Spain 1º Bachillerato Technical Drawing for Art and Design I
Chapters: 4
1. Geometry, art and environment
Geometry in nature and art · Geometry in composition · Representing space in art history · Proportion, symmetry and golden ratio · Scales · Polygon constructions in design · Tangencies and curves in design · Freehand geometric studies
- Geometric Modelling: Describing Real Objects with Simple Solids – Geometric modelling means replacing a real object with simple shapes (cuboid, cylinder, cone, sphere, prism) so we can calculate with it. The cycle is: look at the real object, simplify it, measure, calculate volume or surface area, then check the answer against reality and improve the model. Scale changes lengths by k, areas by k² and volumes by k³. Geometry also helps us see patterns in nature and art, like hexagons in honeycombs.
- Elements of Art and Principles of Design – The elements of art are the building blocks an artist uses: line, shape, form, colour, value, texture and space (many teachers also add the point). The principles of design are the rules for arranging those blocks: balance, contrast, emphasis, movement, rhythm and pattern, proportion and scale, and unity with variety. Knowing both helps you make art on purpose and talk about any artwork clearly.
- Art History: From Cave Walls to Today – People have made art for at least 40,000 years. Prehistoric art shows animals and hands on cave walls. Ancient civilisations made art for rulers, gods and the afterlife. Classical traditions arose in Greece and Rome, India, China, Africa and the Americas. The Renaissance brought perspective and realism; modern art (from about 1860) broke those rules; contemporary art uses any material. To appreciate any artwork, describe it, analyse its elements, interpret its meaning in its context, and judge why it works.
- The Golden Ratio – Cut a length into a big part a and a small part b so that whole ÷ a = a ÷ b. That shared ratio is the golden ratio φ (phi) = (1 + √5) ÷ 2 ≈ 1.618. A rectangle with sides in this ratio is a golden rectangle: cut off a square and the piece left is golden again. Ratios of neighbouring Fibonacci numbers get closer and closer to φ.
- Technical Drawing: Communicating Design Ideas – Technical drawing is a shared visual language for showing the exact shape and size of an object. Designers start with freehand sketches, then use pictorial views (isometric, oblique) to show the object in 3D, and orthographic projection (front, top and side views) with standard lines, dimensions in millimetres and a scale so that anyone can make it. Today most drawings are made with CAD software.
- Geometric Constructions: Drawing Exactly with Compass and Straightedge – A geometric construction draws a figure exactly using only a compass and a straightedge (a ruler used for straight lines). Key constructions: the perpendicular bisector of a segment, the bisector of an angle, a perpendicular from a point to a line, angles of 60°, 30°, 90° and 45°, a triangle from three sides (SSS), two sides and the included angle (SAS) or two angles and a side (ASA), and regular polygons such as the hexagon. Each works because equal compass arcs make equal lengths, which give congruent triangles.
- Tangent to a Circle – A tangent is a line that touches a circle at exactly one point. At that point it makes a 90° angle with the radius, and two tangents drawn from one outside point are always equal in length.
- Circles and Tangents: How to Draw Them and Why They Work – A tangent touches a circle at one point and is at 90 degrees to the radius. From an outside point P you can draw two equal tangents of length √(D² - r²). Two circles have up to four common tangents. A circle can join two lines smoothly, and arcs with changing centres make spirals. Power of a point says PA x PB = D² - r² for every line through P. The radical axis is the straight line of points that have equal power for two circles.
- Drawing and Painting – Drawing is a way of seeing and thinking: we use it to record what we observe, to remember, to plan designs and to express ideas. A good drawing starts by blocking in: seeing objects as simple shapes (sphere, box, cylinder) and checking proportions with light lines. Line then defines edges, and line weight (heavy or light) shows what is near or far. Light gives form: on a lit object we see the highlight, mid-tone, core shadow, reflected light and cast shadow. Tonal value runs from white to black; strong contrast of light and dark is called chiaroscuro, and a picture can be in a high key (mostly light) or low key (mostly dark). Dry media (graphite, charcoal, pastels, coloured pencils) build tone with hatching, cross-hatching, stippling and blending; wet media (ink, watercolour, gouache, acrylic, oil) build it with washes, layers (glazes) and mixing colours. Linear and atmospheric perspective show space, and figure drawing uses proportion, gesture and foreshortening. Artists record ideas in sketchbooks and use traditional, alternative and digital tools safely and sustainably.
