professional model.
Design intent - constrain to origin, planes and stable faces; fillets, drafts and cosmetic features last.
Bezier - degree = (control points − 1), convex hull property, no local control, interpolates only the end points.
B-spline - knot vector gives local control and degree independent of control-point count.
NURBS - weighted (rational) B-spline; represents conics exactly; the universal kernel curve/surface type.
Continuity G0/G1/G2 - position / tangent / curvature; G2 needed for styling surfaces.
Homogeneous coordinates - add a fourth coordinate so translation and projection become 4×4 matrix products that can be concatenated; order of multiplication matters.
Assembly DOF - 6 per free part; mates remove DOF; one part must be grounded.
STEP AP242 - current neutral standard for solids, assemblies and PMI; IGES is legacy; STL is triangles only.
Tessellation - triangular approximation for display, STL and FEA meshing; the stored NURBS model stays exact.
MBD (ISO 16792) - the annotated 3D model, not a 2D sheet, as the released authority.
PDM/PLM - vault, revision control and ECO workflow around CAD data; links design to ERP and manufacturing.

Formulas and examples

2D homogeneous transformations (point as [x y 1]ᵗ)
Translation T(dx,dy) = [[1,0,dx],[0,1,dy],[0,0,1]]; Scaling S(sx,sy) = [[sx,0,0],[0,sy,0],[0,0,1]]
Rotation R(θ) = [[cosθ, −sinθ, 0],[sinθ, cosθ, 0],[0,0,1]], θ positive anticlockwise
Mirror about x-axis = [[1,0,0],[0,−1,0],[0,0,1]]

Rotation about an arbitrary point (x_c, y_c): P′ = T(x_c,y_c) · R(θ) · T(−x_c,−y_c) · P
3D rotation about Z: R_z(θ) = [[cosθ,−sinθ,0,0],[sinθ,cosθ,0,0],[0,0,1,0],[0,0,0,1]]; similarly R_x, R_y

Bezier curve: P(u) = Σ_{i=0..n} P_i · C(n,i) · (1−u)ⁿ⁻ⁱ · uⁱ , 0 ≤ u ≤ 1
P_i = control points, n = degree, C(n,i) = binomial coefficient. Tangents: P′(0) = n(P₁−P₀), P′(1) = n(P_n−P_{n−1})

B-spline: P(u) = Σ P_i N_{i,p}(u); NURBS: P(u) = [Σ w_i P_i N_{i,p}(u)] / [Σ w_i N_{i,p}(u)]
N_{i,p} = B-spline basis of degree p from the knot vector, w_i = weight (w_i = 1 for all i reduces NURBS to a B-spline)

Euler–Poincaré: V − E + F − R = 2(S − G)
V vertices, E edges, F faces, R inner loops (rings), S shells (separate bodies), G genus (through holes/handles). Simple solid: V − E + F = 2

Tessellation of a cylinder/arc of radius R into N chords: chord height (sag) h = R[1 − cos(θ/2)], θ = 2π/N
For small h: N ≈ π / √(2h/R). Binary STL file size = 84 + 50t bytes, t = number of triangles

Mass properties: V = ∫dV, m = ρV, centroid x̄ = Σ(V_i x̄_i)/ΣV_i, I_xx = ∫(y²+z²)dm; parallel axis I = I_cg + m d²
Uniform scaling by factor s: lengths ×s, areas ×s², volume and mass ×s³

Translators for exchange between n systems: direct pairs = n(n−1) one-way translators; via one neutral format = 2n
For n = 10: 90 direct translators against 20 — the economic argument for STEP

Example 1 — Cubic Bezier curve. Control points P₀(0,0), P₁(2,6), P₂(8,6), P₃(10,0) mm. Find the point at u = 0.5 and the end tangents.

