The French painter Édouard Vuillard wanted to cast our lumbering, cloddish, here-to-stay selves in softer, more transient terms. He saw human identity as something fugitive, shrouded in secrecy and best perceived by glancing.

A sequence of silent, origami-like decisions fed into the construction of this 1895 painting. Modest it may be, but I think of it as a little miracle — an efflorescence, a soft explosion of intimacy on the walls of the National Gallery.

“Woman in a Striped Dress” is easier to read than many other Vuillard paintings, where figures are always bleeding into wallpaper and you’re never quite sure whether that softly glowing lamp is actually a face or that tablecloth a dress.

Here, as you can easily see, two women are arranging flowers in a room. Rooms, to state the obvious, are three-dimensional. So why does Vuillard make the picture so flat?

“Remember that a picture,” said the painter Maurice Denis, Vuillard’s contemporary, “before being a battle horse, a female nude or some sort of anecdote, is essentially a flat surface covered with colors assembled in a certain order.” I like to think of Vuillard permanently hesitating — in a state of ecstatic vacillation — between the two possibilities that inhere in representational art: making a thing in itself, or creating an illusion of something else.

Still, even in his quandary, Vuillard made a series of decisions. One was to lean, ever so gently, on one or two basic tricks of illusionism. For instance: The picture’s three human faces all have rudimentary amounts of light and shade to suggest the projection and recession of noses and eyes, and thus three-dimensional volume. And since these faces are smaller and larger, and since two of them overlap, our minds intuitively read their orientation in space. There is even an oblong box in the lower left corner, drawn in perspective to suggest receding space.

But everything else pushes up against the picture plane. And this flatness encourages our eyes to concentrate on the brush marks — Vuillard’s special “touch” — and the colors.

Apart from some slivers of bright primaries (red and turquoise in the flowers, yellow in the background figure’s dress), the composition is dominated by a rich russet, a demure gray-green and white. Vuillard decided to let all three hues operate as figure in some places and ground in others. By alternating their responsibilities — a method reminiscent of the under-and-over, warp-and-weft design of textiles — he created the picture’s compression, its surface tension.

But then there’s his touch. Even when Vuillard is painting stripes (and aren’t stripes always the best thing about any painting in which they appear?), he avoids long, consistent, evenly spaced lines, as if he doesn’t want anything too adamant. Elsewhere in the composition, he sets patches of saturated color beside soft depressions of the brush that let the paint spread unevenly, making them porous and open to interactions with the marks all around them.

The result of all this is that the painting breathes. When you consider how almost violently it crushes space, how claustrophobic it could have been, that’s amazing. Just as air moves through a well-arranged bouquet of flowers, air moves in and around Vuillard’s picture, carrying aromas of grace, serenity, silence and inner life.