Galicia PAU Technical Drawing Applied to Plastic Arts and Design II cheat sheet

Golden ratio φ = (1+√5)/2 ≈ 1.618; a segment divides so that total/major = major/minor. Construction: erect perpendicular at B equal to AB/2, draw hypotenuse from A to that point, subtract AB/2 by arc to get the major part.

Regular polygon inscribed in a circle of radius R: side of n-gon s = 2R·sin(π/n). Useful values: hexagon s = R, square s = R√2, triangle s = R√3, pentagon s ≈ 1.176R, octagon s ≈ 0.765R.

Thales theorem: an angle inscribed in a semicircle is right. Used to draw tangents from an external point P to a circle of centre O by drawing the circle with diameter OP.

Tangent construction between two circles of radii r1, r2: external tangents use an auxiliary circle of radius |r1 − r2|; internal tangents use r1 + r2. Tangent points lie on the line joining centres.

Ovals vs ellipses: a four-centre oval is drawn from arcs with centres on the axes and is not a true ellipse; a true ellipse satisfies PF1 + PF2 = 2a. Do not label an oval an ellipse in technical drawings.

Golden-section rectangle construction: given side a, the other side b = a/φ ≈ 0.618a. The resulting rectangle is self-similar when a square is removed.

Inversion: point P' is inverse of P with respect to circle (O, r) if OP·OP' = r². Circles through the inversion centre map to lines not through O; circles not through O map to circles.

Radical axis: locus of points with equal power to two circles (power = d² − r²). The radical axis is perpendicular to the line of centres and passes through the intersection points of the two circles when they meet.

Dihedral system: horizontal plane (PH) and vertical plane (PV) meet at the ground line (LT). A point has two projections: horizontal a' and vertical a''. The distance from a' to LT equals the height above PH; the distance from a'' to LT equals the depth from PV.

Quadrants: first quadrant (above PH, in front of PV) is standard. A point in Q1 has both projections above LT after unfolding; Q2 has vertical above, horizontal below; Q3 both below; Q4 vertical below, horizontal above.

A line's true length appears when it is parallel to a projection plane. In the dihedral system, true length is obtained by the right-triangle method: hypotenuse of Δ(depth difference, horizontal projection length).

Plane traces: a plane is defined by its horizontal trace (intersection with PH) and vertical trace (intersection with PV). Both traces meet LT at the same point unless the plane is parallel to LT.

Intersection of two planes: find two points common to both planes, typically where traces cross, then join them. The line of intersection may require auxiliary planes when traces are parallel.

Point in a plane: a point belongs to a plane only if it lies on a line of that plane. Use a horizontal or frontal line of the plane to test membership or construct a point at a given height.

Angles: the angle between a line and a plane equals the angle between the line and its orthogonal projection onto that plane. The angle between two planes is measured in a plane perpendicular to their line of intersection.

Change of projection plane: to obtain true shape of an oblique face, introduce an auxiliary plane parallel to that face. The new projection is perpendicular to the chosen direction and preserves distances measured along that direction.

Isometric axonometry: three axes at 120°, equal foreshortening. Along each axis, lengths are drawn at true scale (isometric drawing) or multiplied by 0.816 (true isometric projection). Angles are not preserved.

Dimetric and trimetric systems use unequal axis scales. Cabinet (perspective cavalière) uses one axis at true scale, the receding axis at 1/2 scale and 45°; cavaliera uses full scale on the receding axis.

Axonometric scale relation: for orthogonal axonometry, cos²α + cos²β + cos²γ = 1 where α, β, γ are angles between the projection direction and each axis; the reduction coefficients satisfy u² + v² + w² = 2.

Perspective: one-point uses one vanishing point (front face parallel to picture plane); two-point uses two (vertical edges stay vertical); three-point adds a vertical vanishing point for looking up or down.

Vanishing point of a line family = intersection of the picture plane with the line through the station point parallel to that family. Horizon line = vanishing line of horizontal planes at eye level.

Cone of vision: useful field limited to about 30°–60°; a 45° cone is conventional. Objects outside the cone appear distorted, so station point distance controls apparent deformation.

Perspective of a point: project the station point onto the picture plane via the visual ray. Height of the image on the picture plane = (object height × distance from picture plane) / distance from station point to picture plane.

Shadows in axonometry: light direction is a line; shadow of a point is where the light ray through the point meets the receiving plane. Shadow of a line is the line joining shadow points of its endpoints.

ISO 216 paper sizes: A0 = 1 m², ratio 1:√2. Each subsequent size halves the previous area. A4 = 210 × 297 mm; A3 = 297 × 420 mm; A2 = 420 × 594 mm.

ISO 5455 scale notation: scale = drawing dimension / real dimension. Enlargement scales 2:1, 5:1; reduction scales 1:2, 1:5, 1:10, 1:20, 1:50, 1:100. Scale is stated in the title block, not on each dimension.

Dimensioning rules (ISO 129): dimension lines are parallel to the measured edge, extension lines perpendicular, arrowheads at both ends. Values are placed above the dimension line and read from the bottom or right.

Do not dimension the same feature twice; do not close dimension chains on a single view; place dimensions outside the outline where possible and avoid crossing dimension lines.

Line types (ISO 128): continuous thick for visible outlines; continuous thin for dimension, extension and hatching lines; dashed for hidden edges; dash-dot for centre and symmetry axes; continuous thin with zigzag for break lines.

