Advection‐Based Function Matching on Surfaces

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non‐linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.     

An Interactive Design System of Free‐Formed Bamboo‐Copters

We present an interactive design system for designing free‐formed bamboo‐copters, where novices can easily design free‐formed, even asymmetric bamboo‐copters that successfully fly. The designed bamboo‐copters can be fabricated using digital fabrication equipment, such as a laser cutter. Our system provides two useful functions for facilitating this design activity. First, it visualizes a simulated flight trajectory of the current bamboo‐copter design, which is updated in real time during the user's editing. Second, it provides an optimization function that automatically tweaks the current bamboo‐copter design such that the spin quality—how stably it spins—and the flight quality—how high and long it flies—are enhanced. To enable these functions, we present non‐trivial extensions over existing techniques for designing free‐formed model airplanes [ UKSI14 ], including a wing discretization method tailored to free‐formed bamboo‐copters and an optimization scheme for achieving stable bamboo‐copters considering both spin and flight qualities.     

An Error Estimation Framework for Many‐Light Rendering

The popularity of many‐light rendering, which converts complex global illumination computations into a simple sum of the illumination from virtual point lights (VPLs), for predictive rendering has increased in recent years. A huge number of VPLs are usually required for predictive rendering at the cost of extensive computational time. While previous methods can achieve significant speedup by clustering VPLs, none of these previous methods can estimate the total errors due to clustering. This drawback imposes on users tedious trial and error processes to obtain rendered images with reliable accuracy. In this paper, we propose an error estimation framework for many‐light rendering. Our method transforms VPL clustering into stratified sampling combined with confidence intervals, which enables the user to estimate the error due to clustering without the costly computing required to sum the illumination from all the VPLs. Our estimation framework is capable of handling arbitrary BRDFs and is accelerated by using visibility caching, both of which make our method more practical. The experimental results demonstrate that our method can estimate the error much more accurately than the previous clustering method.     

Path‐space Motion Estimation and Decomposition for Robust Animation Filtering

Renderings of animation sequences with physics‐based Monte Carlo light transport simulations are exceedingly costly to generate frame‐by‐frame, yet much of this computation is highly redundant due to the strong coherence in space, time and among samples. A promising approach pursued in prior work entails subsampling the sequence in space, time, and number of samples, followed by image‐based spatio‐temporal upsampling and denoising. These methods can provide significant performance gains, though major issues remain: firstly, in a multiple scattering simulation, the final pixel color is the composite of many different light transport phenomena, and this conflicting information causes artifacts in image‐based methods. Secondly, motion vectors are needed to establish correspondence between the pixels in different frames, but it is unclear how to obtain them for most kinds of light paths (e.g. an object seen through a curved glass panel). To reduce these ambiguities, we propose a general decomposition framework, where the final pixel color is separated into components corresponding to disjoint subsets of the space of light paths. Each component is accompanied by motion vectors and other auxiliary features such as reflectance and surface normals. The motion vectors of specular paths are computed using a temporal extension of manifold exploration and the remaining components use a specialized variant of optical flow. Our experiments show that this decomposition leads to significant improvements in three image‐based applications: denoising, spatial upsampling, and temporal interpolation.     

4D video textures for interactive character appearance

4D Video Textures (4DVT) introduce a novel representation for rendering video‐realistic interactive character animation from a database of 4D actor performance captured in a multiple camera studio. 4D performance capture reconstructs dynamic shape and appearance over time but is limited to free‐viewpoint video replay of the same motion. Interactive animation from 4D performance capture has so far been limited to surface shape only. 4DVT is the final piece in the puzzle enabling video‐realistic interactive animation through two contributions: a layered view‐dependent texture map representation which supports efficient storage, transmission and rendering from multiple view video capture; and a rendering approach that combines multiple 4DVT sequences in a parametric motion space, maintaining video quality rendering of dynamic surface appearance whilst allowing high‐level interactive control of character motion and viewpoint. 4DVT is demonstrated for multiple characters and evaluated both quantitatively and through a user‐study which confirms that the visual quality of captured video is maintained. The 4DVT representation achieves >90% reduction in size and halves the rendering cost.     

IISPH‐FLIP for incompressible fluids

We propose to use Implicit Incompressible Smoothed Particle Hydrodynamics (IISPH) for pressure projection and boundary handling in Fluid‐Implicit‐Particle (FLIP) solvers for the simulation of incompressible fluids. This novel combination addresses two issues of existing SPH and FLIP solvers, namely mass preservation in FLIP and efficiency and memory consumption in SPH. First, the SPH component enables the simulation of incompressible fluids with perfect mass preservation. Second, the FLIP component efficiently enriches the SPH component with detail that is comparable to a standard SPH simulation with the same number of particles, while improving the performance by a factor of 7 and significantly reducing the memory consumption. We demonstrate that the proposed IISPH‐FLIP solver can simulate incompressible fluids with a quantifiable, imperceptible density deviation below 0.1%. We show large‐scale scenarios with up to 160 million particles that have been processed on a single desktop PC using only 15GB of memory. One‐ and two‐way coupled solids are illustrated.     

Automatic generation of tourist brochures

We present a novel framework for the automatic generation of tourist brochures that include routing instructions and additional information presented in the form of so‐called detail lenses. The first contribution of this paper is the automatic creation of layouts for the brochures. Our approach is based on the minimization of an energy function that combines multiple goals: positioning of the lenses as close as possible to the corresponding region shown in an overview map, keeping the number of lenses low, and an efficient numbering of the lenses. The second contribution is a route‐aware simplification of the graph of streets used for traveling between the points of interest (POIs). This is done by reducing the graph consisting of all shortest paths through the minimization of an energy function. The output is a subset of street segments that enable traveling between all the POIs without considerable detours, while at the same time guaranteeing a clutter‐free visualization.     

Hierarchical opacity optimization for sets of 3D line fields

The selection of meaningful lines for 3D line data visualization has been intensively researched in recent years. Most approaches focus on single line fields where one line passes through each domain point. This paper presents a selection approach for sets of line fields which is based on a global optimization of the opacity of candidate lines. For this, existing approaches for single line fields are modified such that significantly larger amounts of line representatives are handled. Furthermore, time coherence is addressed for animations, making this the first approach that solves the line selection problem for 3D time‐dependent flow. We apply our technique to visualize dense sets of pathlines, sets of magnetic field lines, and animated sets of pathlines, streaklines and masslines.     

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.     

4D MRI Flow Coupled to Physics‐Based Fluid Simulation for Blood‐Flow Visualization

Modern MRI measurements deliver volumetric and time‐varying blood‐flow data of unprecedented quality. Visual analysis of these data potentially leads to a better diagnosis and risk assessment of various cardiovascular diseases. Recent advances have improved the speed and quality of the imaging data considerably. Nevertheless, the data remains compromised by noise and a lack of spatiotemporal resolution. Besides imaging data, also numerical simulations are employed. These are based on mathematical models of specific features of physical reality. However, these models require realistic parameters and boundary conditions based on measurements. We propose to use data assimilation to bring measured data and physically‐based simulation together, and to harness the mutual benefits. The accuracy and noise robustness of the coupled approach is validated using an analytic flow field. Furthermore, we present a comparative visualization that conveys the differences between using conventional interpolation and our coupled approach.