Designing Quad‐dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.     

Reconstructing Animated Meshes from Time‐Varying Point Clouds

In this paper, we describe a novel approach for the reconstruction of animated meshes from a series of time‐deforming point clouds. Given a set of unordered point clouds that have been captured by a fast 3‐D scanner, our algorithm is able to compute coherent meshes which approximate the input data at arbitrary time instances. Our method is based on the computation of an implicit function in ?⁴ that approximates the time‐space surface of the time‐varying point cloud. We then use the four‐dimensional implicit function to reconstruct a polygonal model for the first time‐step. By sliding this template mesh along the time‐space surface in an as‐rigid‐as‐possible manner, we obtain reconstructions for further time‐steps which have the same connectivity as the previously extracted mesh while recovering rigid motion exactly. The resulting animated meshes allow accurate motion tracking of arbitrary points and are well suited for animation compression. We demonstrate the qualities of the proposed method by applying it to several data sets acquired by real‐time 3‐D scanners.     

Implicit Hierarchical Quad‐Dominant Meshes

We present a method for producing quad‐dominant subdivided meshes, which supports both adaptive refinement and adaptive coarsening. A hierarchical structure is stored implicitly in a standard half‐edge data structure, while allowing us to efficiently navigate through the different level of subdivision. Subdivided meshes contain a majority of quad elements and a moderate amount of triangles and pentagons in the regions of transition across different levels of detail. Topological LOD editing is controlled with local conforming operators, which support both mesh refinement and mesh coarsening. We show two possible applications of this method: we define an adaptive subdivision surface scheme that is topologically and geometrically consistent with the Catmull–Clark subdivision; and we present a remeshing method that produces semi‐regular adaptive meshes.     

Exact and Robust (Self‐)Intersections for Polygonal Meshes

We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and self‐intersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate mesh‐based front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness (= correctness) and robustness (= completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a plane‐based BSP‐representation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.     

Non‐Oriented MLS Gradient Fields

We introduce a new approach for defining continuous non‐oriented gradient fields from discrete inputs, a fundamental stage for a variety of computer graphics applications such as surface or curve reconstruction, and image stylization. Our approach builds on a moving least square formalism that computes higher‐order local approximations of non‐oriented input gradients. In particular, we show that our novel isotropic linear approximation outperforms its lower‐order alternative: surface or image structures are much better preserved, and instabilities are significantly reduced. Thanks to its ease of implementation (on both CPU and GPU) and small performance overhead, we believe our approach will find a widespread use in graphics applications, as demonstrated by the variety of our results.     

An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

A perceptual study of four tensor glyphs for symmetric, real, traceless tensors was performed. Each glyph encodes three properties of the system: Orientation, uniaxiality (alignment along the direction of orientation), and biaxiality (alignment along a vector orthogonal to the orientation). Thirty users over two studies were asked to identify these three properties for each glyph type under a variety of permutations in order to evaluate the effectiveness of visually communicating the properties; response time was also measured. We discuss the significant differences found between the methods as guidance to the use of these glyphs for traceless tensor visualization.     

Practical Real‐Time Lens‐Flare Rendering

We present a practical real‐time approach for rendering lens‐flare effects. While previous work employed costly ray tracing or complex polynomial expressions, we present a coarser, but also significantly faster solution. Our method is based on a first‐order approximation of the ray transfer in an optical system, which allows us to derive a matrix that maps lens flare‐producing light rays directly to the sensor. The resulting approach is easy to implement and produces physically‐plausible images at high framerates on standard off‐the‐shelf graphics hardware.     

Fast Parallel Construction of Smooth Surfaces from Meshes with Tri/Quad/Pent Facets

Polyhedral meshes consisting of triangles, quads, and pentagons and polar configurations cover all major sampling and modeling scenarios. We give an algorithm for efficient local, parallel conversion of such meshes to an everywhere smooth surface consisting of low‐degree polynomial pieces. Quadrilateral facets with 4‐valent vertices are ‘regular’ and are mapped to bi‐cubic patches so that adjacent bi‐cubics join C² as for cubic tensor‐product splines. The algorithm can be implemented in the vertex and geometry shaders of the GPU pipeline and does not use the fragment shader. Its implementation in DirectX 10 achieves conversion plus rendering at 659 frames per second with 42.5 million triangles per second on input of a model of 1300 facets of which 60% are not regular.     

Two‐Colored Pixels

In this paper we show how to use two‐colored pixels as a generic tool for image processing. We apply two‐colored pixels as a basic operator as well as a supporting data structure for several image processing applications. Traditionally, images are represented by a regular grid of square pixels with one constant color each. In the two‐colored pixel representation, we reduce the image resolution and replace blocks of N × N pixels by one square that is split by a (feature) line into two regions with constant colors. We show how the conversion of standard mono‐colored pixel images into two‐colored pixel images can be computed efficiently by applying a hierarchical algorithm along with a CUDA‐based implementation. Two‐colored pixels overcome some of the limitations that classical pixel representations have, and their feature lines provide minimal geometric information about the underlying image region that can be effectively exploited for a number of applications. We show how to use two‐colored pixels as an interactive brush tool, achieving realtime performance for image abstraction and non‐photorealistic filtering. Additionally, we propose a realtime solution for image retargeting, defined as a linear minimization problem on a regular or even adaptive two‐colored pixel image. The concept of two‐colored pixels can be easily extended to a video volume, and we demonstrate this for the example of video retargeting.     

