This paper describes a computational framework for constructing point clouds using digital projection patterns. The basic principle behind the approach is to project known patterns on the object using a digital projector. A digital camera is then used to take images of the object with the known projection patterns imposed on it. Due to the presence of 3D faces of the object, the projection patterns appear distorted in the images. The images are analyzed to construct the 3D point cloud that is capable of introducing the observed distortions in the images. The approach described in this paper presents three advances over the previously developed approaches. First, it is capable of working with the projection patterns that have variable fringe widths and curved fringes and hence can provide improved accuracy. Second, our algorithm minimizes the number of images needed for creating the 3D point cloud. Finally, we use a hybrid approach that uses a combination of reference plane images and estimated system parameters to construct the point cloud. This approach provides good run-time computational performance and simplifies the system calibration.