Abstract: A method to image objects from local three-dimensional parallel beam tomographic data (line integrals) over lines parallel an arbitrary curve of directions on a sphere. Such data are used in electron microscopy, SPECT (with weighted integrals), and synchrotron tomography. The algorithm is adaptable to a number of data sets including single-axis and double-axis tilt electron tomography and truly three-dimensional curves of directions. The method stably gives pictures of the internal structure of objects and does not add strong singularities or artefacts. It is less influenced by objects outside the region of interest than standard non-local methods. The algorithm is combined with an electron microscope and computer to provide computer readable files showing the pictures of small objects such as molecules.