Z-buffer rendering of three-dimensional scenes is made more efficient through a method for occlusion culling by which occluded geometry is removed prior to rasterization. The method uses hierarchical z-buffering to reduce the quantity of image and depth information that needs to be accessed. A separate culling stage in the graphics pipeline culls occluded geometry and passes visible geometry on to a rendering stage. The culling stage maintains its own z-pyramid in which z-values are stored at low precision (e.g., in 8 bits). The efficiency of hierarchical z-buffering is improved through hierarchical evaluation of line and plane equations.