An Integer One-Pass Algorithm for Voxel Traversal

Voxel traversing along a line in a uniformly divided voxel space is frequently needed in different applications of computer graphics. The paper presents a new integer one‐pass algorithm for this problem. In 2D, the proposed approach is based on a modification of the well‐known Bresenham algorithm. The algorithm is then extended in 3D where a special case may occur. It is characterized by a simple discriminator. A derivation for this discriminator given in the paper confirms that all calculations can be realized using only integer arithmetic. In this way, the accumulation of rounding errors is completely eliminated, and a robust and compact implementation can be easily achieved. One of the main advantages of the proposed algorithm is that it visits 1–3 voxels during each iteration thus assuring its efficiency. The algorithm has been compared with other algorithms for voxel traversing by measuring spent CPU time. For comparison, Cleary & Wyvill's, Amanatides & Woo's, and Code‐based algorithm have been used. The proposed algorithm is faster than the referenced algorithms.     

Interactive Simulation of the Human Eye Depth of Field and Its Correction by Spectacle Lenses

This paper describes a fast rendering algorithm for verification of spectacle lens design. Our method simulates refraction corrections of astigmatism as well as myopia or presbyopia. Refraction and defocus are the main issues in the simulation. For refraction, our proposed method uses per-vertex basis ray tracing which warps the environment map and produces a real-time refracted image which is subjectively as good as ray tracing. Conventional defocus simulation was previously done by distribution ray tracing and a real-time solution was impossible. We introduce the concept of a blur field, which we use to displace every vertex according to its position. The blurring information is precomputed as a set of field values distributed to voxels which are formed by evenly subdividing the perspective projected space. The field values can be determined by tracing a wavefront from each voxel through the lens and the eye, and by evaluating the spread of light at the retina considering the best human accommodation effort. The blur field is stored as texture data and referred to by the vertex shader that displaces each vertex. With an interactive frame rate, blending the multiple rendering results produces a blurred image comparable to distribution ray tracing output.     

Time‐Adaptive Lines for the Interactive Visualization of Unsteady Flow Data Sets

The quest for the ideal flow visualization reveals two major challenges: interactivity and accuracy. Interactivity stands for explorative capabilities and real‐time control. Accuracy is a prerequisite for every professional visualization in order to provide a reliable base for analysis of a data set. Geometric flow visualization has a long tradition and comes in very different flavors. Among these, stream, path and streak lines are known to be very useful for both 2D and 3D flows. Despite their importance in practice, appropriate algorithms suited for contemporary hardware are rare. In particular, the adaptive construction of the different line types is not sufficiently studied. This study provides a profound representation and discussion of stream, path and streak lines. Two algorithms are proposed for efficiently and accurately generating these lines using modern graphics hardware. Each includes a scheme for adaptive time‐stepping. The adaptivity for stream and path lines is achieved through a new processing idea we call ‘selective transform feedback’. The adaptivity for streak lines combines adaptive time‐stepping and a geometric refinement of the curve itself. Our visualization is applied, among others, to a data set representing a simulated typhoon. The storage as a set of 3D textures requires special attention. Both algorithms explicitly support this storage, as well as the use of precomputed adaptivity information.     

Object-Space Visibility Ordering for Point-Based and Volume Rendering

This paper presents a method to accelerate algorithms that need a correct and complete visibility ordering of their data for rendering. The technique works by pre‐sorting primitives in object‐space using three lists (one for each axis: X, Y and Z), and then combining the lists using graphics hardware by rendering each list to a texture and merging the textures in the end. We validate our algorithm by applying it to the splatting technique using several types of rendering, including point‐based rendering and volume rendering. We also detail our hardware implementation for volume rendering using point sprites.     