Geometric tolerances (ISO 1101): a frame contains the symbol, tolerance value and datum letters. Symbols include flatness, straightness, circularity, parallelism, perpendicularity, position, concentricity.

Surface roughness (ISO 1302): the check mark with a number indicates Ra in micrometres. A bar over the symbol means material removal is required; a circle means it is prohibited.

Sections and cuts (ISO 128): hatching at 45° indicates cut material. Adjacent parts are hatched in opposite directions. Half sections show one half in section, the other in outside view, separated by a centre line.

Type measurement: 1 point = 1/72 inch ≈ 0.3528 mm; 12 points = 1 pica. Cap height, x-height, ascender and descender define the vertical metrics of a typeface.

Font categories: serif (roman), sans serif (grotesque), slab serif, script, blackletter, monospaced. Classification by Vox and by DIN 16518 uses these families.

Kerning adjusts space between specific letter pairs (e.g., AV, To); tracking adjusts uniform spacing across a range of text; leading (interline) is the baseline-to-baseline distance.

Legibility vs readability: legibility is the recognisability of individual characters; readability is the ease of reading a text block. Both depend on x-height, contrast, line length and leading.

Grid systems: a baseline grid aligns text baselines; a modular grid divides the page into columns and rows. The golden ratio and rule of thirds are common proportional guides.

Gestalt principles applied to layout: proximity, similarity, closure, continuity, figure-ground. These explain grouping and hierarchy in visual composition.

Colour in graphic design: CMYK for print (subtractive), RGB for screen (additive), Pantone as a spot-colour matching system. Hex notation #RRGGBB encodes RGB values in base 16.

Visual hierarchy tools: scale, weight, colour contrast, position, whitespace and alignment. F-pattern and Z-pattern describe typical eye-scanning routes on screens and posters.

Design process stages: research and briefing, analysis, ideation, development, prototyping, testing, production. Double Diamond model uses Discover, Define, Develop, Deliver.

Mood board, sketchbook, thumbnail and storyboard are ideation artefacts. Orthographic views, exploded views, sections and renderings are communication artefacts.

Product representation: isometric or axonometric sketch for overall form; orthographic views with dimensions for manufacture; exploded view to show assembly order and parts.

Ergonomics: anthropometric percentiles (5th, 50th, 95th) define reach and clearance. A design for a wide population typically uses 5th percentile for reach and 95th for clearance.

Design brief components: problem statement, target user, constraints, functional requirements, aesthetic criteria, budget and timeline.

Design thinking (IDEO/d.school): empathise, define, ideate, prototype, test. It is iterative and user-centred, not a linear sequence.

BOM (bill of materials) lists parts, quantities and materials. Technical data sheets give tolerances, finishes and material properties needed for production drawings.

Sustainability criteria: material recyclability, disassembly, energy in use, life-cycle assessment (LCA). Design for disassembly favours reversible joints over adhesives.

Additive colour (RGB): primary red, green, blue; secondary cyan, magenta, yellow; all three at full intensity give white. Subtractive colour (CMYK): primary cyan, magenta, yellow; all three give black (K added for depth).

Colour models: RGB, CMYK, HSB/HSL, Lab, Pantone. Lab is device-independent and used for colour management; sRGB is the common screen profile.

Colour attributes: hue (angle 0–360°), saturation or chroma, and value or lightness. Munsell uses hue, value and chroma; HSL uses hue, saturation, lightness.

Colour harmony schemes: complementary (opposite on wheel), analogous (adjacent), triadic (120° apart), split-complementary, tetradic. Simultaneous contrast (Chevreul) makes a colour shift toward the complement of its surround.

Material representation: wood grain, metal (hatching lines), concrete (stipple), glass (diagonal lines), stone (irregular marks). In technical drawing, hatching patterns follow ISO 128 conventions.

Materials: thermoplastics (recyclable, reshape by heating), thermosets (cross-linked, cannot be remelted), elastomers (elastic), composites (fibre plus matrix, anisotropic).

Colour rendering: metallic surfaces show high specular reflection and low diffuse; matte surfaces show diffuse only. Roughness and Fresnel describe the appearance in PBR rendering.

Print vs screen: CMYK conversion cannot reproduce all RGB colours (gamut). Spot colours (Pantone) are used when exact brand colour is required.

Vector vs raster: vector formats (SVG, PDF, AI, DXF, DWG) store geometry mathematically and scale without loss; raster formats (PNG, JPG, TIFF, PSD) store pixels and degrade when scaled.

CAD coordinate systems: absolute (x,y), relative (@dx,dy), polar (@distance<angle). Layers organise geometry by line type, colour and purpose.

Parametric modelling: sketch constraints (coincident, parallel, perpendicular, tangent, equal) drive geometry; dimensions are driving parameters. Changing a parameter updates the model.

CAD file formats: DWG/DXF for 2D exchange, STEP and IGES for 3D interchange, STL and OBJ for mesh, 3MF for additive manufacturing, PDF for drawing output.

3D modelling operations: extrude, revolve, sweep, loft, boolean (union, difference, intersection), fillet and chamfer. Assemblies use mates or constraints.

Rendering pipeline: modelling, materials and textures, lighting (HDRI, three-point), camera, render engine (rasterised or path-traced), post-production.

Print output: 300 dpi for raster images at print size; bleed typically 3 mm; crop marks and registration marks are placed outside the trim area.

Colour management: ICC profiles convert between device spaces. Convert to CMYK with a specific press profile before sending to print; soft-proof to preview gamut loss.