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Real time rendering of three-dimensional scenes in Ray Tracing is a hard problem. However, parallel implementations have been enabling real time performance, as the algorithm can be highly parallelized. Thus, a custom parallel design in hardware is likely to achieve a good performance. In this paper, we further improve the GridRT architecture overall performance by embedding the ray-triangle intersection computation into the precessing elements that form the architecture. Low cost and high rendering performance are the main concerns in this novel design. The results show that the execution time of each intersection computation is reduced by at least 50%, while the area cost is practically unchanged or even reduced when compared to the original GridRT implementation.