We analyze the dynamics of two-dimensional stationary, line-driven winds from accretion disks in cataclysmic variable stars. The driving force is that of line radiation pressure, in the formalism developed by Castor, Abbott, & Klein for O stars. Our main assumption is that wind helical streamlines lie on straight cones. We find that the Euler equation for the disk wind has two eigenvalues, the mass-loss rate and the flow-tilt angle with the disk. Both are calculated self-consistently. The wind is characterized by two distinct regions, an outer wind launched beyond four white dwarf radii from the rotation axis and an inner wind launched within this radius. The inner wind is very steep, up to 80° with the disk plane, while the outer wind has a typical tilt of 60°. In both cases, the wind cone dispersion is small because of a good alignment between the wind and the radiative flux vectors from the disk. We, therefore, provide an insight into the formation of the biconical geometry of disk winds as suggested by observations and kinematical modeling. The wind collimation angle appears to be robust and depends on the disk temperature stratification only. The flow critical points lie high above the disk for the inner wind but close to the disk photosphere for the outer wind. Comparison with existing kinematical and dynamical models is provided. Mass-loss rates from the disk as well as wind velocity laws are discussed in the second paper in this series.