Figure 1: Vector field contours of the electrostatic field around a benzene molecule from different view directions. Using our new technique allows to select those stream lines which have tangent direction and osculating plane perpendicular to the current view direction in the seeding point. We describe an approach to define contours of 3D vector fields and employ them as an interactive flow visualization tool. Although contours are well-defined and commonly used for surfaces and 3D scalar fields, they have no straightforward extension in vector fields. Our approach is to extract and visualize specific stream lines which show the most similar behavior to contours on surfaces. This way, the vector field contours are a particular set of isolated stream line segments that depend on the view direction and few additional parameters. We present an analysis of the usefulness of vector field contours by demonstrating their application to linear vector fields. In order to achieve interactive visualization, we develop an efficient GPU-based implementation for real-time extraction and rendering of vector field contours. We show the potential of our approach by applying it to a number of example data sets. Index Terms: I.3.3 [Computer Graphics]:,—Contours, Flow Visualization 1

Abstract—Conveying shape using feature lines is an important visualization tool in visual computing. The existing feature lines (e.g., ridges, valleys, silhouettes, suggestive contours, etc.) are solely determined by local geometry properties (e.g., normals and curvatures) as well as the view position. This paper is strongly inspired by the observation in human vision and perception that a sudden change in the luminance plays a critical role to faithfully represent and recover the 3D information. In particular, we adopt the edge detection techniques in image processing for 3D shape visualization and present Photic Extremum Lines (PELs) which emphasize significant variations of illumination over 3D surfaces. Comparing with the existing feature lines, PELs are more flexible and offer users more freedom to achieve desirable visualization effects. In addition, the user can easily control the shape visualization by changing the light position, the number of light sources, and choosing various light models. We compare PELs with the existing approaches and demonstrate that PEL is a flexible and effective tool to illustrate 3D surface and volume for visual computing. Index Terms—Surface and volume illustration, illumination, photic extremum lines (PELs), silhouettes, suggestive contours, ridges and valleys, digital geometry processing. 1

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Silhouettes play a crucial role in visualization, graphics and vision. This work focuses on the global behaviors and aspect graphs in computer vision. of silhouettes, especially their topological evolutions, such Silhouettes are one of the major research focuses in Nonas their splitting, merging, appearing and disappearing. The Photorealistic Rendering in graphics. For human visual per-dynamics of silhouettes are governed by the topology, the ception, silhouettes carry the most important shape infor-curvature of the surface, and the viewpoint. mation. Accurately and efficiently computing the silhouettes Some theoretical results are established: the integration has attracted many researchers. In order to improve the effi-of signed geodesic curvature along a silhouette is equal to ciency of computing silhouettes, it is highly desirable to in-the view cone angle; critical events can only happen when terpolate silhouettes from pre-computed ones when the view the view point is on the aspect surfaces (ruled surface of the is moved between sampled views. If the topological struc-asymptotic lines of parabolic points). tures of the pre-computed silhouettes are consistent, the in-We introduce a method to visualize the evolution of silterpolation is sensible and easy to perform. Therefore, it is houettes, especially all the critical events where the topolo- critical to fully understand the topological evolutions of silgies of the silhouettes change. The results have broad aphouettes when the view point is moved in space. plications in computer vision for recognition, graphics for The major goal of this work is to study when, where, rendering and visualization. and how the topologies of the silhouettes will change, along