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This paper presents the design and performance of a new parallel graphics renderer for 3D images. This renderer is based on an adaptive supersampling approach that works for time/space-efficient execution on two classes of parallel computers. Our rendering scheme takes subpixel supersamples only along polygon edges. This leads to a significant reduction in rendering time and in buffer memory requirements. Furthermore, we offer a balanced rasterization of all transformed polygons. Experimental results prove these advantages on both a shared-memory SGI multiprocessor server and a Unix cluster of Sun workstations. We reveal performance effects of the new rendering scheme on subpixel resolution, polygon number, scene complexity, and memory requirements. The balanced parallel renderer demonstrates scalable performance with respect to increase in graphic complexity and in machine size. Our parallel renderer outperforms Crow's scheme in benchmark experiments performed. The improvements are made in three fronts: 1) reduction in rendering time, 2) higher efficiency with balanced workload, and 3) adaptive to available buffer memory size. The balanced renderer can be more cost-effectively embedded within many 3D graphics algorithms, such as those for edge smoothing and 3D visualization. Our parallel renderer is MPI-coded, offering high portability and cross-platform performance. These advantages can greatly improve the QoS in 3D imaging and in real-time interactive graphics.