  We present the general method of constructing curved traversable wormholes in
(3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal
force metric without cross-terms. The (3+1)-d solution is compared with the
recently studied lower-dimensional counterpart, where we identify that the much
richer physics - involving pressures and shear forces of the mass-energy fluid
supporting the former - is attributed to the mixing of all three spatial
coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial
terms appear. An explicit example, the static zero tidal force (3+1)-d catenary
wormhole is analysed and we show the existence of a geodesic through it
supported locally by non-exotic matter, similar to the (2+1)-d version. A key
difference is that positive mass-energy is used to support the entire (3+1)-d
catenary wormhole, though violation of the null energy condition in certain
regions is inevitable. This general approach of first constructing the geometry
of the spacetime and then using the field equations to determine the physics to
support it has the potential to discover new solutions in general relativity or
to generalise existing ones. For instance, the metric of a time-evolving
inflationary wormhole with a conformal factor can actually be geometrically
constructed using our method.
