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

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

Eccentricity of ellipse

For an ellipse, eccentricity e = c/a, where c is focal distance and a is semi-major axis. Value between 0 and 1; e=0 gives circle.

Tangent from external point

To draw tangents from point P to circle center O radius r: draw circle with diameter OP; intersections with given circle are tangent points.

Parabola construction

Given focus F and directrix d, any point P satisfies PF = distance to d. Vertex is midpoint of perpendicular from F to d.

Hyperbola asymptotes

Lines through center with slopes ±b/a for hyperbola x²/a² − y²/b² = 1; curve approaches but never touches them.

Golden rectangle construction

Start with square; midpoint of one side to opposite corner as radius; extend side to arc; complete rectangle with sides in ratio φ:1.

Inscribed angle theorem

Angle subtended by an arc at circumference is half the angle at center. Angle in semicircle is right angle (90°).

Point coordinates in dihedral

A point is given by (x, y, z): x distance along ground line, y depth from vertical plane, z height from horizontal plane.

True length of line

Use right triangle with legs equal to difference in coordinates; true length = √(Δx² + Δy² + Δz²) for spatial line.

Line-plane intersection

Pass auxiliary projecting plane through line; find its intersection with given plane; intersect that line with original line to get piercing point.

Plane traces

Intersections of a plane with horizontal and vertical projection planes; named horizontal trace and vertical trace; meet at ground line.

Visibility rule

In projection, a point is visible if its projection is nearer the observer than the other element at same ray; otherwise hidden.

Auxiliary plane method

Introduce new projection plane perpendicular to one principal plane to obtain edge view or true shape of a geometric element.

Perpendicular line to plane

A line is perpendicular to a plane if its projections are perpendicular to the corresponding traces of the plane.

Theorem of three perpendiculars

If a line in a plane is perpendicular to the projection of an oblique line, then it is perpendicular to the oblique line itself.

Distance point to plane

Measured along perpendicular from point to plane; obtain true length by auxiliary plane perpendicular to given plane.

Angle line to plane

Angle between line and its orthogonal projection on plane; found by auxiliary plane containing line perpendicular to given plane.

Distance between skew lines

Length of common perpendicular; construct by projecting one line as point using auxiliary planes, then measure perpendicular distance.

Euler's polyhedron formula

For convex polyhedra: V − E + F = 2, where V vertices, E edges, F faces. Applies to Platonic solids and prisms.

Platonic solids

Five regular polyhedra: tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), dodecahedron (12 pentagons), icosahedron (20 triangles).

Section of polyhedron

Intersection polygon formed by cutting plane; vertices are piercing points of plane with edges; sides lie on faces.

Development of cone

Sector of radius equal to slant height l; arc length equals base circumference 2πr; sector angle = 360°·r/l.

Development of cylinder

Rectangle width equal to circumference 2πr, height equal to cylinder height; two circular bases attached to top and bottom edges.

Intersection of cylinders

Use auxiliary cutting planes parallel to axes; points common to both surfaces define intersection curve; develop by unfolding.

ISO line types

ISO 128: continuous thick for visible edges; continuous thin for dimension lines; dashed for hidden edges; chain for center lines.

Dimensioning rules

Dimension lines parallel to measured edge, extension lines perpendicular, arrowheads at ends, numerals above line, avoid crossing lines.

First-angle projection

Object between observer and projection plane; front view placed below top view; left view placed on right; standard in Europe (ISO).

Preferred scales

ISO 5455: enlargement 2:1, 5:1, 10:1; full 1:1; reduction 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, etc.

Surface roughness symbol

ISO 1302: tick symbol with Ra value in micrometers; extension line indicates machining allowance; placed on surface or leader.

Rule of thirds

Compositional guideline dividing frame into 3×3 grid; key elements placed at intersections for balanced, dynamic layout.

Visual hierarchy

Arrangement of elements by size, contrast, color, and position to guide viewer's attention to most important information first.

Isometric projection

Axonometric projection with three axes at 120°; equal foreshortening along axes; used for technical illustrations and assembly drawings.

Modular grid

Layout system of consistent columns, margins, and baseline grid; ensures alignment and proportional consistency across pages.

Project documentation set

Complete graphic package: location plan, floor plans, elevations, sections, details, schedules; each at appropriate scale for purpose.

Scale selection for details

General plans 1:100; details 1:20; construction details 1:5; choose scale so drawing remains clear at reproduction size.

Bill of quantities

Itemized list of materials with dimensions, quantities, and units; derived from drawings and specifications for project costing.

Site plan essentials

Shows north arrow, scale bar, boundaries, access, existing features; oriented to true north; includes project title and scale.