3D representations: conical and axonometric perspective
Let's read and learn ~12 min
1. Representations of three-dimensional objects
1.1. Introduction
Throughout history, various drawing systems have been developed to represent the volumes and shapes of three-dimensional objects on two-dimensional surfaces.
A good example is video games. The video game Diablo is made in isometric perspective: it shows the game from a fixed diagonal view of the characters and the environment, which makes it easier to see the action and explore the scenery in three dimensions.
1.2. Types of perspective
1.2.1. Conical perspective
This perspective is based on the perception system of the human eye. It sets up a cone of projection from the observer's point of view, inserting a new plane between the observer and reality. Lines that are parallel in the real world are shown as lines that converge at vanishing points.
The results look quite realistic. However, measurements, angles and other technical details are harder to draw and to interpret afterwards, and the dimensions of objects are distorted. That is why conical perspective is less common in technical drawings and more common in artistic drawings or final product presentations.
1.2.2. Axonometric perspective
Objects are built by projecting the lines we want to represent onto the drawing plane. It is easy to draw and respects the geometry of the objects, so it is useful for showing technical information. It is the most common perspective used in technology.
There are two types of axonometric perspective, depending on the orientation of the projection line relative to the drawing plane, and they are drawn with different methods: choose the most suitable for each situation and type of design.
| vanishing point | punto de fuga |
| conical perspective | perspectiva cónica |
| axonometric | axonométrica |
| projection | proyección |
| viewpoint | punto de vista |
| depth | profundidad |
| three-dimensional | tridimensional |
Practice time ~15 min
1. Sort: conical or axonometric
Tap an item and then its group. Tap a placed item to send it back.
Axonometric: Easy to measure on; Respects the geometry; Most used in technology; Orthogonal or oblique
2. How many vanishing points?
Choose the right option for each figure.
2. 1 vanishing point
3. 2 vanishing points
3. Fill in the gaps
Choose the right word for each gap.
Conical perspective mimics the human and its parallel lines converge at .
perspective projects onto the drawing plane and is the most used in .
There are two types of axonometry: and .
Axonometric perspective projects onto the drawing plane and is the most used in technology.
There are two types of axonometry: orthogonal and oblique.
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
With the iPad, find an example of 1, 2 and 3 vanishing points around school, trace them with Markup and upload them to the shared slides.
Cavalier perspective
Let's read and learn ~12 min
2. Cavalier perspective
Cavalier perspective has two orthogonal axes, meaning they are perpendicular. The third axis is inclined at a variable angle to the other two and gives a sense of depth. If we rotate the X axis by 135° relative to the other axes, we get a projection that can be drawn in a notebook.
This projection is easy to draw on graph paper, since horizontal and vertical lines can coincide with the squares, while depth can be drawn diagonally across the squares.
With this system the axes need not be reduced, so we can draw objects without distorting their real dimensions.
- Draw the front face (the most complex one) undistorted.
- From each vertex draw the depth diagonals, all parallel.
- Measure the depth along them and draw the back face.
- Ink only the visible edges.
| cavalier perspective | perspectiva caballera |
| oblique | oblicua |
| orthogonal axes | ejes ortogonales |
| graph paper | papel cuadriculado |
| depth | profundidad |
| front face | cara frontal |
| hidden edge | arista oculta |
Practice time ~15 min
1. Put the steps for drawing in cavalier in order
Tap two items to swap them and put them in order.
2. Draw the depth diagonals
3. Draw the back face
4. Ink the visible edges
2. Match
Tap an item on the left, then its match on the right.
Depth ↔ Diagonal across the squares
X and Z axes ↔ Perpendicular
Graph paper ↔ Horizontals and verticals follow the squares
3. True or false
Mark true or false.
2. False
3. True
4. False
5. True
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
In pairs: A describes a cube piece using only axis moves (“3 right, 2 up, 1 back”) and B draws it in cavalier without seeing it. Compare and swap.
Isometric perspective
Let's read and learn ~12 min
3. Isometric perspective
The three axes of isometric perspective are separated by a 120° angle and the real dimensions are respected. However, the angles between the main axes are distorted.
In this representation system all vertical and horizontal lines remain parallel to each other, which is useful for drawing objects such as boxes or wooden pieces.
- Draw one vertical axis and two axes at 30° to the horizontal (30°/60° set square).
- Draw the piece's bounding box, measuring along the axes.
- “Carve out” the gaps and ink over.
A square becomes a rhombus (60° and 120° angles). Isometric dot paper can be used.
| isometric | isométrica |
| 30°/60° set square | cartabón |
| 45° set square | escuadra |
| bounding box | caja envolvente |
| dot paper | papel de puntos |
| rhombus | rombo |
| real dimensions | dimensiones reales |
Practice time ~15 min
1. Fill in the gaps
Choose the right word for each gap.
