Stream Surface Parametrization by Flow‐Orthogonal Front Lines

The generation of discrete stream surfaces is an important and challenging task in scientific visualization, which can be considered a particular instance of geometric modeling. The quality of numerically integrated stream surfaces depends on a number of parameters that can be controlled locally, such as time step or distance of adjacent vertices on the front line. In addition there is a parameter that cannot be controlled locally: stream surface meshes tend to show high quality, well‐shaped elements only if the current front line is “globally” approximately perpendicular to the flow direction. We analyze the impact of this geometric property and present a novel solution – a stream surface integrator that forces the front line to be perpendicular to the flow and that generates quad‐dominant meshes with well‐shaped and well‐aligned elements. It is based on the integration of a scaled version of the flow field, and requires repeated minimization of an error functional along the current front line. We show that this leads to computing the 1‐dimensional kernel of a bidiagonal matrix: a linear problem that can be solved efficiently. We compare our method with existing stream surface integrators and apply it to a number of synthetic and real world data sets.     

DTI in Context: Illustrating Brain Fiber Tracts In Situ

We present an interactive illustrative visualization method inspired by traditional pen‐and‐ink illustration styles. Specifically, we explore how to provide context around DTI fiber tracts in the form of surfaces of the brain, the skull, or other objects such as tumors. These contextual surfaces are derived from either segmentation data or generated using interactive iso‐surface extraction and are rendered with a flexible, slice‐based hatching technique, controlled with ambient occlusion. This technique allows us to produce a consistent and frame‐coherent appearance with precise control over the lines. In addition, we provide context through cutting planes onto which we render gray matter with stippling. Together, our methods not only facilitate the interactive exploration and illustration of brain fibers within their anatomical context but also allow us to produce high‐quality images for print reproduction. We provide evidence for the success of our approach with an informal evaluation with domain experts.     

A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.     

Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.     

GeoBrush: Interactive Mesh Geometry Cloning

We propose a method for interactive cloning of 3D surface geometry using a paintbrush interface, similar to the continuous cloning brush popular in image editing. Existing interactive mesh composition tools focus on atomic copy‐and‐paste of preselected feature areas, and are either limited to copying surface displacements, or require the solution of variational optimization problems, which is too expensive for an interactive brush interface. In contrast, our GeoBrush method supports real‐time continuous copying of arbitrary high‐resolution surface features between irregular meshes, including topological handles. We achieve this by first establishing a correspondence between the source and target geometries using a novel generalized discrete exponential map parameterization. Next we roughly align the source geometry with the target shape using Green Coordinates with automatically‐constructed cages. Finally, we compute an offset membrane to smoothly blend the pasted patch with C continuity before stitching it into the target. The offset membrane is a solution of a bi‐harmonic PDE, which is computed on the GPU in real time by exploiting the regular parametric domain. We demonstrate the effectiveness of GeoBrush with various editing scenarios, including detail enrichment and completion of scanned surfaces.     

A Survey of Surface‐Based Illustrative Rendering for Visualization

In this paper, we survey illustrative rendering techniques for 3D surface models. We first discuss the field of illustrative visualization in general and provide a new definition for this sub‐area of visualization. For the remainder of the survey, we then focus on surface‐based models. We start by briefly summarizing the differential geometry fundamental to many approaches and discuss additional general requirements for the underlying models and the methods' implementations. We then provide an overview of low‐level illustrative rendering techniques including sparse lines, stippling and hatching, and illustrative shading, connecting each of them to practical examples of visualization applications. We also mention evaluation approaches and list various application fields, before we close with a discussion of the state of the art and future work.     

Image‐Based Surface Compression

We present a generic framework for compression of densely sampled three‐dimensional (3D) surfaces in order to satisfy the increasing demand for storing large amounts of 3D content. We decompose a given surface into patches that are parameterized as elevation maps over planar domains and resampled on regular grids. The resulting shaped images are encoded using a state‐of‐the‐art wavelet image coder. We show that our method is not only applicable to mesh‐ and point‐based geometry, but also outperforms current surface encoders for both primitives.     

