In flow visualization, integral surfaces rapidly tend to expand, fold and produce vast amounts of occlusion. While silhouette enhancements and local transparency mappings proved useful for semi‐transparent depictions, they still introduce visual clutter when surfaces grow more complex. An effective visualization of the flow requires a balance between the presentation of interesting surface parts and the avoidance of occlusions that hinder the view. In this paper, we extend the concept of opacity optimization to surfaces to obtain a global approach to the occlusion problem. Starting with a partition of the surfaces into patches, we compute per‐patch opacity as minimizer of a bounded‐variable least‐squares problem. For the final rendering, opacity is interpolated on the surfaces. The resulting visualization technique is interactive, frame‐coherent, view‐dependent and driven by domain knowledge.

In this article, we study the regularization of quadratic energies that are integrated over discrete domains. This is a fairly general setting, often found in, but not limited to, geometry processing. The standard Tikhonov regularization is widely used such that, for instance, a low-pass filter enforces smoothness of the solution. This approach, however, is independent of the energy and the concrete problem, which leads to artifacts in various applications. Instead, we propose a regularization that enforces a low variation of the energy and is problem specific by construction. Essentially, this approach corresponds to minimization with respect to a different norm. Our construction is generic and can be plugged into any quadratic energy minimization, is simple to implement, and has no significant runtime overhead. We demonstrate this for a number of typical problems and discuss the expected benefits.

Stream surfaces are a well‐studied and widely used tool for the visualization of 3D flow fields. Usually, stream surface seeding is carried out manually in time‐consuming trial and error procedures. Only recently automatic selection methods were proposed. Local methods support the selection of a set of stream surfaces, but, contrary to global selection methods, they evaluate only the quality of the seeding lines but not the quality of the whole stream surfaces. Global methods, on the other hand, only support the selection of a single optimal stream surface until now. However, for certain flow fields a single stream surface is not sufficient to represent all flow features. In our work, we overcome this limitation by introducing a global selection technique for a set of stream surfaces. All selected surfaces optimize global stream surface quality measures and are guaranteed to be mutually distant, such that they can convey different flow features. Our approach is an efficient extension of the most recent global selection method for single stream surfaces. We illustrate its effectiveness on a number of analytical and simulated flow fields and analyze the quality of the results in a user study.

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