  We develop a non-perturbative theoretical framework to treat collisions with
generic anisotropic interactions in quasi-one-dimensional geometries. Our
method avoids the limitations of pseudopotential theory allowing to include
accurately long-range anisotropic interactions. Analyzing ultracold dipolar
collisions in a harmonic waveguide we predict dipolar confinement-induced
resonances (DCIRs) which are attributed to different angular momentum states.
The analytically derived resonance condition reveals in detail the interplay of
the confinement with the anisotropic nature of the dipole-dipole interactions.
The results are in excellent agreement with ab initio numerical calculations
confirming the robustness of the presented approach. The exact knowledge of the
positions of DCIRs may pave the way for the experimental realization e.g.
Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective
one-dimensional dipolar gases.