Free Path Sampling in High Resolution Inhomogeneous Participating Media

This paper presents efficient algorithms for free path sampling in heterogeneous participating media defined either by high‐resolution voxel arrays or generated procedurally. The method is based on the concept of mixing ‘virtual’ material or particles to the medium, augmenting the extinction coefficient to a function for which the free path can be sampled in a straightforward way. The virtual material is selected such that it modifies the volume density but does not alter the radiance. We define the total extinction coefficient of the real and virtual particles by a low‐resolution grid of super‐voxels that are much larger than the real voxels defining the medium. The computational complexity of the proposed method depends just on the resolution of the super‐voxel grid and does not grow with the resolution above the scale of super‐voxels. The method is particularly efficient to render large, low‐density, heterogeneous volumes, which should otherwise be defined by enormously high resolution voxel grids and where the average free path length would cross many voxels.     

Investigative Visual Analysis of Global Terrorism

Recent increases in terrorist activity around the world have made analyzing and understanding such activities more critical than ever. With the help of organizations such as the National Center for the Study of Terrorism and Responses to Terrorism (START), we now have detailed historical information on each terrorist event around the world since 1970. However, due to the size and complexity of the data, identifying terrorists' patterns and trends has been difficult. To better enable investigators in understanding terrorist activities, we propose a visual analytical system that focuses on depicting one of the most fundamental concepts in investigative analysis, the five W's (who, what, where, when, and why). Views in our system are highly correlated, and each represents one of the W's. With this approach, an investigator can interactively explore terrorist activities efficiently and discover reasons of attacks (why) by identifying patterns temporally (when), geo‐spatially (where), between multiple terrorist groups (who), and across different methods or modes of attacks (what). By coupling a global perspective with the details gleaned from asking these five questions, the system allows analysts to think both tactically and strategically.     

On-the-fly Curve-skeleton Computation for 3D Shapes

The curve-skeleton of a 3D object is an abstract geometrical and topological representation of its 3D shape. It maps the spatial relation of geometrically meaningful parts to a graph structure. Each arc of this graph represents a part of the object with roughly constant diameter or thickness, and approximates its centerline. This makes the curve-skeleton suitable to describe and handle articulated objects such as characters for animation. We present an algorithm to extract such a skeleton on-the-fly, both from point clouds and polygonal meshes. The algorithm is based on a deformable model evolution that captures the object's volumetric shape. The deformable model involves multiple competing fronts which evolve inside the object in a coarse-to-fine manner. We first track these fronts' centers, and then merge and filter the resulting arcs to obtain a curve-skeleton of the object. The process inherits the robustness of the reconstruction technique, being able to cope with noisy input, intricate geometry and complex topology. It creates a natural segmentation of the object and computes a center curve for each segment while maintaining a full correspondence between the skeleton and the boundary of the object.     

Interpolatory and Mixed Loop Schemes

This paper presents a new interpolatory Loop scheme and an unified and mixed interpolatory and approximation subdivision scheme for triangular meshes. The former which is C¹ continuous as same as the modified Butterfly scheme has better effect in some complex models. The latter can be used to solve the “popping effect” problem when switching between meshes at different levels of resolution. The scheme generates surfaces coincident with the Loop subdivision scheme in the limit condition having the coefficient k equal 0. When k equal 1, it will be changed into a new interpolatory subdivision scheme. Eigen‐structure analysis demonstrates that subdivision surfaces generated using the new scheme are C¹ continuous. All these are achieved only by changing the value of a parameter k. The method is a completely simple one without constructing and solving equations. It can achieve local interpolation and solve the “popping effect” problem which are the method's advantages over the modified Butterfly scheme.     

Efficient and Dynamic Simplification of Line Drawings

In this paper we present a pipeline for rendering dynamic 2D/3D line drawings efficiently. Our main goal is to create efficient static renditions and coherent animations of line drawings in a setting where lines can be added, deleted and arbitrarily transformed on‐the‐fly. Such a dynamic setting enables us to handle interactively sketched 2D line data, as well as arbitrarily transformed 3D line data in a unified manner. We evaluate the proximity of screen projected strokes to simplify them while preserving their continuity. We achieve this by using a special data structure that facilitates efficient proximity calculations in a dynamic setting. This on‐the‐fly proximity evaluation also facilitates generation of appropriate visibility cues to mitigate depth ambiguities and visual clutter for 3D line data. As we perform all these operations using only line data, we can create line drawings from 3D models without any surface information. We demonstrate the effectiveness and applicability of our approach by showing several examples with initial line representations obtained from a variety of sources: 2D and 3D hand‐drawn sketches and 3D salient geometry lines obtained from 3D surface representations.     

