A novel technique for designing holographic optical elements that can perform general types of coordinate transformation is presented. The design is based on analytic ray-tracing techniques for finding the grating vector of the element, from which the holographic grating function is obtained as a solution of a Poissonlike equation. The grating function can be formed either as a computer-generated or as a computer-originated hologram. The design and realization procedure are illustrated for a specific holographic element that performs a logarithmic coordinate transformation on two-dimensional patterns.