2. Applied spatial representation systems
Types of projection · Orthographic views, first angle · Isometric, cavalier and packaging · Perspective in comics and illustration
- Projections: Central, Parallel and Orthogonal – A projection draws a 3D object on a flat surface using straight rays. If all rays start at one point (a lamp, your eye) it is a central projection: images change size with distance and give perspective. If all rays are parallel (sunlight) it is a parallel projection: sizes do not depend on distance. If the parallel rays are at 90° to the screen it is an orthogonal projection: faces parallel to the screen show their true size. Engineers use orthogonal views, artists use perspective.
- Orthographic Views of Solids – An orthographic view shows a solid as seen straight on from one direction, with no perspective. The three main views are the front view (front elevation), the top view (plan) and the side view (side or end elevation). Each view loses one dimension, so we usually need all three to fix the shape. Views are arranged in a standard layout: first-angle projection (plan below the front view; used in India, Europe and ISO standards) or third-angle projection (plan above; used in the USA). Visible edges are thick continuous lines, hidden edges are dashed, and centre lines are chain lines. A net is the flat pattern that folds into a solid, and a cross-section is the shape you see when you cut through it.
- Isometric Projection and Axonometric Drawing – An axonometric drawing shows a solid in one picture with three axes: width, depth and height. In isometric projection the three axes are 120° apart and every axis is shortened equally (scale ≈ 0.82). An isometric drawing uses full lengths instead. Dimetric shortens two axes the same, trimetric all three differently. Oblique (cavalier, cabinet) keeps the front face true size and draws depth at 45°, full length (cavalier) or half (cabinet). Circles on faces become ellipses.
3. Standardisation and project design
Standardisation · Project graphic documentation · Sketches and drafts
- National and International Standards in Design – A standard is an agreed document that sets sizes, quality, safety or test methods so products fit, work safely and can be traded. ISO and IEC write world standards; regional (EN) and national bodies such as BIS, BSI, DIN, UNE and ANSI adopt them. Marks like CE, ISI and the Kitemark show conformity. ISO 216 A-series paper starts at A0 = 1 m², halves at each size and keeps a 1 : √2 ratio. Drawing standards fix line types, scales, dimensions, title blocks and how to fold sheets to A4.
- Technical Drawing: Communicating Design Ideas – Technical drawing is a shared visual language for showing the exact shape and size of an object. Designers start with freehand sketches, then use pictorial views (isometric, oblique) to show the object in 3D, and orthographic projection (front, top and side views) with standard lines, dimensions in millimetres and a scale so that anyone can make it. Today most drawings are made with CAD software.
4. Digital design tools
2D vector drawing · Introduction to 3D modelling
- Graphic Design – Graphic design is planning pictures, words and shapes so that a message is clear, useful and attractive. Designers use elements (line, shape, colour, type, image, space) and principles (alignment and grid, hierarchy, contrast, proximity, repetition, balance and white space). They follow a process: brief, research, ideas, sketches, digital drafts, feedback and final artwork. Graphic design is used in posters, logos, book covers, packaging, signs, websites and apps.
- 3D Modelling: From a Cube to a Printed Object – A 3D model is a shape stored in a computer as points (vertices) joined by edges into flat faces: a mesh. We build models by starting from simple shapes (primitives), moving, rotating and scaling them, and pulling faces out (extrude). Then we add materials and lights and the computer renders a picture. The same model can be sliced into thin layers and built by a 3D printer, or used in games, films, VR and product design.