The three isometric axes form with each other.
The dimensions are respected along the axes.
The inclined axes form with the horizontal.
A square looks like a .
The real dimensions are respected along the axes.
The inclined axes form 30° with the horizontal.
A square looks like a rhombus.
2. Put the steps in order
Tap two items to swap them and put them in order.
2. Draw the bounding box
3. “Carve out” the gaps
4. Ink over the piece
3. Match
Tap an item on the left, then its match on the right.
Dot paper ↔ Guides the isometric lines
Bounding box ↔ The first thing you draw
Rhombus ↔ How a square looks
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
Draw your initial extruded in isometric. Level 1: L, T, E, H. Level 2: A, N. Level 3: your name as a skyline.
Standardisation: lines and scales
Let's read and learn ~12 min
4. Standardisation
Technical standardisation is the set of rules that bring together and regulate aspects of technical drawing such as line types, symbols, scales and perspectives. Thanks to it a drawing can be understood in any workshop (UNE standards in Spain and ISO internationally).
4.1. Line types
| Line | Sample | Use |
|---|---|---|
| Thick continuous line | Outlines and visible edges | |
| Thin continuous line | Dimension and extension lines | |
| Dashed line | Hidden edges | |
| Thin chain line | Axes and centres |
Reference thicknesses: thick line 0.5 mm, thin line 0.25 mm.
4.2. Scales
The scale is the relation between a measurement on the drawing and the real one: drawing : real.
| Scale | Type | Meaning |
|---|---|---|
| 1:1 | Full size | The drawing is the same size as the part. |
| 1:2 | Reduction | The drawing is half size. |
| 2:1 | Enlargement | The drawing is double size. |
Careful: the scale changes the drawing, not the dimensions. Always write the real measurement.
| standardisation | normalización |
| thick continuous line | línea continua gruesa |
| thin continuous line | línea continua fina |
| dashed line | línea de trazos |
| chain line | línea de trazo y punto |
| scale | escala |
| full size | tamaño natural |
| enlargement | ampliación |
| reduction | reducción |
Practice time ~15 min
1. Match each line with its use
Tap an item on the left, then its match on the right.
Thin continuous ↔ Dimension and extension lines
Dashed ↔ Hidden edges
Thin chain ↔ Axes and centres
2. Sort the scales
Tap an item and then its group. Tap a placed item to send it back.
Reduction: 1:2; 1:50; 1:100
Enlargement: 2:1; 5:1
3. Fill in the gaps
Choose the right word for each gap.
A 100 mm part at scale 1:2 measures mm on paper, but the dimension written is .
Scale 2:1 is an .
Hidden edges are drawn with a line.
Scale 2:1 is an enlargement.
Hidden edges are drawn with a dashed line.
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
Measure the classroom with a tape, work out the scale that fits an A4 sheet (hint: 1:50) and draw the plan with the door and your desk.
Dimensioning
Let's read and learn ~12 min
5. Annotation (dimensioning)
Annotating (dimensioning) means putting the real measurements of an object on the drawing to make it easier to read and understand. To do it we follow certain rules and use specific elements.
5.1. Dimensioning elements
- Dimension line: thin, with an arrowhead at each end.
- Extension lines: thin, they leave the drawing and limit the dimension.
- Arrowheads.
- Dimension figure: the real measurement.
- Symbols: Ø diameter, R radius.
5.2. Dimensioning rules
- Dimensions show the real measurements of the part. If no other unit is given, they are in millimetres.
- Dimensions must be drawn with lower intensity than the edges of the part.
- The part's own edges cannot be used to dimension on; dimensions must be separated from the drawing by at least 8 mm using extension lines, and 6 mm between parallel dimensions.
- The dimension figure must be centred on the dimension line and written above it.
- If the arrows or figures do not fit inside the dimension line they may be placed outside; if there are several aligned dimensions, dots may be used between them.
- Only inner features may be dimensioned inside the part.
- Radii and diameters are dimensioned on the features themselves with an arrow touching the circumference.
- Use the minimum number of dimensions that define the object.
| dimensioning | acotación |
| dimension line | línea de cota |
| extension line | línea de referencia |
| arrowhead | flecha |
| dimension figure | cifra de cota |
| diameter | diámetro |
| radius | radio |
Practice time ~15 min
1. Match
Tap an item on the left, then its match on the right.
Extension line ↔ Leaves the drawing and limits the dimension
Dimension figure ↔ The real measurement
R ↔ Radius
2. Correct or dimensioning mistake?
Tap an item and then its group. Tap a placed item to send it back.
