CAD Principles Notes

Last reviewed 16 Sept 2026 · 7 min read

What is CAD?

Computer-aided design (CAD) is the use of computers to create, modify, analyse and document designs. Computer-aided drafting focuses on producing 2D drawings; CADD (computer-aided design and drafting) covers both.

Early interactive graphics research in the 1960s (e.g. Ivan Sutherland's Sketchpad, 1963) laid the foundation.
AutoCAD by Autodesk, released in 1982, brought CAD to personal computers and became widely used in civil engineering and architecture.
Other tools: MicroStation, BricsCAD, DraftSight; 3D/BIM tools — Revit, SketchUp, Tekla, Civil 3D; mechanical — SolidWorks, CATIA, Inventor.

Advantages of CAD over manual drafting

Advantage	Explanation
Speed and productivity	Copy, mirror, array and blocks avoid redrawing repeated features
Accuracy	Exact coordinates, object snaps and precise dimensions
Easy modification	Changes without redrawing the whole sheet
Reusability	Libraries of blocks, templates, standard details
Consistency and standards	Layers, text and dimension styles, templates
Automatic dimensioning and quantities	Associative dimensions; areas, lengths, schedules
Storage and retrieval	Digital files, version control, less physical space
Communication and collaboration	Electronic sharing, cloud, external references
3D visualisation and analysis	Models, rendering, clash detection, integration with analysis/CAM
Reduced errors	Checking tools, fewer transcription errors

Limitations: initial cost of hardware/software and training, dependence on software versions and file compatibility, risk of data loss without backups, possible over-reliance on software.

CAD system components

Hardware

Category	Devices
Input devices	Keyboard, mouse, digitiser/graphics tablet (with puck/stylus), scanner, light pen, touch screens, 3D mouse, laser scanners (point clouds)
Processing	CPU, RAM, graphics processing unit (GPU) — important for 3D display and rendering
Output devices	Monitors (display), printers, plotters (pen plotters historically; now inkjet large-format plotters), 3D printers
Storage	Hard disks/SSDs, network servers, cloud storage, removable media

Software

Operating system and CAD application (graphics engine, geometric modelling kernel, user interface, database).
Add-ons: libraries, analysis/estimation modules, rendering engines, programming interfaces (e.g. AutoLISP, .NET, Python in some tools).

Raster vs vector graphics

Aspect	Raster (bitmap)	Vector
Representation	Grid of pixels	Mathematical objects — lines, arcs, curves defined by coordinates
Scaling	Loses quality (pixelation) when enlarged	Scales without loss of quality
File size	Depends on resolution	Depends on number of objects
Editing	Pixel-level	Object-level (move, stretch, modify)
Examples	Scanned drawings, photographs (JPG, PNG, TIFF, BMP)	CAD drawings (DWG, DXF), SVG, PDF (vector content)

CAD drawings are vector-based; scanned paper drawings are raster and may be vectorised.

2D drafting and 3D modelling

Model type	Description	Features / limits
2D drafting	Lines, arcs, text, dimensions on a plane	Standard construction drawings
Wireframe model	Edges only (lines and curves in 3D)	Light, but ambiguous; no surfaces or volume; cannot hide lines automatically
Surface model	Edges + surfaces (faces, meshes, NURBS)	Visual realism, hidden-line removal; no mass/volume properties
Solid model	Complete volume description	Mass properties (volume, CG, moment of inertia), Boolean operations, sections, interference checks

Solid modelling representations

Constructive solid geometry (CSG) — solids built from primitives (box, cylinder, sphere, cone, wedge, torus) combined by Boolean operations — union, subtraction (difference), intersection — stored as a tree.
Boundary representation (B-rep) — solid described by its boundary — faces, edges, vertices and their topology.
Sweep representation — extrusion or revolution of 2D profiles.

Parametric and feature-based modelling

Geometry controlled by parameters (dimensions) and constraints (geometric — parallel, perpendicular, tangent; dimensional — lengths, angles).
Changing a parameter updates the model automatically.
AutoCAD supports parametric constraints in 2D; dedicated parametric modellers (Inventor, SolidWorks, Revit families) use it extensively.

Building Information Modelling (BIM)

BIM is an object-based, information-rich digital representation of a facility — walls, doors, beams know their properties and relationships.
Drawings (plans, sections, schedules) are generated from the model, staying coordinated.
Supports clash detection, 4D (time), 5D (cost), facility management (sometimes called 6D/7D).
Exchange standard IFC (Industry Foundation Classes).

Geometric transformations

CAD operations such as MOVE, SCALE, ROTATE and MIRROR are implemented using transformation matrices.

Formula2D transformations (homogeneous coordinates)

A point $(x, y)$ is written as $[x y 1]^{T}$ .

