Catalonia PAU Technical Drawing Applied to Plastic Arts and Design II flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Golden ratio value

φ = (1+√5)/2 ≈ 1.618. A segment is divided in mean and extreme ratio when the whole is to the larger part as the larger part is to the smaller.

Thales semicircle theorem

Any angle inscribed in a semicircle is a right angle, so the locus of points from which segment AB is seen at 90° is the circle with AB as diameter.

Regular hexagon construction

In a regular hexagon the side equals the circumradius, so the hexagon is inscribed by stepping the compass radius six times around the circle.

Tangent from external point

To draw tangents from point P to circle O, draw the circle with diameter OP; its intersections with the given circle are the two tangency points.

Ellipse focal property

For an ellipse with major axis 2a and foci F, F', every point P on the curve satisfies PF + PF' = 2a, which underlies the string and trammel constructions.

Circle inversion relation

Inversion with centre O and radius r maps P to P' on ray OP such that OP·OP' = r²; circles through O become lines not through O.

Dihedral system fold line

The fold line LT is the intersection of the horizontal and vertical projection planes; rotating the horizontal plane 90° about LT brings both projections onto one sheet.

Point coordinates in dihedral

A point with coordinates x, y, z has its horizontal projection at distance x from LT with depth y, and its vertical projection at distance x with height z.

True length by rotation

A segment's true length is found by making it parallel to a projection plane, or as the hypotenuse of a right triangle with legs equal to one projection and the coordinate difference.

Line piercing a plane

Contain the line in an auxiliary projecting plane, intersect that plane with the given plane to get a line, then intersect that line with the original line.

Profile plane purpose

The profile plane, perpendicular to both PH and PV, is used to resolve true lengths and ambiguities of profile lines and planes that are perpendicular to the fold line.

Plane traces

A plane is represented by its traces, the lines where it cuts the horizontal and vertical planes; a horizontal plane has only a vertical trace parallel to LT.

Isometric ellipse axes

In isometric projection a circle of diameter d lying in a coordinate plane appears as an ellipse with major axis about 1.22d and minor axis about 0.71d.

Cabinet projection reduction

Cabinet (perspectiva caballera) draws the front face true shape and the receding axis, usually at 45°, at half scale; cavalier keeps the receding axis at full scale.

Vanishing point construction

In two-point perspective a horizontal line's vanishing point is found by drawing through the station point a parallel to that line and rotating it onto the horizon.

Horizon line meaning

The horizon line is the trace of the picture plane on the horizontal plane through the observer's eye; its height equals the observer's eye level.

A-series sheet ratio

ISO A formats use sides in ratio √2 with A0 equal to one square metre; each successive size halves the larger side, giving A4 = 210 × 297 mm.

Hidden edge line type

Hidden edges are drawn with a thin dashed line, while visible outlines use a continuous thick line and symmetry axes use a thin dash-dot line.

Dimensioning prefixes

ISO 129 prefixes: Ø for diameter, R for radius, SR for spherical radius, □ for square; reference dimensions are placed in parentheses and not used for production.

Scale factor on areas

Scale is drawing length divided by real length; areas scale as the square of the linear factor, so at 1:50 a real area is 2500 times the drawn area.

First versus third angle

In first-angle projection, standard in Europe, the top view is placed below the front view; in third-angle projection the top view is placed above it.

Cone development sector

A right cone of base radius r and generatrix g develops into a circular sector of radius g with central angle α = 360°·r/g.

Developable versus non-developable

Prisms, cylinders, cones and pyramids are developable and unroll without distortion; spheres and toruses are doubly curved and have no exact plane development.

Equal cylinder intersection

Two cylinders of equal diameter with perpendicular intersecting axes meet along two ellipses, which appear as straight lines crossing at the axis intersection in projection.

Euler polyhedron formula

For any convex polyhedron the numbers of vertices V, edges E and faces F satisfy V − E + F = 2, which checks a solid's topology before development.

Helix development triangle

One turn of a helix on a cylinder of radius r with pitch p unrolls into a right triangle with legs 2πr and p, giving helix angle tan θ = p/(2πr).

Sketching bounding box method

Enclose the object in a proportional box, subdivide it to locate main features, then refine edges and ellipses before adding interior detail.

CAD object snaps

Object snaps lock the cursor to exact geometric points such as endpoint, midpoint, intersection, tangent and perpendicular, ensuring constructed geometry is exact rather than approximate.

Parametric constraint behaviour

Geometric and dimensional constraints make a model update automatically when a driving dimension changes, keeping tangency, parallelism and equality relationships intact.

Simultaneous contrast

A colour appears shifted toward the complement of its surround, so a neutral grey looks greenish on a red field and reddish on a green field.

Additive versus subtractive colour

RGB mixes light additively and is used for screens; CMYK mixes pigments subtractively for print, and their gamuts differ, so some colours need spot inks.

Print-ready artwork requirements

Production files need 300 ppi resolution at final size, embedded fonts or outlined type, CMYK or spot colour specification, crop marks and typically 3 mm bleed.