Mistake: Figure below the line; Using an edge as the dimension line; Repeated dimensions
3. True or false
Mark true or false.
2. False
3. True
4. False
5. True
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
With the printed sheet from the guide, find the 8 dimensioning errors in the plate and say which rule each breaks.
Measuring instruments and precision
Let's read and learn ~12 min
6. Measuring instruments and precision
To measure lengths we have several instruments. We use one or another depending on the size, shape, location and characteristics of the object, and on the degree of precision we need.
| Instrument | What it is for |
|---|---|
| Metal ruler | Measuring or marking paper with millimetre precision. |
| Tape measure | Flexible, adapts to curves: contours and outer edges of curved objects. |
| Carpenter's rule | Handy for wooden pieces: it folds and unfolds. |
| Self-retracting tape measure | Distances up to 30 m. The most common are rigid and metallic, 2 to 5 m. |
6.1. Measuring precisely
6.1.1. Vernier caliper
A caliper is made of a fixed ruler (in millimetres) and a vernier, or sliding scale, with subdivisions: the more there are, the more precise the measurement. With a 50-division vernier the precision is 0.02 mm.
Reading = whole mm on the ruler + (matching vernier division × 0.02) · E.g. 23 + 14 × 0.02 = 23.28 mm
6.1.2. Micrometer
A micrometer is a nut-and-bolt mechanism. When the ends touch it reads zero; as they separate, the measurement of the gap is read on the graduated drum. A full turn equals half a millimetre and the drum has 50 divisions, so each one equals 0.5 mm / 50 = 0.01 mm.
Reading = mm on the fixed scale (plus 0.5 if visible) + drum × 0.01 · E.g. 6.5 + 23 × 0.01 = 6.73 mm
Good practice: check zero, read straight on (parallax error) and do not overtighten the micrometer (use the ratchet).
| ruler | regla |
| tape measure | cinta métrica |
| carpenter's rule | regla de carpintero |
| vernier caliper | calibre |
| vernier | nonio |
| micrometer | micrómetro |
| precision | precisión |
Practice time ~15 min
1. Match instrument and use
Tap an item on the left, then its match on the right.
Flexible tape ↔ Curved outlines
Carpenter's rule ↔ Wooden pieces; it folds
Self-retracting tape ↔ Distances up to 30 m
2. Caliper or micrometer?
Tap an item and then its group. Tap a placed item to send it back.
Micrometer: Precision 0.01 mm; Graduated drum; Ratchet
3. Readings: calculate
Choose the right word for each gap.
Caliper: 17 + 36 × 0.02 = mm
Caliper: 23 + 14 × 0.02 = mm
Micrometer: 6.5 + 23 × 0.01 = mm
One turn of the micrometer equals mm.
Caliper: 23 + 14 × 0.02 = 23.28 mm
Micrometer: 6.5 + 23 × 0.01 = 6.73 mm
One turn of the micrometer equals 0.5 mm.
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
Estimate the length of 3 classroom objects, then measure them with ruler, caliper or micrometer and calculate your error (|estimate − measurement|).
Technical instructions
Let's read and learn ~12 min
7. Technical instructions
Drawings often accompany assembly instructions and user manuals for many devices, since they can be easier to understand than written instructions. This is the case of the BILLY shelf or the exploded view of a switch.
These drawings usually consist of simplified views of the objects, with extra elements such as arrows, numbers, comments and annotations. They normally begin with a description of the object and its most important parts, which are numbered on the drawing and described later.
- One step = one action.
- Arrows that show movement.
- Numbered parts and quantities (×4).
- Warnings with ✓ and ✗.
- No clutter: only what is needed.
| assembly instructions | instrucciones de montaje |
| exploded view | vista despiece |
| part | pieza |
| step | paso |
| arrow | flecha |
| annotation | anotación |
| user manual | manual de usuario |
Practice time ~15 min
1. Put the creation of instructions in order
Tap two items to swap them and put them in order.
2. Number the parts on the drawing
3. Draw each step with simplified views
4. Add arrows and quantities
5. Test the instructions with a real user
2. Match element and purpose
Tap an item on the left, then its match on the right.
Number ↔ Identifies the part
Exploded view ↔ Pulls parts apart along the assembly axis
✓ / ✗ ↔ Warnings
3. True or false
Mark true or false.
2. False
3. True
4. False
5. True
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
Draw wordless instructions (3 steps) to assemble a cube piece. Another pair builds it from your sheet alone and you note where they hesitate.
