The complexity of graphics hardware is currently undergoing a major change with the introduction of geometry engines on relatively inexpensive single chip ASICs which now contain the complete graphics rendering pipeline in full custom hardware. While the highest performance in measured in frames per second is the ultimate criteria for judging these chips, the focus is now starting to shift towards new features and different rendering techniques and pipelines. This dissertation introduces new hardware architectures for more realistic surface rendering of three dimensional objects and the rendering of volumetric datasets. Surface rendering is dealt with in the first part of the dissertation where the architectures for displacement map rendering in hardware are proposed. This work represents the first to appear in scientific literature on displacement map hardware rendering. Where possible these architectures propose components that integrate into currently available pipelines and make use of existing units in those pipelines.