Rectilinear & Curvilinear

Rectilinear (pronounced rek-tl-in-ee-er)

(1) Forming or formed by straight lines.

(2) In geometry, as rectilinear grid, a tessellation by rectangles or rectangular cuboids (also known as rectangular parallelepipeds) that are not, in general, all congruent to each other.

(3) Of, pertaining to or characterized by straight lines.

(4) In, moving in, or characterized by a movement in a straight line or lines.

(5) In architecture, as the rectilinear style, the third historical division of English Gothic architecture.

1650–1660: From the post-Classical Latin, either from rectilīneāris or from rectilīneus (the source also of rectiline) + -ar, in either case the ultimate sources being rectus (straight) + līnea (line).  Rectus was from the primitive Indo-European root reg- (move in a straight line) with derivatives meaning "to direct in a straight line".  The suffix -ar is from the Latin from -ālis with dissimilation of “l” to “r” after roots containing an “l” thus āris and used to form adjectives (usually from a noun) to convey the sense of a relationship or “of; pertaining to”.  The English adjectival suffix –ar (of, near, or pertaining to) is widely appended, usually to nouns and is not restricted to those of Latin origin (the synonymous forms including -al, -an, -ary, -ese, -ic, -id, -ish, -like, -oid, -ory, -ous & -y).  Rectilinear came to be used in the sense of “a figure bounded by straight lines" by 1728, an evolution of the earlier meaning “straight lined”.  Rectilinear & rectilineal are adjectives, rectilinearity is a noun.

Curvilinear (pronounced kur-vuh-lin-ee-er)

(1) Consisting of or bounded by curved lines.

(2) Forming or moving in a curved line.

(3) Formed or characterized by curved lines.

(4) Of lines, having bends; curved.

(4) In mathematics, a set of coordinates determined by or determining a system of three orthogonal surfaces

1690s: From the Latin, derived from curvi (a combined form of the Latin curvus (crooked, bent, curved) + līneāris, from līnea (line).  The construct of līneāris was līnea (line) + -āris (the adjectival suffix).  The Latin curvus was ultimately from the primitive Indo-European sker & ker (to bend, curve, turn) + -wós (before it became associated with perfect stems, the suffixes -wós- & -us- had a more general function, forming athematic verb participles with the meaning "having x-en").  The earlier form was curvilineal, dating from the 1650s.  Curvilinear is an adjective, curvilinearity a noun and curvilinearly an adverb.

A juxtaposition of curvilinearity and rectilinearity: Lindsay Lohan, Vanity Fair shoot, October 2010.

In engineering, as in nature, matters of rectilinearity and curvilinearity tend to be products variously of inheritance, circumstance, economics or necessity.  In design however, sometimes fashion is allowed (indeed sometimes encouraged) to prevail over function and in automotive styling, the rectilinear (known in its most extreme form as knife-edge or razor-edge design) was a motif which came and went.  In the early days when things were truly little more than starkly functional, straight lines were dominant but the industry also inherited many of the traditions of the architecture of the horse-drawn carriage and embellishments could be quite curvaceous.  Line and curve co-existed in the inter-war years and as interest grew in streamlining to improve aerodynamics, the curves actually assumed a functional purpose.  At the same time, severity of line became itself a defined style, associated with formality and wealth, structurally because the straight lines tended to exaggerate size so the bigger cars appeared larger still and perhaps psychologically because they conveyed a message of casual disregard for something like streamlining, relying instead on power.  The big, bustle-backed limousines of the pre-war years were the exemplars.

Rolls-Royce Phantom IV (1950-1956 (left)), Triumph 1800-2000 Renown (1946-1954 (centre)) & Triumph Mayflower (1949-1953 (right)).

