A pair of exhibitions at the Metropolitan Museum of Art, “Frank Stella: Painting into Architecture” and “Frank Stella on the Roof,” function as a crash course for newcomers to the protean and prolific artist’s career, and bring the rest of us up to date on his ruminations on the builder’s art. Mr. Stella has said that many of his large-scale projects are not “architecture,” which for him implies habitability. This places him at a remove from other painters-turned-architects, such as Steven Holl and Peter Wheelwright. Mr. Stella designs for the “abstract joy of the space itself.”

His structures’ uses are sometimes mysterious. “The Ship” (2007), for example, is represented at the Met by both a tiny model and a full-scale section in charcoalgray fiberglass that nearly reaches the ceiling of the museum’s Kimmelman Gallery, dominating the space. Its open latticework of beams forms an irregular, enlarged basket-weave resulting in hexagonal and much smaller triangular openings. Extrapolated from the pattern of veins in a leaf, this permeable non-wall, formed here into a cage-like flattened pod and suspended off the ground on pillars, constitutes the outer surface of a number of Mr. Stella’s projects. The stepped walkway that curls around and through the model suggests that “The Ship” may be a clubhouse, a folly, or an enormous lawn ornament, but it’s no more “architecture” than a bus-stop shelter or a telephone booth. It’s how inside segues into outside that makes this work interesting — how Mr. Stella protracts the threshold between the two.

The “Guest House” (2007) looks to be quite livable — for a weekend, anyway. The gaps in the lattice are outfitted with windows, a scheme that would afford not much privacy, but lots of light. The brand-new model even shows where the furniture could go, a refreshingly specific touch. This fascinating project is a considerable advance over Mr. Stella’s clunky 1990 model for a rooftop addition the Groninger Museum in the Netherlands, which is little more than a leaf-shaped canopy set atop the existing structure.

Splayed, spiraling bands characterize the other major direction Mr. Stella has taken in the ordering of space. This motif was inspired by an expandable, foamrubber beach hat in which, by means of a swirling pattern of almost-parallel, curved cuts, a flat plane balloons to a head-enclosing volume. In a variety of materials, Mr. Stella riffs on this dome-like element; the visitor enters the plywood-and-pine model, 12 feet tall, of “The Broken Jug” (2007), which recalls the sinuous lines of Hector Guimard. The artist’s baroque impulses get the better of him in the model, in cast stainless steel, for the “Chapel of the Holy Ghost” (1992) where the twisting ribbons look a bit like Venetian blinds mangled by a stiff wind.

Providing context are shaped paintings from the 1960s and ’70s, such as “Sunapee II” (1966) and “Jarmalince III” (1973), notable for their inexorable physical presence as much as for their flat-footed subdivision of the picture plane into units that wed surface to edge. The freestanding fiberglass mural “Severinda” (1995) is a mess, 30 feet of pictorial bad road. Not particularly architectural, it forms a zigzag where it meets the floor, and a meandering curve at its top edge, some 10 feet up.

More relevant is “The Dart (D-15)1X” (1990), a rollicking, 6-foothigh relief. In black-and-white enamel on undulating, ribbonlike aluminum, it is as close as we get to the frankly, frantically decorative works of the ’80s. With its deft blend of actual and implied overlapping planes, “The Dart” bridges the gap between the pictorial and architectonic in Mr. Stella’s oeuvre, and is among the last works the viewer encounters in this show.

Meanwhile, three large sculptures and two more models luxuriate in the Cantor Roof Garden. Of them, “admanjoe” (2004) and “memantra” (2005) were seen two years ago at Paul Kasmin Gallery, where more of Mr. Stella’s work will go on display May 11. They are made of enormous, corkscrewing stainless steel tubing outfitted with sail-like slabs of blackish carbon fiber. Outdoors, their visual aggressiveness is considerably tamed; the pair seem playful. At the press preview Monday morning, Mr. Stella demonstrated that “admanjoe” can be moved around the circular rail, about 15 feet in diameter, on which it rests. Ideally, the work would be installed at ground level, the track sunken inconspicuously into the earth.

Nearby is “Chinese Pavilion,” a work in progress. The portion seen here is roughly 30 feet across and 15 feet high, in carbon epoxy composite, and follows the openweave pod design of “The Ship” on a smaller scale. It is similarly supported by three widely-spaced columns. The underside is about 4 feet off the ground; it will be a tough job keeping children from scampering under and into it. The jazzy interchange of sun and shadow that pools beneath it underscores the work’s resemblance to the interlocking puzzle-like shapes of the Basque sculptor Eduardo Chillida.

To date, none of Mr. Stella’s architectural projects has been realized. “The Broken Jug” received some attention a few years ago, when it appeared that it would be installed in downtown Miami and do service as a bandshell. Fabricated in aluminum, the 33-foot-tall structure sits in storage in a shipyard in Cherbourg, France, its fate uncertain. Here’s hoping that these exhibitions will provide the needed interest and momentum to give it a home — out in public.

Until October 28 (1000 Fifth Ave. at 82nd Street, 212-535-7710).