A computer-implemented system for synthesizing a fixture layout for a part to be manufactured, comprising: a potential configuration comprising a plurality of locations on the boundary of the part against which to contact a plurality of fixture elements configured to be affixed to a base plate; a determination module to determine a collision free region about each of the locations comprising basis vectors representing an access direction, thickness and width, and collision free distances along each of the basis vectors; a part definition module to define a part envelope comprising a geometric representation of a region defined about the boundary of the part said region being formed by the sweep of the part along a set up direction along which the part may be loaded and unloaded from the fixture layout; a part identification module to identify a distance that each of the fixture elements needs to translate along the access direction to avoid interference with the part envelope in order to provide interference free loading and unloading of the part from the fixture layout; a catalog comprising a multiplicity of fixture elements specific to a manufacturing facility and configurable to fixture the part; a filter module (i) to filter each candidate fixture element listed in the catalog that would not allow interference free loading and unloading of the part based on the distance identified by the part identification module, (ii) to filter each candidate fixture element listed in the catalog that does not fit within the collision free region, and (iii) to remove from further consideration the filtered candidate fixture elements; a transformation computation module to compute, for each of the candidate fixture elements listed in the catalog and not filtered, a transformation between the part and the base plate, and to align the part with the base plate by the transformation; and an elimination module to eliminate both the candidate fixture elements that are listed in the catalog and not filtered and attachment points of those candidate filter elements to the base plate, which are situated where that fixture element would overlap with another of the remaining fixture elements, the candidate fixture elements and their attachment points remaining after overlap elimination comprising a fixture layout. a potential configuration comprising a plurality of locations on the boundary of the part against which to contact a plurality of fixture elements configured to be affixed to a base plate; a determination module to determine a collision free region about each of the locations comprising basis vectors representing an access direction, thickness and width, and collision free distances along each of the basis vectors; a part definition module to define a part envelope comprising a geometric representation of a region defined about the boundary of the part said region being formed by the sweep of the part along a set up direction along which the part may be loaded and unloaded from the fixture layout; a part identification module to identify a distance that each of the fixture elements needs to translate along the access direction to avoid interference with the part envelope in order to provide interference free loading and unloading of the part from the fixture layout; a catalog comprising a multiplicity of fixture elements specific to a manufacturing facility and configurable to fixture the part; a filter module (i) to filter each candidate fixture element listed in the catalog that would not allow interference free loading and unloading of the part based on the distance identified by the part identification module, (ii) to filter each candidate fixture element listed in the catalog that does not fit within the collision free region, and (iii) to remove from further consideration the filtered candidate fixture elements; a transformation computation module to compute, for each of the candidate fixture elements listed in the catalog and not filtered, a transformation between the part and the base plate, and to align the part with the base plate by the transformation; and an elimination module to eliminate both the candidate fixture elements that are listed in the catalog and not filtered and attachment points of those candidate filter elements to the base plate, which are situated where that fixture element would overlap with another of the remaining fixture elements, the candidate fixture elements and their attachment points remaining after overlap elimination comprising a fixture layout.