PAU Technical Drawing II (Aragón) key terms

A transformation that enlarges or reduces a figure from a fixed center by a constant ratio, so every line stays parallel to its image and all lengths scale by the same factor.

The constant quotient between corresponding lengths of two similar figures; it equals the homothety factor and its square gives the ratio between their areas.

The fixed point from which a homothety or similarity is performed; it lies on every line joining a point of the original figure to its image point.

A transformation mapping each point to another lying on the same ray from a fixed center, at a distance whose product with the original distance equals a constant power.

A plane correspondence that preserves incidence and cross-ratio but not lengths or angles; in technical drawing it links a figure to its perspective or section image through an axis and a center.

The quantity (AC/BC)÷(AD/BD) for four collinear points; it is the invariant that projective transformations preserve, unlike distances or angles.

The single point shared by a line and a curve, or by two curves, where they touch without crossing; locating it is essential to finish any tangency construction accurately.

The straight line formed by all points whose tangent lengths to two given circles are equal; it is perpendicular to the line joining their centers and is the key to circle tangency problems.

For a point and a circle, the square of the distance to the center minus the radius squared; it is constant along any secant through the point and underpins tangency and inversion constructions.

A closed conic whose points have a constant sum of distances to two fixed foci; it results from cutting a cone with a plane that meets every generatrix.

An open conic whose points are equidistant from a fixed focus and a fixed directrix line; the cutting plane is parallel to exactly one generatrix of the cone.

An open conic with two branches where the absolute difference of distances to two foci is constant; its cutting plane crosses both nappes of the cone.

The fixed line used with the focus to define a conic through constant distance ratios; for a parabola the ratio equals one, giving equal focus and directrix distances.

The ratio of the distance from a conic point to the focus over its distance to the directrix; values below, equal to, or above one give an ellipse, parabola, or hyperbola.

A line that a curve approaches indefinitely without meeting; the hyperbola has two, passing through its center and obtained from the rectangle built on its axes.

A line touching a conic at one point, found by bisecting the angle between the focal radii at that point, or by classical constructions using the directrix or conjugate diameters.

The separation between the two foci of an ellipse or hyperbola; together with the major or transverse axis it fixes the curve completely.

A plane curve traced by a point moving at constant speed along a ray that itself rotates at constant angular speed, producing equal spacing between successive turns.

The curve traced by the end of a taut string unwound from a given curve; the involute of a circle is the standard profile for gear teeth.

The curve tangent to every member of a family of lines or curves; classical examples include the parabola enveloped by perpendicular bisectors and the astroid formed by a moving ladder.

The two orthographic views of descriptive geometry: the plan on a horizontal plane and the elevation on a vertical plane, joined by reference lines so heights and depths transfer between them.

The real size of a segment, angle, or plane figure obtained by projecting it onto a plane parallel to it, usually through a change of projection plane or a rotation.

A descriptive-geometry method that replaces one projection plane with another, keeping the object fixed, to turn an oblique line or plane into a parallel or perpendicular one.

The single point shared by a line and a plane, found by containing the line in an auxiliary plane and intersecting that plane with the given one.

The straight line common to two planes; it is determined by finding where pairs of lines from each plane meet, or by using auxiliary cutting planes.

The plane figure produced where a cutting plane passes through a solid; in descriptive geometry it is built from the intersection points with the solid's edges or faces.

The flat pattern obtained by unfolding the surfaces of a solid onto a plane without stretching; prisms and cylinders develop exactly, while cones and spheres require approximation.

A solid cut by a plane so that part of it is removed; its development combines the true shapes of the cut faces with the unfolded lateral surfaces.

An axonometric projection in which the three coordinate axes appear equally foreshortened at 120 degrees apart; true lengths are read by applying the 0.816 reduction or the usual 1:1 drawing convention.

A parallel projection of a solid onto a plane not parallel to any of its main faces, so that three dimensions appear in one view; isometric, dimetric, and trimetric variants differ by axis angles.

An oblique axonometric drawing where the front face is shown true size and receding edges are drawn at half scale, typically at 45 degrees, to suggest depth.

A multiview arrangement where the object sits between the observer and the projection plane, so the view seen from the left is placed on the right of the front view.

A multiview arrangement where the projection plane lies between the observer and the object, so each view is placed on the same side as the direction from which it is seen.

The set of rules for placing numerical values, dimension lines, extension lines, and arrowheads on a drawing so that every size is stated once, clearly and without redundancy.

The ratio between a drawn length and the real length it represents, written as 1:n for reduction, n:1 for enlargement, and 1:1 for full size.

The standardized meanings of line types: continuous thick for visible edges, dashed for hidden edges, chain for axes and symmetry, and thin continuous for dimension and extension lines.

The standardized sheet size, such as the A series based on halving the previous area, together with its frame, title block, and folding marks.

A CAD approach where geometry is driven by dimensions, constraints, and features, so editing a parameter rebuilds the model and its associated drawings automatically.

A 3D modeling command that combines solids by union, subtraction, or intersection, producing new volumes from existing ones while keeping the operation editable in history-based systems.

A modeling operation that sweeps a closed 2D profile along a straight path to create a solid of constant cross-section; a draft angle or taper can be applied.

A named organizational level in a CAD drawing that groups entities and controls their color, line type, line weight, visibility, and whether they can be printed.

The ratio set when sending a CAD drawing to a printer or file, linking paper millimetres to drawing units so the printed sheet matches the intended scale.