An apparatus for rendering a two dimensional polygon image from volume data defining a volume and plane data defining a two dimensional plane which intersects the volume. The apparatus comprises a graphics processing unit (GPU). The apparatus is operable to generate triangle data comprising an indirect representation of each triangle of a set of candidate triangles. For a given plane/volume interaction a subset of the candidate triangles are valid triangles which are within the volume and on the given plane and the remaining triangles are invalid triangles. The GPU is operable to process the indirect representation of each triangle of the set of candidate triangles to output for a valid triangle for the defined plane a direct representation of the valid triangle and to output for an invalid triangle for the defined plane a direct representation of a degenerate triangle. The GPU is operable to reject each direct representation of a degenerate triangle from further processing. The GPU is also operable to process each direct representation of a valid triangle to form one or more triangle images which form the two dimensional polygon image.