Computer-processed or computer-generated objects can be used to build holograms (10) whose images are close to or stradddle the hologram surface (10). No preliminary or first hologram is required. The hologram (10) is built up from a number of contiguous, small elemental pieces (12). Unorthodox views from inside the object (30) are required for the creation of these elements (12). One method of generating the views employs unique object manipulations. The computational transformations ensure that no singularities arise and that more or less conventional modeling and rendering routines can be used. With a second method, a multiplicity of conventional object views are collected. Then all pixels (22) in these conventional viewplanes (20) are reassigned to new and different locations in the new viewplanes (20) for the element views (22). These methods may be used to build rainbow holograms or full parallax holograms. When properly executed they are visually indistinguishable from other types.