A small number of filmmakers achieve such singularity of style, theme, or personality that they establish their own category. We speak of the Bressonian, Hitchcockian, Altmanesque. No time soon will the name Robert Beavers enter common currency in this manner, but if any living filmmaker has offered a superior definition of moving image clarity and precision, I’ve never see it. Sample the complete retrospective of his work currently in progress at the Whitney Museum and you’ll find yourself evaluating much else by its measure.

Mr. Beavers makes strict, lucid, intensely focused poems out of light and sound. Such work is habitually labeled “avant-garde” and relegated to specialized cinemas, film festival sidebars, academic venues, or the galleries of the art world. That’s one reason these enthralling films remain so little known. Another stems from Mr. Beavers’s former reluctance to screen them in America, a result of his uncompromising control over every aspect of their creation and exhibition. It’s a long story spanning many decades, much geography, and a great deal of idiosyncrasy.

In 1964, at the age of 16, Mr. Beavers left his native Massachusetts for New York City. His enthusiasm for film drew him to the Film Maker’s Cinematheque and into the company of Gregory Markopoulos, one of the major figures of the avant-garde scene. Encouraged by the elder artist (who also became his lover), Mr. Beavers began to make films. Due to a set of frustrations and aspirations too complex to summarize here, America proved inhospitable to the filmmakers. Shortly after completing his first film, Mr. Beavers left for Brussels, then Greece. Markopoulos soon joined him, and from that point onward, they would live, work, and exhibit exclusively abroad.

Until his death in 1992 Markopoulos endeavored to realize the “Temenos,” a project that entailed the laborious shaping of his lifework into a monumental 80-hour cycle known as “Eniaios,” together with a related archive and site-specific screening area in a remote Greek village. Mr. Beavers has since carried on the effort to establish the Temenos, while relaxing the (Markopoulos-enforced?) resistance to an American reputation.

In the past decade, a fresh look at Markopoulos’s films of the 1960s has reestablished his stature as a key figure of the American avant-garde, but the real news has been the simultaneous revelation of Mr. Beavers’s own extraordinary, and perhaps superior achievement.

The Whitney’s presentation of “My Hand Outstretched: Films by Robert Beavers” takes its name from the overarching title Mr. Beavers has given to a cycle of films made from 1967-2002: My Hand Outstretched to the Winged Distance and Sightless Measure.” Most of the individual works have been recently completed into their final form, and several have never before been shown in this country.

Excluded by Mr. Beavers from the larger film cycle, “Early Monthly Segments” takes the form of a film diary or journal. Fragments of daily life with Markopoulos in Europe and Greece are joined to nature studies, lyric interludes, and experiments with mattes, filters, and gels that crop the image, create frames within frames, or pattern zones of color. The first-person address is disciplined by rigorous discipline and an almost geometric conception of form. Mr. Beavers wields his camera-stylo at hard, right angles; we’re worlds away from Bakhage-style gestural expressionism.

“Early Monthly Segments” is a rich depository of juvenilia, sections of which the filmmaker would later incorporate into “official” early works like “The Count of Days,” “Palinode,” and “Diminished Frame.” These films refine the methodology of his initial diaristic mode, which comes to its apotheosis in “From the Notebook of …”

Inspired by Leonardo da Vinci, Paul Valery, and a sojourn in Florence, Mr. Beavers illuminates the working of his own mind and its extension through the technologies of camera, eye, and hand. “From the Notebook of …” perfects the use of mattes as a means of cutting within the frame to all manner of ingenious effects. The technique here centers on a hinge-like movement of black matte quickly manipulated to uncover or hide a dizzying array of images. Mr. Beavers rhymes the device with the flapping of a bird wing, the opening of shutters, and the turning of pages.

Another motif has the young filmmaker seated before his desk in a darkened room, moving his head back and forth through a bar of light falling through the window. “From the Notebook of …” puts the experiment in experimental: It is an endeavor, an essay, a research, a reaching out, a sophisticated kind of studio art, sublime autobiography. This is Mr. Beavers’s ars poetica, the clearest statement of his essential theme: the discipline of his own mind. It would be the first of his masterpieces. He was 23 years old.

We might term this cinema “experimental,” but “avant-garde” isn’t quite right. Mr. Beavers is an extremely classical, conservative artist. He is drawn to the high culture of Europe (Renaissance architecture and painting, 19th-century literature) and the enduring values – formal, ethical, and erotic – of the ancient world.

“Still Light,” his magnificent portrait of a handsome youth bathed in limpid color fields, is what you might get if Anacreon worked with 16mm. “The Painting” weaves details of a 15th-century triptych into an orderly Swiss intersection, spray of shattered glass, and cloud of dust particles. “Work Done” contemplates the binding of a Latin text with luxurious materials and meticulous craftsmanship. A reading of “The Stones of Venice” inspired a long film called “Ruskin.”

If there is connoisseurship, dandyism, and even a tinge of the aristocratic to Mr. Beavers’s work, there is also melancholy, sincerity, and a powerful emotional undertow to his images that can leave you in tears. “Sotiros” arrays its sounds and images around a mysterious hurt – existential, perhaps, or romantic. You enter the film rapt by the thrilling leaps of montage and luminescent textures, and exit gently whelmed by sadness and introspection.

The art of Mr. Beavers has clear stylistic affinities with the synedochic films of Robert Bresson. Less apparent is their communion as the supreme poets of isolation in the cinema. “The Stoas” commences as a brown-beige study in haunted urban space: the back alley of some anonymous metropolis, its rusted metal infrastructure and cardboard detritus. Partway in, sunlit green washes over the frame, as the setting shifts to a lush mountain stream. Splendors of light, leaf, and running water dazzle the eye, while an ancient stone bridge reiterates Mr. Beavers’s pull toward the past and his penchant for half-circle shapes.

Interspersed throughout is an emblematic image: a pair of hands lit up in the foreground of utter darkness. They make a gesture of movement, one over the other, and a sign of measure, empty space held between. Whatever else it says, “The Stoas,” is a hushed testament to the adventure of consciousness, the eternal drama of perception, selection, patience, and skill.

Mind can be comic too, and “Amor” is wonderfully witty in its juxtaposition of hedges, scaffolding, and the making of a custom suit. Mr. Beavers gets one of his smartest effects from the switch between a pair of clapping hands and the slice of scissors through fabric. There’s no more perfect quarter hour of film in existence. Add Robert Beavers to the pantheon. This is an epochal event.

Until October 30 (945 Madison Avenue at 75th Street, 800-WHITNEY).