Openings constitute one of the fundamental operators in mathematical morphology. They can be applied to a wide range of applications, including noise reduction and feature extraction and enhancement. In this paper, we introduce a new, efficient and adaptable algorithm to compute one dimensional openings along discrete lines, in arbitrary orientation. The complexity of this algorithm is linear with respect to the number of pixels of the image. More interestingly, the average complexity per pixel is constant, with respect to the size of the opening.