A method for rendering a three dimensional graphic object in a two dimensional display space by segmenting the object into parallelepipeds and decomposing the parallelepipeds into rods of voxels that are parallel to the depth axis (Z) of the display and by projecting the rods of voxels onto the X-Y plane of the display as lines of pixels and a method for drawing antialiased volumetric images. An apparatus for implementing both methods includes an interpolator, having a set-up unit and an iterator unit, and a blender. The set-up unit determines various parameters of the image to be drawn, including the total number of voxels to be blended together into each pixel to be drawn, and selects a pixel pair adjacent to and straddling an idealized line representing a line to be drawn. The iterator unit determines the coverages of the pixel pair based on parameters output by the set-up unit. The blender determines the color intensity values of the pixel pair as a function of the coverages, and the opacity of voxels in the voxel rod corresponding to each pixel, and writes the color values into a memory that drives the display. The memory is split into at least four banks so that color values of the pair of pixel can be simultaneously stored in different memory banks. A method for resolving accumulation error in the derivation of each pixel's position and a method for accommodating for the effect of additional intersected pixels may be used in connection with the above-described methods.