Afew years ago I visited a building designed by Zaha Hadid, the renowned visionary architect. It was, at the time, only her second actual building, and a modest job at that -- a fire station on the grounds of a furniture factory in a small German town.

When the little building was completed, in 1994, the architect already had been famous in the profession for more than a decade. Ever since 1979, when the Baghdad-born Hadid opened an office in London after acquiring her professional degree at the Architectural Association in that city, she had been sending forth designs like commandments -- complex, incredibly sure-handed images of a universe of buildings that seemed to erupt with elegant, gravity-defying ease.

The designs were unconventional, unsettling and memorable. Widely published, they attracted acolytes and imitators worldwide. Yet, in the main, they did not get built.

Year by year Hadid found herself more eerily entrapped. Along with Frank Gehry, Daniel Libeskind, Rem Koolhaas and a few others, she was lionized on the A-list of the international avant-garde. Yet through most of the 1990s, while the others were winning large, prominent commissions, Hadid's designs kept getting sidetracked. It was as if the world -- or at least people with the power to build buildings -- had reached a consensus: Hadid's work was brilliant, yes, but unbuildable.

Such an impression was always totally unfair and partially inaccurate, but it was hard to contest without more concrete evidence than a firehouse and a small apartment building in Berlin. Finally, however, more real-world evidence is on the way, and we can get a superb preview starting today at the National Building Museum in "Zaha Hadid Laboratory," an exhibition of recent designs.

To anyone reasonably familiar with Hadid's published work, it is not surprising that the show is a testament to brilliance and buildability. The spectacular complexity and imaginative force of Hadid's graphics often masked the practicality at the core -- but it was there. You had to read the fine print, as it were, in the floor plans and cross sections. Sometimes, at book- or magazine-scale, this was hard to do.

One advantage of the exhibition format, then, is sheer size -- visitors can really get into the big drawings, paintings and model photographs on view in the ground-floor galleries. (There is fine print here, as well -- lots of words, if you are in a reading frame of mind.) Quantity is important, too. Several of the projects are thoroughly documented so that, in the end, you come out with a clear understanding of how things are put together.

Most crucial, however, is the show's currency. It focuses on 11 projects -- three newly completed, three under construction and five in some sort of development limbo (a familiar location to Hadid). So dies, happily, the legend of impracticality. And so vanishes Hadid's unfortunate record of marginal jobs. Two of the projects being built are of the career-making sort, world-class cultural commissions for contemporary arts centers in Cincinnati and Rome.

The exhibition begins with inclusive presentations of these two important projects, but in my mental reconstruction I start at the end, with Hadid's master plan for a science-centered urban complex in Singapore. Covering 194 hectares of land, this is the Asian city's aggressive attempt to stake out a leading position in 21st-century technology. The first major installment, we are told, will be "a hub for biomedical research and development."

Hadid's master plan is characteristically visual. I'm sure that somewhere there are thousands of pages of traffic projections, environmental studies and so forth. But here we are treated gloriously to a visual overview of a densely packed mid-rise city that rises and falls like an extension of the land. It is a poetic vision, though not wholly reassuring. God, as they say, is in the details.

In their scope and complexity, the Singapore plans demonstrate Hadid's disposition to think big. This is why, without equivocation, we can refer to her as a visionary. She conceives of her designs for individual buildings as parts of a larger whole, a better world, a liberating city of the future. Her intention, right from the beginning, was to reinvigorate modern architecture from within by shattering its by-then stodgy reliance on pure, right-angled forms. In so doing, she hoped both to recapture and reshape the dynamic, optimistic world view of the early modernists.

Come to think of it, this sophisticated utopianism may have caused some of Hadid's real-world difficulties. Call it postmodernism, cynicism, realism or whatever, ours is not a time that cuddles up to grand visions -- even generous ones. But there is no question that the larger view feeds Hadid's creativity, providing a philosophical and psychological context for an astonishing flow of formal ideas.

And now, as we see, her ideas are getting built. The projects range from the little to the big, the mundane to the extraordinary.

On the opposite end of the spectrum from the Singapore plan, for instance, is the parking lot and tram station Hadid designed for the outskirts of Strasbourg, France. It was a low-budget municipal deal, and Hadid approached it almost as a graphic artist -- every line in the macadam, every light pole, every support column was shaped and placed to project a lively pattern appropriate to such an interchange.

Movement -- of people, vehicles, clouds, rivers -- happens to be one of the chief inspirations for Hadid. It helps her define a building's relationship to its site and, often, helps to determine its form.

The connection can be straightforward, as in the building called Land Formation One, an exhibition-and-service hall for an annual garden festival in Weil am Rhein, Germany. (Curiously, this is the town where the firehouse is, but the hall wasn't there at the time of my visit.) Rising gently from the ground, the low, curving structure takes its very form from the pathways that traverse the site. It is a simple idea -- and how fresh! So, too, the dramatic form of the ski jump and tower cafe nearing completion in Innsbruck, Austria.

More complex is the unbuilt design for the BMW Central Building, a factory "brain center" that derives its sleek form and interior spaces from the comings and goings of a mass-production line. And then come really complex buildings such as the Center of Contemporary Art in Rome or the Rosenthal Center for Contemporary Arts in Cincinnati, both under construction.

These two projects are presented in lots of detail, and are worth every minute you can spend with them. They show the promise of Hadid's architecture in full force. One is horizontal, the other vertical, but both exemplify the architect's compulsion to create dynamic spaces and to move people through them in interesting ways.

In Rome, the long, low, building snakes through its site, never rising more than three stories high. An amazing complexity of spaces, however, has been slipped into the building frame, and they interrupt or penetrate one another in surprising ways. The Rome building is basically about the horizontal flow of movement -- the swooping stairwells are memorable even in blown-up model photographs.

In Cincinnati, by contrast, the movement is up and down through a rich assortment of spaces stacked atop one another in a prominent, if constricted, downtown site. Here, instead of stairways, there is a long ramp that zigs and zags from bottom to top, with a plethora of interesting views and stops along the way.

The Cincinnati center will be finished first -- by spring, they say. I've seen enough at the Building Museum to start making plans for the trip. I have, after all, already seen one building by Hadid, on the grounds of the Vitra factory in Weil am Rhein. Frank Gehry built an important building there. So did Japan's Tadao Ando. Hadid's firehouse matched them in aspiration, if not in size. It is small, but exciting.

Cincinnati, here I come.

Zaha Hadid Laboratory, organized by the Yale School of Architecture, remains on view through Nov. 17 at the National Building Museum, 401 F St. NW. Open Monday-Saturday 10 a.m.-5 p.m., and Sunday 11 a.m.-5 p.m. Free.

Zaha Hadid, top, draws inspiration from the setting, stacking spaces atop one another for Cincinnati's Rosenthal Center for Contemporary Arts, above, emphasizing motion at a France transit station, below, and molding building to landscape in Weil am Rhein, Germany, left.