Basis at u = 0.5: (1−u)³ = u³ = 0.125; 3u(1−u)² = 3(0.5)(0.25) = 0.375; 3u²(1−u) = 0.375. (Sum = 1 ✓)
x = 0.125(0) + 0.375(2) + 0.375(8) + 0.125(10) = 0 + 0.75 + 3 + 1.25 = 5.0 mm
y = 0.125(0) + 0.375(6) + 0.375(6) + 0.125(0) = 2.25 + 2.25 = 4.5 mm
P′(0) = 3(P₁−P₀) = 3(2,6) = (6,18) → start slope 18/6 = 3; P′(1) = 3(P₃−P₂) = 3(2,−6) = (6,−18) → end slope −3.
Note the curve reaches y = 4.5 although both middle control points are at y = 6 — a Bezier does not pass through its interior control points, only within their convex hull.

Example 2 — Composite transformation. Rotate the point P(40, 20) by 30° anticlockwise about the sketch point C(10, 10).

Translate to origin: P − C = (30, 10).
Rotate: cos30° = 0.8660, sin30° = 0.5.

x′ = 30(0.8660) − 10(0.5) = 25.981 − 5 = 20.981 y′ = 30(0.5) + 10(0.8660) = 15 + 8.660 = 23.660

Translate back: (20.981 + 10, 23.660 + 10) = (30.98, 33.66) mm.
Check: distance from C stays √(30²+10²) = 31.62 mm, and √(20.981² + 23.660²) = √(440.2 + 559.8) = √1000 = 31.62 ✓.

Example 3 — Degrees of freedom. (a) *Sketch:* a rectangle drawn as four connected lines has 4 vertices × 2 = 8 DOF. Apply 2 horizontal + 2 vertical constraints (−4) → 4 DOF; a coincident constraint tying one corner to the origin (−2) → 2 DOF; two driving dimensions (length and width) → 0 DOF, fully constrained. A third dimension (say a diagonal) would be redundant and rejected. (b) *Assembly:* a shaft loose in space has 6 DOF. A concentric/cylindrical mate to the housing bore removes 4 → 2 DOF (spin + slide). A coincident mate between the shaft shoulder face and the housing face would remove 3, but 2 of those are already removed by the concentric mate, so only 1 new DOF (axial slide) is taken out and the remaining DOF = 1 rotation — a revolute joint. Mating a second face axially as well would over-constrain it.

Example 4 — STL tessellation of a cylindrical boss. Boss Ø50 mm × 40 mm long, exported with a chord-height tolerance of 0.05 mm.

R = 25 mm, h/R = 0.05/25 = 0.002 → N ≈ π/√(2×0.002) = π/0.06325 = 49.7 → use 50 facets around.
Check at N = 50: θ = 360/50 = 7.2° = 0.12566 rad; h = 25[1 − cos(3.6°)] = 25(1 − 0.998027) = 0.0493 mm ≤ 0.05 ✓.
Triangle count: curved side 2 × 50 = 100; two flat ends (triangle fans) 50 each = 100; total t = 200 triangles.
Binary STL size = 84 + 50 × 200 = 10,084 bytes ≈ 9.8 KiB.
If the tolerance is tightened 10× to 0.005 mm, N ≈ π/√(0.0004) = 157 facets, t ≈ 628, file ≈ 31.5 KB — cost grows roughly as 1/√h, which is why over-tight STL settings bloat print files for no visible gain.

Example 5 — Mass properties and a validity check. (a) *Mass:* a mild-steel plate 100 × 60 × 10 mm with two Ø12 mm through holes, ρ = 7,850 kg/m³ = 7.85 × 10⁻³ g/mm³.

Gross volume = 100 × 60 × 10 = 60,000 mm³.
Holes = 2 × (π/4)(12²)(10) = 2 × 1,130.97 = 2,261.9 mm³.
Net V = 57,738 mm³ → m = 57,738 × 7.85 × 10⁻³ = 453.2 g (0.453 kg).
If the same part is scaled up ×1.5, mass becomes 0.453 × 1.5³ = 1.530 kg.

