Judith Heintz, a landscape architect, designed that spot some 15 years ago, when the museum last expanded, adding the Rose Center for Earth and Science to the north, and the Weston Pavilion, which Gilder will replace, at 79th Street. One neighborhood group, Defenders of Teddy Roosevelt Park, offered on its website a model of the current museum, with an ominous red line where the still-sight-unseen center would supposedly devour the allée.

Well, now we know more or less what the actual project looks like. It bids to be the city’s next architectural spectacle.

The museum’s trustees approved a conceptual design on Wednesday and released drawings and renderings. The project promises much more room for education, exhibitions, laboratories, the library, open storage and a live butterfly conservatory. It includes a new theater devoted to invisible worlds — meaning microscopic creatures, the human brain, the ocean depths and the edge of the universe. The proposed center also solves humdrum but critical layout problems, integrating dead-end galleries and bringing public spaces, classrooms and research together in a single, soaring, canyonlike, central hall, behind an undulating stone-and-glass facade.

That’s the big move. With reinforced-concrete arches and balconies shaped like immense rocky outcroppings or glacial formations, the hall vies with the Theodore Roosevelt Rotunda, the museum’s towering entrance on the opposite side of the campus. It’s part Dr. Seuss, part Jurassic Park, part parametric extravaganza, adding a kind of naturalism to abstract, airborne forms associated with contemporary architecture at its most theatrical.