Flow fields are usually visualized relative to a global observer, i.e., a single frame of reference. However, often no global frame can depict all flow features equally well. Likewise, objective criteria for detecting features such as vortices often use either a global reference frame, or compute a separate frame for each point in space and time. We propose the first general framework that enables choosing a smooth trade-off between these two extremes. Using global optimization to minimize specific differential geometric properties, we compute a time-dependent observer velocity field that describes the motion of a continuous field of observers adapted to the input flow. This requires developing the novel notion of an observed time derivative. While individual observers are restricted to rigid motions, overall we compute an approximate Killing field, corresponding to almost-rigid motion. This enables continuous transitions between different observers. Instead of focusing only on flow features, we furthermore develop a novel general notion of visualizing how all observers jointly perceive the input field. This in fact requires introducing the concept of an observation time, with respect to which a visualization is computed. We develop the corresponding notions of observed stream, path, streak, and time lines. For efficiency, these characteristic curves can be computed using standard approaches, by first transforming the input field accordingly. Finally, we prove that the input flow perceived by the observer field is objective. This makes derived flow features, such as vortices, objective as well.
Abstract-Direct volume rendering techniques map volumetric attributes (e.g., density, gradient magnitude, etc.) to visual styles. Commonly this mapping is specified by a transfer function. The specification of transfer functions is a complex task and requires expert knowledge about the underlying rendering technique. In the case of multiple volumetric attributes and multiple visual styles the specification of the multi-dimensional transfer function becomes more challenging and non-intuitive. We present a novel methodology for the specification of a mapping from several volumetric attributes to multiple illustrative visual styles. We introduce semantic layers that allow a domain expert to specify the mapping in the natural language of the domain. A semantic layer defines the mapping of volumetric attributes to one visual style. Volumetric attributes and visual styles are represented as fuzzy sets. The mapping is specified by rules that are evaluated with fuzzy logic arithmetics. The user specifies the fuzzy sets and the rules without special knowledge about the underlying rendering technique. Semantic layers allow for a linguistic specification of the mapping from attributes to visual styles replacing the traditional transfer function specification.
Fig. 1. Observer motion relative to the time evolution of features: Hurricane Isabel in a time-dependent global wind data set. (Bottom left) The actual path of Isabel (from NHC/Wikipedia). (Top left) Our observer field u automatically follows the motion of Isabel without explicit tracking of its path. The shown path is simply a path line of u. (Right) Feature-relative visualization, focused on Isabel in the center, enabling analysis of its time evolution "in place." The hurricane appears steady, with the Earth moving inversely underneath.
The computer graphics group at TU Vienna has created some of most beautiful and effective illustrative visualizations. In this article, they share with us their unique perspective on illustrative visualization. --- Kwan-Liu Ma
In this paper, we introduce a novel framework for the compositing of interactively rendered 3D layers tailored to the needs of scientific illustration. Currently, traditional scientific illustrations are produced in a series of composition stages, combining different pictorial elements using 2D digital layering. Our approach extends the layer metaphor into 3D without giving up the advantages of 2D methods. The new compositing approach allows for effects such as selective transparency, occlusion overrides, and soft depth buffering. Furthermore, we show how common manipulation techniques such as masking can be integrated into this concept. These tools behave just like in 2D, but their influence extends beyond a single viewpoint. Since the presented approach makes no assumptions about the underlying rendering algorithms, layers can be generated based on polygonal geometry, volumetric data, point-based representations, or others. Our implementation exploits current graphics hardware and permits real-time interaction and rendering.
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