This paper presents a novel optimization-based method for non-line-of-sight (NLOS) imaging that aims to reconstruct hidden scenes under general setups with significantly reduced reconstruction time. In NLOS imaging, the visible surfaces of the target objects are notably sparse. To mitigate unnecessary computations arising from empty regions, we design our method to render the transients through partial propagations from a continuously sampled set of points from the hidden space. Our method is capable of accurately and efficiently modeling the view-dependent reflectance using surface normals, which enables us to obtain surface geometry as well as albedo. In this pipeline, we propose a novel domain reduction strategy to eliminate superfluous computations in empty regions. During the optimization process, our domain reduction procedure periodically prunes the empty regions from our sampling domain in a coarse-to-fine manner, leading to substantial improvement in efficiency. We demonstrate the effectiveness of our method in various NLOS scenarios with sparse scanning patterns. Experiments conducted on both synthetic and real-world data clearly support the efficacy and efficiency of the proposed method in general NLOS scenarios.