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.     

Modeling a Generic Tone-mapping Operator

Although several new tone‐mapping operators are proposed each year, there is no reliable method to validate their performance or to tell how different they are from one another. In order to analyze and understand the behavior of tone‐mapping operators, we model their mechanisms by fitting a generic operator to an HDR image and its tone‐mapped LDR rendering. We demonstrate that the majority of both global and local tone‐mapping operators can be well approximated by computationally inexpensive image processing operations, such as a per‐pixel tone curve, a modulation transfer function and color saturation adjustment. The results produced by such a generic tone‐mapping algorithm are often visually indistinguishable from much more expensive algorithms, such as the bilateral filter. We show the usefulness of our generic tone‐mapper in backward‐compatible HDR image compression, the black‐box analysis of existing tone mapping algorithms and the synthesis of new algorithms that are combination of existing operators.     

Depth-of-Field Rendering by Pyramidal Image Processing

We present an image-based algorithm for interactive rendering depth-of-field effects in images with depth maps. While previously published methods for interactive depth-of-field rendering suffer from various rendering artifacts such as color bleeding and sharpened or darkened silhouettes, our algorithm achieves a significantly improved image quality by employing recently proposed GPU-based pyramid methods for image blurring and pixel disocclusion. Due to the same reason, our algorithm offers an interactive rendering performance on modern GPUs and is suitable for real-time rendering for small circles of confusion. We validate the image quality provided by our algorithm by side-by-side comparisons with results obtained by distributed ray tracing.     

Anti-Aliased Lines Using Run-Masks

In recent work, a set of line digitization algorithms based on the hierarchy of runs in the digital line has unified and generalized the iterative line‐drawing algorithms used in computer graphics. In this paper, the additional structural information generated by these algorithms is leveraged to describe a run‐based approach to draw anti‐aliased line segments in which anti‐aliased run‐masks are substituted for the individual run lengths as the line is being drawn. The run‐masks are precomputed using a prefiltering technique such that one or more run‐masks are defined for each of the one or two possible run lengths that occur in the line. The run‐masks can be defined for any order or level of the hierarchy of runs in the digital line and the technique is illustrated using runs of pixels. Comparing the use of run‐masks to applying the prefiltering technique for each pixel in the line, a line of similar visual quality can be produced more efficiently. We place no restrictions on the placement of the end points of the line, which may reside anywhere on the two‐dimensional plane.     

Floating Textures

We present a novel multi‐view, projective texture mapping technique. While previous multi‐view texturing approaches lead to blurring and ghosting artefacts if 3D geometry and/or camera calibration are imprecise, we propose a texturing algorithm that warps (“floats”) projected textures during run‐time to preserve crisp, detailed texture appearance. Our GPU implementation achieves interactive to real‐time frame rates. The method is very generally applicable and can be used in combination with many image‐based rendering methods or projective texturing applications. By using Floating Textures in conjunction with, e.g., visual hull rendering, light field rendering, or free‐viewpoint video, improved rendering results are obtained from fewer input images, less accurately calibrated cameras, and coarser 3D geometry proxies.     