Sketch, draft and views
Let's read and learn ~12 min
8. Sketch, draft and technical drawing
Before the final drawing there are several stages. Each has a different goal:
| Sketch | Draft (croquis) | Technical drawing | |
|---|---|---|---|
| How | Freehand, quick | Freehand, careful | With instruments or CAD |
| Measurements | No | Yes, proportioned and dimensioned | Yes, to scale and standardised |
| Purpose | Explore and share ideas | Record the data of a real object | Manufacture or document |
- Observe the object and choose the main face.
- Fit the piece in a box with the right proportions (graph paper helps).
- Draw the details with light lines and ink over with standard lines.
- Measure and add the dimensions.
- Check: could someone else make it from my draft alone?
9. Standard views of a part
With orthogonal projection a part is shown through several flat views, with no perspective and with real measurements. The three main views are:
- Front view: viewed from the front. Choose the face that gives the most information.
- Top view (plan): seen from above. It goes below the front view.
- Side view: from the left. It goes to the right of the front view.
The views must line up: the width of the top view equals the front view's, and the height of the side view equals the front view's. Draw only the views needed to define the part and use the standard line types (hidden edges dashed).
| sketch | boceto |
| draft (croquis) | croquis |
| technical drawing | dibujo técnico |
| front view | alzado |
| top view | planta |
| side view | perfil |
| hidden edge | arista oculta |
Practice time ~15 min
1. Sketch, draft or technical drawing
Tap an item and then its group. Tap a placed item to send it back.
Draft: Freehand with proportions and dimensions; Records the data of a real object
Technical drawing: With instruments or CAD; To scale and standardised
2. Match view and position
Tap an item on the left, then its match on the right.
Top view ↔ Below the front view
Left side view ↔ To the right of the front view
Hidden edge ↔ Dashed line
3. Fill in the gaps
Choose the right word for each gap.
The top view is placed the front view.
The left side view goes to the of the front view.
Hidden edges are drawn .
The views must in width and height.
The left side view goes to the right of the front view.
Hidden edges are drawn dashed.
The views must line up in width and height.
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
Draw the three views of a 6-cube piece and pass them to another pair, who must build it. Check afterwards against the original piece.
CAD and technical documentation
Let's read and learn ~12 min
10. Drawing with the computer (CAD)
CAD stands for Computer-Aided Design. It lets you draw with exact measurements, edit without erasing and obtain views, drawings and files ready for manufacturing.
| 2D CAD | 3D CAD |
|---|---|
| Drawings, diagrams, circuits and views. | Models of objects that can be rotated, measured and exported for 3D printing. |
- Examples: Tinkercad (3D, in the browser), LibreCAD (2D, free), Autodesk Fusion or SketchUp (3D).
- Basic workflow: create shapes → set exact sizes → rotate to see the views → dimension → export (PDF, image or STL).
- Advantages: precision, fast corrections and teamwork in the cloud.
Tip: model your cube piece with 20 × 20 × 20 mm boxes and compare the program's view with your isometric drawing.
11. Document and share: vocabulary and digital etiquette
A technical project does not end with drawing: you have to communicate it. Technical documentation includes sketches, drawings, views, a parts list and instructions, gathered in one clear document.
- Digital tools: word processor, presentations (Google Slides, Keynote), PDF and images. One shared file allows teamwork, also remotely.
- Technical vocabulary: use the exact terms in the glossary (dimension, front view, scale, vernier…) in English and Spanish.
- Digital etiquette: name files clearly (Part_TopView_v2.pdf), credit sources and images that are not yours, comment respectfully and save versions before changing.
- Title, authors and date.
- Perspective and views with standard lines.
- Correct dimensions and scale.
- Measurement table with units.
- Assembly instructions.
- Sources credited.
| CAD | diseño asistido por ordenador |
| 3D model | modelo 3D |
| to export | exportar |
| STL file | archivo STL |
| technical documentation | documentación técnica |
| digital etiquette | etiqueta digital |
| version | versión |
Practice time ~15 min
1. Match
Tap an item on the left, then its match on the right.
LibreCAD ↔ Free 2D CAD
STL ↔ File for 3D printing
PDF ↔ Document to share
2. Digital etiquette: good or bad
Tap an item and then its group. Tap a placed item to send it back.
Bad: Using images without crediting; File called “Document1”; Rude comments
3. Fill in the gaps
Choose the right word for each gap.
CAD stands for -aided .
A technical dossier includes title, authors and .
In a file you work as a team, also remotely.
A technical dossier includes title, authors and date.
In a shared file you work as a team, also remotely.
Quiz time! ~15 min
Your teacher will launch the live quiz from the device. Get ready!
✦ If we have extra time ~10 min
In pairs, open a shared presentation and split the slides (perspective, views, dimensions, measurements, instructions). Leave a respectful comment on another pair's work.