DESIGN OF TRAM ALGORITHM BASED ON GRAPH TRANSFORMATION

Abstract

In this study, the TRAM (Trigonometric Reduction and Acceleration for Matrices) algorithm, based on small-angle approximation, table lookup, and matrix compression, is proposed to address the arithmetic bottleneck and real-time constraints of the ARM Cortex-M4 processor in laser graphics processing. The small-angle approximation replaces the generalized trigonometric function on floating point; the double-indexed table is designed to reduce the trigonometric function storage; and the matrix compression strategy is proposed to reduce the computational complexity. The experimental results show that the computation time of the algorithm for a single graphical transformation is significantly shorter than that of the traditional table lookup method and a single hardware acceleration strategy under a 240MHz main frequency. At the same time, the computation error is always kept lower than 0.035% so that the scanning system can realize a higher laser scanning frame rate to meet the real-time requirement of industrial laser dynamic projection and provide a reusable methodological framework for the real-time graphical processing of the resource-constrained embedded system. It provides a reusable methodological framework for real-time graphics processing in resource-constrained embedded systems, which is of great applied value.