A method and apparatus for generating geometric data are to be used in the building of an object using a layer-by-layer additive manufacturing process. The method includes providing object data defining the object, identifying from the object data one or more regions of a surface of the object to be supported during the additive manufacturing process and, for the or each region, identifying one or more supporting structures that will provide support for the region and generating an arrangement of supports within the region. A support location of each support of the arrangement relative to the other supports of the arrangement is derived from a location of the supporting structures.