A point data set is a set of independent point samples that are typically acquired from a D scanning process. We are interested in detecting and rendering silhouettes in such data set, for the purpose of Non-Photorealistic Rendering (NPR). Traditionally, work on silhouette extraction and rendering tends to assume a polygonal mesh input, where connectivity information is available and the formation of silhouettes involves tracking of edges. A point data set, however, does not contain connectivity information. In a previous paper (38), we presented the first hybrid image/object-space method to directly detect and render silhouettes for point data set. In this paper, we describe the essence of the method in more detail, emphasizing on the mathematics applied. We describe as well a simple variant of the method to detect silhouette points using ray casting instead of point splatting. This variant is useful in the absence of dedicated graphics hardware.