An apparatus and methods for generating geometric data for use in an additive manufacturing process. The apparatus includes a processing unit. The processing unit may be arranged for receiving data defining surface geometry of a plurality of objects to be built together in an additive manufacturing process, providing a user interface that allows a user to define a location of each object within a common build volume and carrying out a slicing operation on at least one of the objects located in the common build volume independently from another one of objects located in the common build volume. The slicing operation determines sections of the at least one object to be built in the additive manufacturing process. In one embodiment, the objects are defined in a hierarchical data structure. Supports for supporting the objects during the build may be defined with reference to a 2-dimensional support cross-section.