Scalable Multi‐view Registration for Multi‐Projector Displays on Vertically Extruded Surfaces

Recent work have shown that it is possible to register multiple projectors on non‐planar surfaces using a single uncalibrated camera instead of a calibrated stereo pair when dealing with a special class of non‐planar surfaces, vertically extruded surfaces. However, this requires the camera view to contain the entire display surface. This is often an impossible scenario for large displays, especially common in visualization, edutainment, training and simulation applications. In this paper we present a new method that can achieve an accurate geometric registration even when the field‐of‐view of the uncalibrated camera can cover only a part of the vertically extruded display at a time. We pan and tilt the camera from a single point and employ a multi‐view approach to register the projectors on the display. This allows the method to scale easily both in terms of camera resolution and display size. To the best of our knowledge, our method is the first to achieve a scalable multi‐view geometric registration of large vertically extruded displays with a single uncalibrated camera. This method can also handle a different situation of having multiple similarly oriented cameras in different locations, if the camera focal length is known.     

Sets of Globally Optimal Stream Surfaces for Flow Visualization

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.     

Hybrid mesh‐volume LoDs for all‐scale pre‐filtering of complex 3D assets

We address the problem of constructing appearance‐preserving level of details (LoDs) of complex 3D models such as trees. We propose a hybrid method that combines the strengths of mesh and volume representations. Our main idea is to separate macroscopic (i.e. larger than the target spatial resolution) and microscopic (sub‐resolution) surfaces at each scale and to treat them differently, because meshes are very efficient at representing macroscopic surfaces while sub‐resolution geometry benefits from volumetric approximations. We introduce a new algorithm that detects the macroscopic surfaces of a mesh for a given resolution. We simplify these surfaces with edge collapses and we provide a method for pre‐filtering their normal distributions and albedos. To approximate microscopic details, we use a heterogeneous microflake participating medium and we introduce a new artifact‐free voxelization algorithm that preserves local occlusion. Thanks to our macroscopic surface analysis, our algorithm is fully automatic and it generates seamless LoDs at arbitrarily coarse resolutions for a wide range of 3D models.     

Comparative Visualization of Molecular Surfaces Using Deformable Models

The comparison of molecular surface attributes is of interest for computer aided drug design and the analysis of biochemical simulations. Due to the non‐rigid nature of molecular surfaces, partial shape matching is feasible for mapping two surfaces onto each other. We present a novel technique to obtain a mapping relation between two surfaces using a deformable model approach. This relation is used for pair‐wise comparison of local surface attributes (e.g. electrostatic potential). We combine the difference value as well as the comparability as derived from the local matching quality in a 3D molecular visualization by mapping them to color. A 2D matrix shows the global dissimilarity in an overview of different data sets in an ensemble. We apply our visualizations to simulation results provided by collaborators from the field of biochemistry to evaluate the effectiveness of our results.     

Robust Segmentation of Multiple Intersecting Manifolds from Unoriented Noisy Point Clouds

We present a method for extracting complex manifolds with an arbitrary number of (self‐) intersections from unoriented point clouds containing large amounts of noise. Manifolds are formed in a three‐step process. First, small flat neighbourhoods of all possible orientations are created around all points. Next, neighbourhoods are assembled into larger quasi‐flat patches, whose overlaps give the global connectivity structure of the point cloud. Finally, curved manifolds are extracted from the patch connectivity graph via a multiple‐source flood fill. The manifolds can be reconstructed into meshed surfaces using standard existing surface reconstruction methods. We demonstrate the speed and robustness of our method on several point clouds, with applications in point cloud segmentation, denoising and medial surface reconstruction.     

Improving the Parameterization of Approximate Subdivision Surfaces

We provide a method for improving the parameterization of patching schemes that approximate Catmull‐Clark subdivision surfaces, such that the new parameterization conforms better to that of the original subdivision surface. We create this reparameterization in real‐time using a method that only depends on the topology of the surface and is independent of the surface's geometry. Our method can handle patches with more than one extraordinary vertex and avoids the combinatorial increase in both complexity and storage associated with multiple extraordinary vertices. Moreover, the reparameterization function is easy to implement and fast.     

Blue‐Noise Remeshing with Farthest Point Optimization

In this paper, we present a novel method for surface sampling and remeshing with good blue‐noise properties. Our approach is based on the farthest point optimization (FPO), a relaxation technique that generates high quality blue‐noise point sets in 2D. We propose two important generalizations of the original FPO framework: adaptive sampling and sampling on surfaces. A simple and efficient algorithm for accelerating the FPO framework is also proposed. Experimental results show that the generalized FPO generates point sets with excellent blue‐noise properties for adaptive and surface sampling. Furthermore, we demonstrate that our remeshing quality is superior to the current state‐of‐the?art approaches.     