(b) *Centroid of an L-shaped extrusion*, 10 mm thick: vertical leg 20 wide × 100 tall (area 2,000 mm², centroid 10, 50), horizontal leg 80 long × 20 tall (area 1,600 mm², centroid 60, 10).

x̄ = (2,000×10 + 1,600×60)/3,600 = 116,000/3,600 = 32.22 mm; ȳ = (2,000×50 + 1,600×10)/3,600 = 32.22 mm; z̄ = 5 mm. This is the hand check against the CAD mass-property output.

(c) *Euler–Poincaré check* on a cube with a square through hole: V = 16, E = 24, F = 10 (4 side faces + 2 pierced faces + 4 tunnel faces), R = 2 inner loops, S = 1, G = 1.

16 − 24 + 10 − 2 = 0 and 2(S − G) = 2(1 − 1) = 0 ✓ — a valid single-body, genus-1 solid.

Representation	Stores	Strength	Weakness
Wireframe	Edges, vertices	Tiny files, fast	Ambiguous, no mass or hidden-line data
Surface	Bounding faces	Free-form styling shapes	No volume unless closed; gap/sew problems
CSG	Boolean tree of primitives	Compact, always valid	No explicit faces; fillets, free-forms hard
B-rep	Faces, edges, vertices + topology	Fast display, local edits, free-form	Larger files; validity must be enforced

Format	Carries	Typical use	Caution
STEP AP242	Solids, assemblies, PMI	Default neutral exchange	No feature tree (dumb solid)
IGES	Surfaces, wireframe	Legacy exchange	Gaps, needs healing
Parasolid x_t / ACIS sat	Kernel solids	Same-kernel transfer, high fidelity	Version-dependent
STL	Triangles + normals	3D printing, quick viewing	No units, tolerance or topology
JT / 3D PDF	Lightweight tessellation + PMI	Review, supplier sharing, MBD	Not for editing
DXF / DWG	2D geometry	Sheet metal flats, laser cutting	2D only

Curve type	Control	Conics exact?	Local control?
Hermite cubic	End points + end tangents	No	Limited
Bezier	n+1 control points, degree n	No	No
B-spline	Control points + knot vector	No	Yes
NURBS	Control points + knots + weights	Yes	Yes

Where it is used

Automotive and tier-1 suppliers: CATIA and NX for body-in-white, powertrain and interiors at Maruti Suzuki, Tata Motors, Mahindra, Bajaj, TVS, Ashok Leyland, with Bosch, Sundram Fasteners and Minda supplying modelled assemblies against OEM STEP/CATIA data and PLM (Teamcenter, 3DEXPERIENCE) workflows.
Aerospace and defence: HAL, ISRO/VSSC, DRDO labs, Godrej Aerospace and Tata Advanced Systems work in NX/CATIA with MBD, configuration control and strict revision discipline on long-life parts.
Capital goods, process plant and energy: BHEL, L&T, Thermax and Kirloskar model pressure parts, structures and layouts; plant design uses specialised 3D tools for piping and equipment on the same kernel principles.
Tooling, moulds and dies: CAD draft analysis, parting-line and undercut checks, core/cavity split and electrode design feed directly into CAM at mould shops around Pune, Chennai, Rajkot, Coimbatore and Ludhiana.
Engineering services and product design: Tata Technologies, L&T Technology Services, Tata Elxsi, Cyient, Quest Global, KPIT and Infosys engineering teams deliver CAD/CAE/CAM packages to global OEMs — the largest single employer of fresh mechanical graduates in this skill.
Job roles and tools: design engineer, CAD/CAE engineer, tool designer, PLM/PDM administrator, drafting technician (NSQF/NSDC CAD qualification packs, NTTF and CIPET courses), reverse-engineering and 3D-scanning specialist, additive manufacturing engineer.

