This paper introduces a novel haptic rendering technique devised to perceptualize a “haptic edge” correctly with respect to its stiffness and height models. Our previous study showed that the traditional penalty-based haptic rendering methods are not adequate to the collocated data of surface topography and stiffness since surface topography perceived by the user can be distorted from its model. In order to overcome the problem, we have developed a topography compensation algorithm based on the theory of force constancy which states that the user maintains a constant contact force when s/he strokes a surface to feel its topography. To the best of our knowledge, our technique is the first of its kind that explicitly considers the effect of user exploratory patterns in haptic rendering. Computationally, the algorithm is adaptive and efficient, not requiring any preprocessing of original data. We also demonstrate the performance and robustness of the proposed algorithm through a psychophysical experiment.