Abstract: We present a new, Eulerian-on-Lagrangian approach for modeling cloth. When a cloth modeled using the traditional Lagrangian approach is moved around an object with sharp corners, such as the edge of a table, the cloth cannot always bend smoothly around the object because it can bend only at its nodes. With our method, these constraints are built into the discretization of the cloth, giving us an equation of motion that directly honors these constraints. This allows the cloth to bend and move smoothly around such constraints. We show how our method can efficiently handle challenging simulations, such as pulling a table cloth from under wine glasses without knocking them over.