  Kirigami tessellations, regular planar patterns formed by cutting flat, thin
sheets, have attracted recent scientific interest for their rich geometries,
surprising material properties and promise for technologies. Here we pose and
solve the inverse problem of designing the number, size, and orientation of
cuts that allows us to convert a closed, compact regular kirigami tessellation
of the plane into a deployment that conforms approximately to any prescribed
target shape in two and three dimensions. We do this by first identifying the
constraints on the lengths and angles of generalized kirigami tessellations
which guarantee that their reconfigured face geometries can be contracted from
a non-trivial deployed shape to a novel planar cut pattern. We encode these
conditions in a flexible constrained optimization framework which allows us to
deform the geometry of periodic kirigami tesselations with three, four, and
sixfold symmetry, among others, into generalized kirigami patterns that deploy
to a wide variety of prescribed boundary target shapes. Physically fabricated
models verify our inverse design approach and allow us to determine the tunable
material response of the resulting structures. We then extend our framework to
create generalized kirigami patterns that deploy to approximate curved surfaces
in $\mathbb{R}^3$. Altogether, this work illustrates a novel framework for
designing complex, shape-changing sheets from simple cuts showing the power of
kirigami tessellations as flexible mechanical metamaterials.
