Allowing for a seamless transition between two parallel lines through the construction of tangents, the Bezier curve enabled Minoru Yamasaki to design a building with a unified elevation strategy that promotes the simultaneous expression of the demands made by the different parts of the architecture.
Several of Yamasaki’s later architectural elevations feature curved lines of structure that follow a similar logic seen in the structural ribs in Gothic Architecture. While the gothic employed the arc to spatially divide bundled-ribbed columns and support tessellated grids of vaults above, Yamasaki employs the Bezier curve to bifurcate lines to achieve similar goals in the plane of the elevation. These transitions between curves and lines in the elevations of the World Trade Center create one cohesive system, unifying the discrete parts of the tower, while simultaneously allowing the system to adapt and perform various functional goals.
The design for the World Trade Center, featured a vertical expression of the structural exoskeleton on the outer four planes of the building, a design trait used in his earlier tower designs including One M&T Plaza in New York and the IBM Building in Seattle. The structural facades were designed to have a spacing that reflected the office-planning grid from the time of its construction. The column-free space maintains internal office flexibility, allowing for fenestration to be linked to this grid. All three of these projects, feature a structural transition above the base in order to create a ground level with fewer overall columns to ease movement in and out of the buildings.
Yamasaki's two earlier towers employed a secondary system of planar arcs, which was facilitated by a horizontal transfer beam that allowed the load to spread over fewer columns. By contrast in the World Trade Center, he employs a different strategy for the transition at the base of the towers. Vertical structural lines move down the Trade Center's facade and upon reaching the third floor, every other line transitions into a Bezier curve, joining with its neighbors to form bundles of three. These bundled columns create a spacing of 3 times that of the office-planning grid above, and the wider individual columns show that the structural flow lines have been re-routed but not eliminated. This patterned expression of the structural lines optically acts to unite the base of the elevation with the body of the tower, allowing the eye to seamlessly transcend the form from ground to the infinitum of sky without falter.
Yamasaki's creation of a facade system unified from top to bottom, marked a distinct departure from the then prevalent paradigm of skyscraper design as prescribed by the Chicago school, which emphasized the pronunciation of the classical order of the tower through the stacking of its discrete parts: the base, shaft and cap. The Bezier curve, as used in the World Trade Center, created a new paradigm of architecture in which a singular system could modulate and accommodate differing parameters for localized functions within a unified whole.