Abstract: Relief mapping using the secant method offers an efficient method for adding per-pixel displacement based on height fields to an arbitrary polygonal mesh in real time. The technique utilizes an interval-based method in which bounds of the interval are computed in the beginning and are refined at every iteration until the intersection point is reached. The search space defined by the interval reduces and converges to the intersection point rapidly and outperforms the currently popular method based on binary search (relief mapping) used for performing this task. We compute the bounds using a simple ray-segment intersection method. We demonstrate the algorithm and show empirical and explicit evidence of the speed-up. Source code is available online.