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Recently, SIMD processors have become popular architectures for multimedia. Though most of the 3D graphics pipeline can be implemented on such SIMD platforms in a straightforward manner, polygon clipping tends to cause clumsy and expensive interruptions to the SIMD pipeline. This paper describes a way to increase the efficiency of SIMD clipping without sacrificing the efficient flow of a SIMD graphics pipeline. In order to fully utilize the parallel execution units, we have developed two methods to avoid serialization of the execution stream: Deferred clipping postpones polygon clipping and uses hardware assistance to buffer polygons that need to be clipped. SIMD Clipping partitions the actual polygon clipping procedure between the SIMD engine and a conventional RISC processor. To increase the efficiency of SIMD clipping, we introduce the concepts of clip-plane pairs and edge batching. Clip-plane pairs allow clipping a polygon against two clip planes without introducing corner vertices. Edge batching reduces the communication and control overhead for starting of clipping on the SIMD engine.