An apparatus (100, 200) to generate control data for production of a three-dimensional object, the apparatus comprising: a halftone generator to apply a halftoning operation to received data defining a three-dimensional object, the halftone generator being arranged to process the received data defining the three-dimensional object in association with a three-dimensional threshold matrix to output discrete material formation instructions for at least one production material; and a matrix generator (120, 430) to generate the three-dimensional threshold matrix for use by the halftone generator, the apparatus characterized in that the matrix generator (120, 430) is arranged to: define a structural volume coverage representation (160, 350, 410) with reference to at least one volume element corresponding to the three-dimensional object, the structural volume coverage representation (160, 350, 410) comprising a structural volume coverage vector (340, 420) representing a proportional volumetric coverage of at least two different predefined structures available for the production of the three-dimensional object, the at least two different predefined structures being implemented using respective different predefined three-dimensional threshold matrices for halftoning; determine, for the at least one volume element, a convex combination of the at least two different predefined structures based on the structural volume coverage vector (340, 420); and assign a data value to at least one corresponding volume element of the three-dimensional threshold matrix based on the convex combination determined, wherein the at least one corresponding volume element of the three-dimensional threshold matrix is used by the halftone generator to apply a halftoning operation to a corresponding volume element of the three-dimensional object. a halftone generator to apply a halftoning operation to received data defining a three-dimensional object, the halftone generator being arranged to process the received data defining the three-dimensional object in association with a three-dimensional threshold matrix to output discrete material formation instructions for at least one production material; and a matrix generator (120, 430) to generate the three-dimensional threshold matrix for use by the halftone generator, the apparatus characterized in that the matrix generator (120, 430) is arranged to: define a structural volume coverage representation (160, 350, 410) with reference to at least one volume element corresponding to the three-dimensional object, the structural volume coverage representation (160, 350, 410) comprising a structural volume coverage vector (340, 420) representing a proportional volumetric coverage of at least two different predefined structures available for the production of the three-dimensional object, the at least two different predefined structures being implemented using respective different predefined three-dimensional threshold matrices for halftoning; determine, for the at least one volume element, a convex combination of the at least two different predefined structures based on the structural volume coverage vector (340, 420); and assign a data value to at least one corresponding volume element of the three-dimensional threshold matrix based on the convex combination determined, wherein the at least one corresponding volume element of the three-dimensional threshold matrix is used by the halftone generator to apply a halftoning operation to a corresponding volume element of the three-dimensional object. define a structural volume coverage representation (160, 350, 410) with reference to at least one volume element corresponding to the three-dimensional object, the structural volume coverage representation (160, 350, 410) comprising a structural volume coverage vector (340, 420) representing a proportional volumetric coverage of at least two different predefined structures available for the production of the three-dimensional object, the at least two different predefined structures being implemented using respective different predefined three-dimensional threshold matrices for halftoning; determine, for the at least one volume element, a convex combination of the at least two different predefined structures based on the structural volume coverage vector (340, 420); and assign a data value to at least one corresponding volume element of the three-dimensional threshold matrix based on the convex combination determined, wherein the at least one corresponding volume element of the three-dimensional threshold matrix is used by the halftone generator to apply a halftoning operation to a corresponding volume element of the three-dimensional object.