  A flat sheet programmed with a planar pattern of spontaneous shape change
will morph into a curved surface. Such metric mechanics is seen in growing
biological sheets, and may be engineered in actuating soft matter sheets such
as phase-changing liquid crystal elastomers (LCEs), swelling gels and inflating
baromorphs. Here, we show how to combine multiple patterns in a sheet by
stitching regions of different shape changes together piecewise along
interfaces. This approach allows simple patterns to be used as building blocks,
and enables the design of multi-material or active/passive sheets. We give a
general condition for an interface to be geometrically compatible, and explore
its consequences for LCE/LCE, gel/gel, and active/passive interfaces. In
contraction/elongation systems such as LCEs, we find an infinite set of
compatible interfaces between any pair of patterns along which the metric is
discontinuous, and a finite number across which the metric is continuous. As an
example, we find all possible interfaces between pairs of LCE logarithmic
spiral patterns. In contrast, in isotropic systems such as swelling gels, only
a finite number of continuous interfaces are available, greatly limiting the
potential of stitching. In both continuous and discontinuous cases, we find the
stitched interfaces generically carry singular Gaussian curvature, leading to
intrinsically curved folds in the actuated surface. We give a general
expression for the distribution of this curvature, and a more specialized form
for interfaces in LCE patterns. The interfaces thus also have rich geometric
and mechanical properties in their own right.
