We develop a theoretical framework for the quasi-low-dimensional confinement-induced resonances (CIRs) of particles with the arbitrary three-dimensional two-body interactions, based on the HuangYang pseudopotential and the treatment of Feshbach resonances. Using this new approach, we analytically obtain some universal properties of dipolar CIRs in quasi-one-dimensional (1D) waveguides. We also show that the dipolar CIRs can be induced by tuning the angle between the dipole moments and the waveguide, which is experimentally observable in quasi-1D Cr and Dy atomic gases. We expect that these tilting angle induced CIRs will open up a new simpler way to control the resonant scatterings in quasi-low-dimensional systems. Introduction.-Recently, ultracold gases in quasi-lowdimensional (QLD) geometries have attracted much attention [1][2][3] as the reduced dimensionality leads to rich many-body physics, such as the one-dimensional (1D) Tonks-Girardeau gases [4,5] and the BerezinskiiKosterlitz-Thouless transitions in two-dimensional (2D) gases [6]. Remarkably, the tightly confining traps that define the QLD geometries offer an alternative means for tuning the effective two-body interactions via the confinement-induced resonances (CIRs) [7]. In terms of the Feshbach resonance, the modes of the confining potential provide the open and closed channels for the QLD systems, which are coupled by the two-body interactions. A CIR occurs when the bound state energy induced by the interactions in the closed channels matches the threshold energy of the open channel [8]. Over the past decade, significant progress has been made on the theoretical [8][9][10][11][12][13][14][15] and experimental [16][17][18] studies of the CIRs with isotropic interactions.