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A direct determination of the fractal dimensions of a fracture surface is essential for a better understanding of its complete topographic characteristics. In this paper, a laser profilometer is employed to measure the topography of a rock's fracture surface. With the use of the triangular prism surface area and projective covering methods, the resultant data set enables us to directly determine the fractal dimensions of a rock's fracture surface. Moreover, a new method, referred to as the cubic covering method, is proposed. The theoretical issues of fractal dimension estimation are also discussed.