Spain 2º Bachillerato Technical Drawing for Art and Design II
Chapters: 4
1. Geometry, art and environment
Modular compositions · Geometry and optical illusions · Conics in nature and design · Space in contemporary art and design · Tessellations and patterns · Joins and tangencies in design
- 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.
- 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.
- Conic Sections (Class 11): Circle, Parabola, Ellipse and Hyperbola – Cutting a double cone with a plane gives a circle, an ellipse, a parabola or a hyperbola; a cut through the vertex gives a point, a line or a pair of lines (degenerate conics). Circle: (x − h)² + (y − k)² = r². Parabola y² = 4ax: focus (a, 0), directrix x = −a, latus rectum 4a, e = 1. Ellipse x²/a² + y²/b² = 1 (a > b): c² = a² − b², foci (±c, 0), e = c/a < 1, latus rectum 2b²/a, PF₁ + PF₂ = 2a. Hyperbola x²/a² − y²/b² = 1: c² = a² + b², e = c/a > 1, latus rectum 2b²/a, |PF₁ − PF₂| = 2a.
- Modern Art and Modernism – Between about 1880 and 1945, artists stopped copying reality and asked what art itself could do. Colour and brushwork showed feeling (Post-Impressionism, Expressionism); objects were seen from many sides (Cubism); speed and machines were celebrated (Futurism); art became pure shape and colour (abstraction, De Stijl, Constructivism); chance and dreams came in (Dada, Surrealism); and design followed function (Bauhaus, the Modern Movement). The same break happened in music, theatre and dance, and modernism spread worldwide through exchange, including India.
- Transformations: Slide, Flip, Turn and Resize a Shape – A transformation moves a shape to a new place. Translation slides it, reflection flips it in a mirror line, rotation turns it about a centre, enlargement changes its size from a centre. The first three keep size and shape (congruent image). Enlargement keeps shape but changes size (similar image). Each has a simple coordinate rule.
- 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.
2. Applied spatial representation systems
Circles and solids in perspective · Polyhedra and Platonic solids · Perspective for spaces and objects
- 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.
- Polyhedra: Prisms, Pyramids and the Platonic Solids – A polyhedron is a closed solid whose surface is made only of flat polygons (faces). Faces meet along edges, and edges meet at vertices. Prisms have two equal parallel bases joined by parallelograms; pyramids have one base and triangles meeting at an apex; a frustum is a pyramid with its top cut off by a plane parallel to the base. For every convex polyhedron, Euler's formula holds: V − E + F = 2. There are exactly five regular (Platonic) polyhedra.
- 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.
3. Standardisation and project design
Design project phases · Dimensioned views and sections
- The Design Process: From Problem to Product – The design process is a loop of steps designers use to solve a real problem for real people: investigate the need, define it in a brief and a measurable specification, generate many ideas, build a prototype, then test and evaluate it against the specification. Whatever fails sends you back round the loop. This repeating is called iteration, and it is how almost every product, app, building and artwork is improved.
- 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.
4. Digital design tools
CAD for art and design
- CAD Modelling: From a Sketch to a 3D Part – CAD (computer-aided design) means using a computer to draw and build exact models of objects before they are made. A design starts as a freehand sketch. In CAD it becomes a 2D sketch with constraints and dimensions. 3D tools such as extrude, revolve and cut turn the sketch into a solid. Each step is saved in a feature tree, so changing one size rebuilds the whole model. Parts are joined in assemblies, tested by simulation, shared as drawings and sent to 3D printers, laser cutters or CNC machines.