In the post war-years, in Europe and US, designers were attracted to the new.  In Europe that meant the avant-garde while across the Atlantic it could mean anything from restrained formalism to macropterous absurdity.  In England however, there was still a hankering for the familiar and among the coachbuilders (and Rolls-Royce which had begun building its own “standard” bodies) it was “business as usual” and, barely updated, the razor-edged lines returned.  Remarkably, as a niche, the style would be produced in tiny numbers until the 1990s even as modernity overtook the land.  So clearly, on a big scale it worked for the small, exclusive market at which it was targeted, a rolling denotation of wealth and power and this was what attracted others to apply the rectilinear lines on a smaller scale, at a lower price.  The leading proponents were Standard-Triumph which in 1946 released their middle-class 1800 as a kind of shrunken (though no less angular) Rolls-Royce or Bentley.  Generally, it was judged an aesthetic success although it quickly became dated and before long, the company was emulating American cars, their shrunken versions of those rather less pleasing.  The 1800 however maintained sufficient popularity to remain in production for eight years and that encouraged the idea the motif might translate well to something even smaller.  Hence in 1949, the Triumph Mayflower, small, stubby and wholly unsuited to a style which worked only at scale; the only thing more absurd than its existence was that the company designed it with the US market in mind.  The advertising agency suggested advertising it as “the watch charm Rolls-Royce” but whether that was vetoed by threats from Rolls-Royce or watch charm makers isn’t recorded.  A failure in every market in which it was offered (conspicuously so in the US), it was replaced by an anonymous-looking blob which might have designed by someone French in an unimaginative moment or an Italian on a bad day.

1967 Cadillac Eldorado (left), 1971 Fiat 130 Coupé (centre) and 1983 Volvo 760 GLE (right).

Until the oil shocks of the 1970s forced just about everyone to take aerodynamics seriously, the rectilineal would come and go as a fashion trend.  Cadillac’s 1967 Eldorado was an outstanding example and has aged better even than its curvier companion, the Oldsmobile Toroando of a year earlier but probably the high point of the modern razor-edge was Pininfarina’s Fiat 130 Coupé, its dimensions a stylistic sweet-spot which proved as suited to the saloon and shooting brake the designer world later exhibit; regrettably, neither reached production and the coupé proved a commercial failure, albeit one much admired.  That wasn’t something often said of one of Europe’s less successful straight-edged ventures, the 1982 Volvo 700 series.  Looking something like an earnest but uninspired student at a technical college might have submitted for assessment, Volvo at the time claimed it would remain timeless over the years to come while the rounded shapes around it soon became dated.  In that they were certainly wrong, the competition becoming more curvilinear still and soon Volvos nip-and-tuck specialists were finding ways to smooth the corners, not an easy task given the shape the patient was in and something really not possible until the re-skinned 900 was released in 1990.  The 700 had, by Volvo’s standards, a short life but it’s remembered for a bon mot from another designer who mused that it “…might be a good-looking car when they take it out of the packing-case”.

1953 Jaguar C-Type (XK120-C) continuation (left), 1957 Jaguar XKSS (centre) & 1961 Jaguar E-Type (XK-E) (1961).

Curves can be mere styling devices and in the 1960s General Motors (GM) actually created a motif they called cokebottle, summoning the idea of a Coca-Cola bottle on its side, itself evocative of the female form supine.  Plans to trademark the word were abandoned when the lawyers assured everyone using a lowercase “c” and claiming it to be a portmanteau word would fool neither the Coca-Cola company nor the judge.  Sometimes though, the curves were functional, Jaguar in 1950 shaping the aluminum skin on the XK120-C (C-Type) simply to be as low and aerodynamic as possible, the curves bulging only where necessary to provide coverage for the wheels and tyres.  On the subsequent D-Type (and the road-going derivative the XKSS), the impression was that the curves had become exaggerated, bulging more sensually still.  It’s not entirely an optical illusion but the shape is wholly functional, the designers actually lowering the centre, a revised mounting of a now dry-sumped engine permitting a lower bonnet (hood) line and thus a smaller frontal area.  The wheels and tyres remained much the same height so the curvature of the skin enveloping them is so much more obvious on a body otherwise lower.  The remarkably small frontal area did the job at Le Mans; the D-Type nearly 20 mph (32 km/h) faster than Ferrari's far more powerful 375.  By the time the E-Type was released in 1961, it could actually have been done with a little less curvature but we should all be grateful it looks as it does.

1960s original (left), 2022 modern (centre) & 2022 retro (right).

Objects like refrigerators offer designers a little more scope given that a low drag coefficient hardly matters although the modern, rectilinear versions presumably optimize space efficiency, offering the highest internal volume relative to external dimensions.  That said, there’s clearly still some demand for fridges which emulate the rounded style most associated with the 1950s and 1960s, several manufacturers with a retro line and they’re available in the pastel shades of the era.