The question of what are good views of a 3D object has been addressed by numerous researchers in perception, computer vision, and computer graphics. This has led to a large variety of measures for the goodness of views as well as some special-case viewpoint selection algorithms. In this article, we leverage the results of a large user study to optimize the parameters of a general model for viewpoint goodness, such that the fitted model can predict people's preferred views for a broad range of objects. Our model is represented as a combination of attributes known to be important for view selection, such as projected model area and silhouette length. Moreover, this framework can easily incorporate new attributes in the future, based on the data from our existing study. We demonstrate our combined goodness measure in a number of applications, such as automatically selecting a good set of representative views, optimizing camera orbits to pass through good views and avoid bad views, and trackball controls that gently guide the viewer towards better views.

To create collections, like music playlists from personal media libraries, users today typically do one of two things. They either manually select items one-by-one, which can be time consuming, or they use an example-based recommendation system to automatically generate a collection. While such automatic engines are convenient, they offer the user limited control over how items are selected. Based on prior research and our own observations of existing practices, we propose a semi-automatic interface for creating collections that combines automatic suggestions with manual refinement tools. Our system includes a keyword query interface for specifying high-level collection preferences (e.g., "some rock, no Madonna, lots of U2,") as well as three example-based collection refinement techniques: 1) a suggestion widget for adding new items in-place in the context of the collection; 2) a mechanism for exploring alternatives for one or more collection items; and 3) a two-pane linked interface that helps users browse their libraries based on any selected collection item. We demonstrate our approach with two applications. SongSelect helps users create music playlists, and PhotoSelect helps users select photos for sharing. Initial user feedback is positive and confirms the need for semi-automated tools that give users control over automatically created collections.

The nascent field of discrete differential geometry deals with discrete geometric objects (such as polygons) which act as analogues to continuous geometric objects (such as curves). The discrete objects can be measured (length, area) and can interact with other discrete objects (collision/response). From a computational standpoint, the discrete objects are attractive, because they have been designed from the ground up with data-structures and algorithms in mind. From a mathematical standpoint, they present a great challenge: the discrete objects should have properties which are analogues of the properties of continuous objects. One important property of curves and surfaces is their curvature, which plays a significant role in many application areas (see, e.g., Chapters 4 and 5). In the continuous domain there are remarkable theorems dealing with curvature; a key requirement for a discrete curve with discrete curvature is that it satisfies analogous theorems. In this chapter we examine the curvature of continuous and discrete curves on the plane.