Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-imaging. They are robust to flow and motion, have diffuse aliasing patterns, and support short readouts and echo times. One drawback is that standard implementations do not support anisotropic field-of-view (FOV) shapes, which are used to match the imaging parameters to the object or region-of-interest. A set of fast, simple algorithms for 2-D and 3-D PR, and 3-D cones acquisitions are introduced that match the sampling density in frequency space to the desired FOV shape. Tailoring the acquisitions allows for reduction of aliasing artifacts in undersampled applications or scan time reductions without introducing aliasing in fully-sampled applications. It also makes possible new radial imaging applications that were previously unsuitable, such as imaging elongated regions or thin slabs. 2-D PR longitudinal leg images and thin-slab, single breath-hold 3-D PR abdomen images, both with isotropic resolution, demonstrate these new possibilities. No scan time to volume efficiency is lost by using anisotropic FOVs. The acquisition trajectories can be computed on a scan by scan basis.