Fast Extraction of High‐quality Crease Surfaces for Visual Analysis

We present a novel algorithm for the efficient extraction and visualization of high‐quality ridge and valley surfaces from numerical datasets. Despite their rapidly increasing popularity in visualization, these so‐called crease surfaces remain challenging to compute owing to their strongly nonlinear and non‐orientable nature, and their complex boundaries. In this context, existing meshing techniques require an extremely dense sampling that is computationally prohibitive. Our proposed solution intertwines sampling and meshing steps to yield an accurate approximation of the underlying surfaces while ensuring the geometric quality of the resulting mesh. Using the computation power of the GPU, we propose a fast, parallel method for sampling. Additionally, we present a new front propagation meshing strategy that leverages CPU multiprocessing. Results are shown for synthetic, medical and fluid dynamics datasets.     

Detecting Symmetries and Curvilinear Arrangements in Vector Art

Understanding symmetries and arrangements in existing content is the first step towards providing higher level content aware editing capabilities. Such capabilities may include edits that both preserve existing structure as well as synthesize entirely new structures based on the extracted pattern rules. In this paper we show how to detect regular symmetries and arrangement along curved segments in vector art. We determine individual elements in the art by using the transformation similarity for sequences of sample points on the input curves. Then we detect arrangements of those elements along an arbitrary curved path. We can un-warp the arrangement path to detect symmetries near the path. We introduce novel applications inform of editing elements that are arranged along a curved path. This includes their sliding along the path, changing of their spacing, or their scale. We also allow the user to brush the elements that the system recognized along new paths.     

Improved Stochastic Progressive Photon Mapping with Metropolis Sampling

This paper presents an improvement to the stochastic progressive photon mapping (SPPM), a method for robustly simulating complex global illumination with distributed ray tracing effects. Normally, similar to photon mapping and other particle tracing algorithms, SPPM would become inefficient when the photons are poorly distributed. An inordinate amount of photons are required to reduce the error caused by noise and bias to acceptable levels. In order to optimize the distribution of photons, we propose an extension of SPPM with a Metropolis‐Hastings algorithm, effectively exploiting local coherence among the light paths that contribute to the rendered image. A well‐designed scalar contribution function is introduced as our Metropolis sampling strategy, targeting at specific parts of image areas with large error to improve the efficiency of the radiance estimator. Experimental results demonstrate that the new Metropolis sampling based approach maintains the robustness of the standard SPPM method, while significantly improving the rendering efficiency for a wide range of scenes with complex lighting.     

Uncertainty‐Aware Exploration of Continuous Parameter Spaces Using Multivariate Prediction

Systems projecting a continuous n‐dimensional parameter space to a continuous m‐dimensional target space play an important role in science and engineering. If evaluating the system is expensive, however, an analysis is often limited to a small number of sample points. The main contribution of this paper is an interactive approach to enable a continuous analysis of a sampled parameter space with respect to multiple target values. We employ methods from statistical learning to predict results in real‐time at any user‐defined point and its neighborhood. In particular, we describe techniques to guide the user to potentially interesting parameter regions, and we visualize the inherent uncertainty of predictions in 2D scatterplots and parallel coordinates. An evaluation describes a real‐world scenario in the application context of car engine design and reports feedback of domain experts. The results indicate that our approach is suitable to accelerate a local sensitivity analysis of multiple target dimensions, and to determine a sufficient local sampling density for interesting parameter regions.     

Implicit Brushes for Stylized Line‐based Rendering

We introduce a new technique called Implicit Brushes to render animated 3D scenes with stylized lines in realtime with temporal coherence. An Implicit Brush is defined at a given pixel by the convolution of a brush footprint along a feature skeleton; the skeleton itself is obtained by locating surface features in the pixel neighborhood. Features are identified via image‐space fitting techniques that not only extract their location, but also their profile, which permits to distinguish between sharp and smooth features. Profile parameters are then mapped to stylistic parameters such as brush orientation, size or opacity to give rise to a wide range of line‐based styles.     

Efficient Parallel Vectors Feature Extraction from Higher‐Order Data

The parallel vectors (PV) operator is a feature extraction approach for defining line‐type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher‐order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher‐order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU‐based prototype. We apply our method to higher‐order data obtained from discontinuous Galerkin fluid simulations.