Methods and apparatus for three-dimensional fabrication by tomographic back projections

A method for producing a three-dimensional object comprising computing a sequence of back-projections describing the three-dimensional object to be formed from different orientation angles of said object, defining a sequence of patterns of light using said back-projections, and irradiating with each of said patterns of light at the respective corresponding orientation angle and according to the defined sequence a photoresponsive material that is capable of alteration of its material phase upon irradiation by light, thereby creating a three-dimensional distribution of alterations within the photoresponsive medium which physically reproduces said three- dimensional object, thereby creating the three-dimensional object.