This study introduces a novel and efficient least squares based method for rectangle fitting, using a continuous fitness function that approximates a unit square accurately. The proposed method is compared with the existing method in the literature using both simulated data and real data. The real data is derived from aerial photogrammetry point clouds of a rectangular building. The simulated tests show that the proposed method performs better than the reference method, reducing the root-mean-square error by about 93% and 14% for clean datasets and noisy point clouds, respectively. The proposed method also improves the fitting of the real dataset by about 81%, achieving centimetre level accuracy. Furthermore, the test results show that the proposed method converges in fewer than 10 iterations.

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