Interview questions

Q: What is the difference between geometry and topology in a CAD model? A: Geometry is the mathematical shape of each entity (the equation of a surface or curve); topology is the connectivity — which edges bound which faces and which vertices they share. A valid solid needs both.
Q: Compare CSG and B-rep. A: CSG stores a Boolean tree of primitives — compact and always valid, but with no explicit faces; B-rep stores the actual bounding faces, edges and vertices, giving fast display and local operations like filleting a single edge at the cost of bigger files and validity checking.
Q: State Euler's formula for solids and why it matters. A: V − E + F − R = 2(S − G) for a general solid, reducing to V − E + F = 2 for a simple one; kernels use it to verify that a boundary representation is a topologically valid solid.
Q: Why are NURBS preferred over Bezier curves in modelling kernels? A: NURBS give local control, allow degree to be chosen independently of the number of control points, and because they are rational they represent circles and conics exactly — so one entity type covers both analytic and free-form geometry.
Q: A Bezier curve's middle control points sit at y = 6, yet the curve peaks at 4.5. Why? A: A Bezier interpolates only its first and last control points; the interior ones pull the curve, which always stays inside the convex hull of the control polygon.
Q: Why are transformations done in homogeneous coordinates? A: Adding an extra coordinate makes translation and projection matrix multiplications, so a whole chain of operations can be concatenated into one matrix and applied in a single pass.
Q: What does "fully constrained" mean, and why insist on it? A: Every degree of freedom in the sketch is removed by geometric constraints and driving dimensions, so geometry cannot drift when something is edited and the design intent is explicit and auditable.
Q: A part has 6 DOF. Which mates make it a revolute joint? A: A concentric/cylindrical mate between the axes removes 4 DOF, and an axial location (distance or coincident face) removes the remaining translation, leaving one rotation.
Q: Why is STEP preferred over IGES? A: STEP (ISO 10303, AP242 currently) carries solids, assemblies and PMI with a formal information model, whereas IGES typically transfers surfaces and wireframe and often arrives with gaps that must be healed.
Q: What are the limitations of STL? A: It is an unordered list of triangles with normals — no units, topology, tolerances, colour or features — and curved surfaces are only approximated, so the facet tolerance decides accuracy and file size.
Q: What does model-based definition change? A: The annotated 3D model with embedded PMI becomes the released authority instead of a 2D drawing, under ISO 16792 practice, so downstream CAM and inspection read the model directly.
Q: You receive a customer STEP file with no feature tree and must change a wall thickness. How? A: Use direct/synchronous editing to select and offset the faces, or build new features on the imported body; feature recognition can sometimes recover extrudes and holes, but re-modelling from scratch may be safer for a critical part.
Q: Why does a CAD assembly sometimes report interference that is really fine? A: Threads, splines and press fits are usually modelled nominally or cosmetically, so interference detection flags intentional overlap; set those pairs to be ignored rather than changing the geometry.

Common mistakes

Leaving sketches under-constrained (dragging geometry "to size") or over-constrained with redundant dimensions — the model then changes unpredictably on the next edit.
Referencing fillet faces, rounded edges or imported dumb geometry in later features, so the tree collapses with dangling references when the fillet changes.
Modelling the shape instead of the manufacturing sequence — no draft, no fillets on cast parts, cosmetic features sketched before the base form, which makes CAM and tooling work impossible.
Stating a Bezier curve passes through all its control points, or claiming Bezier curves have local control.
Reversing the order of transformation matrices, or rotating about the origin when rotation about a given point was asked.
Mixing units on import (inch model read as mm, or a 25.4× scale error) and not checking overall dimensions and mass against a hand calculation.
Exporting STL with default coarse tolerance for a functional 3D print, or with absurdly fine tolerance that bloats the file without improving the part.
Treating the CAD mass property as truth without a sanity check — the wrong material density or a missing hole changes the quoted mass and the structural result that follows from it.