1. A method for producing an image with nuclear magnetic resonance employing a k-space trajectory proceeding on an irregular grid, comprising the steps of: obtaining magnetic resonance signals while a magnetic gradient field is activated, said magnetic gradient field having a gradient with a direction; modifying the direction of the gradient of the gradient field while obtaining said magnetic resonance signals, thereby producing a k-space trajectory proceeding on an irregular grid; sampling said magnetic resonance signals with a variable sampling rate to obtain samples, and digitizing said samples; entering said samples into k-space along said k-space trajectory and varying said sampling rate so that an occupation density of k-space with said samples is substantially uniform; producing samples on a rectangular grid in k-space by interpolating the samples entered into k-space along said k-space trajectory proceeding on an irregular grid; Fourier transforming said samples on said rectangular grid in k-space to generate image data; and generating a displayable image from said image data.