Translation by $(t_{x}, t_{y})$ :

100010 t_{x} t_{y} 1

Scaling about the origin by $(s_{x}, s_{y})$ :

s_{x} 00 0 s_{y} 0 001

Rotation about the origin by angle $θ$ (anticlockwise positive):

cos θ sin θ 0 - sin θ cos θ 0 001

Reflection about the x-axis: $diag (1, - 1, 1)$ ; about the y-axis: $diag (- 1, 1, 1)$ .

Homogeneous coordinates allow translation to be expressed as a matrix multiplication, so a series of transformations can be concatenated into one matrix.
Order matters — matrix multiplication is not commutative (rotate-then-translate differs from translate-then-rotate).
Rotation/scaling about an arbitrary point $(p, q)$ : translate the point to the origin, transform, translate back: $T (p, q) R (θ) T (- p, - q)$ .

CAD file formats

Format	Description
DWG	Native AutoCAD drawing format (binary)
DXF (Drawing Exchange Format)	Autodesk's exchange format for sharing with other CAD programs
DWT	AutoCAD template file
DWF / DWFx	Design Web Format — lightweight files for viewing/markup
PDF	Portable document — plotting/sharing (vector)
BAK / `SV$`	AutoCAD backup and autosave files
IGES, STEP	Neutral formats for 3D geometry exchange
STL	Triangulated surface — 3D printing
IFC	Open BIM exchange
RVT	Revit project files

CAD standards and data management

Templates with predefined units, layers, text styles, dimension styles, title blocks and plot settings.
Layer naming conventions (e.g. discipline–element–status), colour and lineweight standards.
Standard blocks and details libraries.
File naming, version control and revision management.
External references (Xrefs) for coordinated multi-discipline drawings.
Backups and archiving; access control.

Worked examples

Worked ExampleExample 1 — rotation

Rotate the point (4, 0) by 90° anticlockwise about the origin.

Solution. $x^{'} = 4 cos 90° - 0 = 0$ ; $y^{'} = 4 sin 90° + 0 = 4$ → (0, 4)

Worked ExampleExample 2 — rotation about a point

Rotate the point (5, 2) by 90° anticlockwise about (3, 2).

Solution. Translate: $(5 - 3, 2 - 2) = (2, 0)$ ; rotate: $(0, 2)$ ; translate back: (3, 4)

Worked ExampleExample 3 — scaling and translation

Scale the point (2, 3) by 2 about the origin and then translate by (5, −1).

Solution. Scale → (4, 6); translate → (9, 5) If translated first: (7, 2) → scaled → (14, 4) — different, showing that order matters.

Worked ExampleExample 4 — Boolean operation

A 100 mm cube has a 40 mm diameter through-hole along one axis. Which CSG operation creates it and what is the resulting volume?

Solution. Subtraction of a cylinder (Ø40, length 100) from the cube. $V = 10 0^{3} - π \times 2 0^{2} \times 100 = 1000000 - 125664 =$ 874 336 mm³

Frequently tested points

CAD — computer-aided design/drafting; Sketchpad (1963); AutoCAD by Autodesk (1982).
Advantages: speed, accuracy, easy modification, reuse, consistency, storage, collaboration, 3D.
Input: keyboard, mouse, digitiser, scanner; output: monitor, printer, plotter; GPU for 3D.
Raster = pixels (loses quality on scaling); vector = mathematical objects (CAD).
Wireframe (edges, ambiguous) → surface (faces, no mass) → solid (volume, mass properties).
CSG — primitives + Booleans (union, subtract, intersect); B-rep — faces, edges, vertices.
Parametric modelling — dimensions and constraints drive geometry.
BIM — object-based information model; IFC exchange.
Homogeneous coordinates allow translation as matrix multiplication; order of transformations matters.
DWG native, DXF exchange, DWT template, BAK backup, SV$ autosave, STL 3D printing, IGES/STEP neutral 3D.

Common MistakeCommon mistakes

Assuming transformations can be applied in any order.
Treating wireframe models as solids with volume.
Sharing DWG files with incompatible software instead of using DXF/PDF.

Revision SummaryChapter summary

CAD uses computers to create, modify and document designs, offering speed, accuracy, reuse and collaboration over manual drafting.
CAD systems comprise input, processing, output and storage hardware and modelling software.
CAD drawings are vector-based; models progress from 2D drafting to wireframe, surface and solid models using CSG or B-rep, with parametric control and BIM.
Translation, scaling, rotation and reflection are expressed with homogeneous transformation matrices whose order matters.
File formats (DWG, DXF, DWT, PDF, STEP, STL, IFC), standards and data management support reliable exchange.

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