Boundary Detection in Particle‐based Fluids

This paper presents a novel method to detect free‐surfaces on particle‐based volume representation. In contrast to most particle‐based free‐surface detection methods, which perform the surface identification based on physical and geometrical properties derived from the underlying fluid flow simulation, the proposed approach only demands the spatial location of the particles to properly recognize surface particles, avoiding even the use of kernels. Boundary particles are identified through a Hidden Point Removal (HPR) operator used for visibility test. Our method is very simple, fast, easy to implement and robust to changes in the distribution of particles, even when facing large deformation of the free‐surface. A set of comparisons against state‐of‐the‐art boundary detection methods show the effectiveness of our approach. The good performance of our method is also attested in the context of fluid flow simulation involving free‐surface, mainly when using level‐sets for rendering purposes.     

Illustrative Visualization of Mesoscale Ocean Eddies

Feature‐based time‐varying volume visualization is combined with illustrative visualization to tell the story of how mesoscale ocean eddies form in the Gulf Stream and transport heat and nutrients across the ocean basin. The internal structure of these three‐dimensional eddies and the kinematics with which they move are critical to a full understanding of ocean eddies. In this work, we apply a feature‐based method to track instances of ocean eddies through the time steps of a high‐resolution multi‐decadal regional ocean model and generate a series of eddy paths which reflect the life cycle of individual eddy instances. Based on the computed metadata, several important geometric and physical properties of eddy are computed. Illustrative visualization techniques, including visual effectiveness enhancement, focus+context, and smart visibility, are combined with the extracted volume features to explore eddy characteristics at different levels. An evaluation by domain experts indicates that combining our feature‐based techniques with illustrative visualization techniques provides an insight into the role eddies play in ocean circulation. The domain experts expressed a preference for our methods over existing tools.     

Local Painting and Deformation of Meshes on the GPU

We present a novel method to adaptively apply modifications to scene data stored in GPU memory. Such modifications may include interactive painting and sculpting operations in an authoring tool, or deformations resulting from collisions between scene objects detected by a physics engine. We only allocate GPU memory for the faces affected by these modifications to store fine‐scale colour or displacement values. This requires dynamic GPU memory management in order to assign and adaptively apply edits to individual faces at runtime. We present such a memory management technique based on a scan‐operation that is efficiently parallelizable. Since our approach runs entirely on the GPU, we avoid costly CPU–GPU memory transfer and eliminate typical bandwidth limitations. This minimizes runtime overhead to under a millisecond and makes our method ideally suited to many real‐time applications such as video games and interactive authoring tools. In addition, our algorithm significantly reduces storage requirements and allows for much higher resolution content compared to traditional global texturing approaches. Our technique can be applied to various mesh representations, including Catmull–Clark subdivision surfaces, as well as standard triangle and quad meshes. In this paper, we demonstrate several scenarios for these mesh types where our algorithm enables adaptive mesh refinement, local surface deformations and interactive on‐mesh painting and sculpting.     

Lazy Solid Texture Synthesis

Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.     

Continuous Self‐Collision Detection for Deformable Surfaces Interacting with Solid Models

In this paper, we propose a new continuous self‐collision detection (CSCD) method for a deformable surface that interacts with a simple solid model. The method is developed based on the radial‐view‐based culling method. Our method is suitable for the deformable surface that has large contact region with the solid model. The deformable surface may consist of small round‐shaped holes. At the pre‐processing stage, the holes of the deformable surface are filled with ghost triangles so as to make the mesh of the deformable surface watertight. An observer primitive (i.e. a point or a line segment) is computed so that it lies inside the solid model. At the runtime stage, the orientations of triangles with respect to the observer primitive are evaluated. The collision status of the deformable surface is then determined. We evaluated our method for several animations including virtual garments. Experimental results show that our method improves the process of CSCD.     

T‐SAH: Animation Optimized Bounding Volume Hierarchies

We propose a method for creating a bounding volume hierarchy (BVH) that is optimized for all frames of a given animated scene. The method is based on a novel extension of surface area heuristic to temporal domain (T‐SAH). We perform iterative BVH optimization using T‐SAH and create a single BVH accounting for scene geometry distribution at different frames of the animation. Having a single optimized BVH for the whole animation makes our method extremely easy to integrate to any application using BVHs, limiting the per‐frame overhead only to refitting the bounding volumes. We evaluated the T‐SAH optimized BVHs in the scope of real‐time GPU ray tracing. We demonstrate, that our method can handle even highly complex inputs with large deformations and significant topology changes. The results show, that in a vast majority of tested scenes our method provides significantly better run‐time performance than traditional SAH and also better performance than GPU based per‐frame BVH rebuild.