Motion based Painterly Rendering

Previous painterly rendering techniques normally use image gradients for deciding stroke orientations. Image gradients are good for expressing object shapes, but difficult to express the flow or movements of objects. In real painting, the use of brush strokes corresponding to the actual movement of objects allows viewers to recognize objects' motion better and thus to have an impression of the dynamic. In this paper, we propose a novel painterly rendering algorithm to express dynamic objects based on their motion information. We first extract motion information (magnitude, direction, standard deviation) of a scene from a set of consecutive image sequences from the same view. Then the motion directions are used for determining stroke orientations in the regions with significant motions, and image gradients determine stroke orientations where little motion is observed. Our algorithm is useful for realistically and dynamically representing moving objects. We have applied our algorithm for rendering landscapes. We could segment a scene into dynamic and static regions, and express the actual movement of dynamic objects using motion based strokes.     

Illustrative Parallel Coordinates

Illustrative parallel coordinates (IPC) is a suite of artistic rendering techniques for augmenting and improving parallel coordinate (PC) visualizations. IPC techniques can be used to convey a large amount of information about a multidimensional dataset in a small area of the screen through the following approaches: (a) edge‐bundling through splines; (b) visualization of “branched ” clusters to reveal the distribution of the data; (c) opacity‐based hints to show cluster density; (d) opacity and shading effects to illustrate local line density on the parallel axes; and (e) silhouettes, shadows and halos to help the eye distinguish between overlapping clusters. Thus, the primary goal of this work is to convey as much information as possible in a manner that is aesthetically pleasing and easy to understand for non‐experts.     

Real‐Time Depth‐of‐Field Rendering Using Point Splatting on Per‐Pixel Layers

We present a real‐time method for rendering a depth‐of‐field effect based on the per‐pixel layered splatting where source pixels are scattered on one of the three layers of a destination pixel. In addition, the missing information behind foreground objects is filled with an additional image of the areas occluded by nearer objects. The method creates high‐quality depth‐of‐field results even in the presence of partial occlusion, without major artifacts often present in the previous real‐time methods. The method can also be applied to simulating defocused highlights. The entire framework is accelerated by GPU, enabling real‐time post‐processing for both off‐line and interactive applications.     

Per‐Vertex Defocus Blur for Stochastic Rasterization

We present user‐controllable and plausible defocus blur for a stochastic rasterizer. We modify circle of confusion coefficients per vertex to express more general defocus blur, and show how the method can be applied to limit the foreground blur, extend the in‐focus range, simulate tilt‐shift photography, and specify per‐object defocus blur. Furthermore, with two simplifying assumptions, we show that existing triangle coverage tests and tile culling tests can be used with very modest modifications. Our solution is temporally stable and handles simultaneous motion blur and depth of field.     

Crack‐free rendering of dynamically tesselated B‐rep models

We propose a versatile pipeline to render B‐Rep models interactively, precisely and without rendering‐related artifacts such as cracks. Our rendering method is based on dynamic surface evaluation using both tesselation and ray‐casting, and direct GPU surface trimming. An initial rendering of the scene is performed using dynamic tesselation. The algorithm we propose reliably detects then fills up cracks in the rendered image. Crack detection works in image space, using depth information, while crack‐filling is either achieved in image space using a simple classification process, or performed in object space through selective ray‐casting. The crack filling method can be dynamically changed at runtime. Our image space crack filling approach has a limited runtime cost and enables high quality, real‐time navigation. Our higher quality, object space approach results in a rendering of similar quality than full‐scene ray‐casting, but is 2 to 6 times faster, can be used during navigation and provides accurate, reliable rendering. Integration of our work with existing tesselation‐based rendering engines is straightforward.     

Structure‐Aware Mesh Decimation

We present a novel approach for the decimation of triangle surface meshes. Our algorithm takes as input a triangle surface mesh and a set of planar proxies detected in a pre‐processing analysis step, and structured via an adjacency graph. It then performs greedy mesh decimation through a series of edge collapse, designed to approximate the local mesh geometry as well as the geometry and structure of proxies. Such structure‐preserving approach is well suited to planar abstraction, i.e. extreme decimation approximating well the planar parts while filtering out the others. Our experiments on a variety of inputs illustrate the potential of our approach in terms of improved accuracy and preservation of structure.     

Adaptive Cross‐sections of Anatomical Models

Medical illustrations have been used for a long time for teaching and communicating information for diagnosis or surgery planning. Illustrative visualization systems create methods and tools that adapt traditional illustration techniques to enhance the result of renderings. Clipping the volume is a popular operation in volume rendering for inspecting the inner parts, though it may remove some information of the context that is worth preserving. In this paper we present a new editing technique based on the use of clipping planes, direct structure extrusion, and illustrative methods, which preserves the context by adapting the extruded region to the structures of interest of the volumetric model. We will show that users may interactively modify the clipping plane and edit the structures to highlight, in order to easily create the desired result. Our approach works with segmented volume models and non‐segmented ones. In the last case, a local segmentation is performed on‐the‐fly. We will demonstrate the efficiency and utility of our method.     

Shape‐simplifying Image Abstraction

This paper presents a simple algorithm for producing stylistic abstraction of a photograph. Based on mean curvature flow in conjunction with shock filter, our method simplifies both shapes and colors simultaneously while preserving important features. In particular, we develop a constrained mean curvature flow, which outperforms the original mean curvature flow in conveying the directionality of features and shape boundaries. The proposed algorithm is iterative and incremental, and therefore the level of abstraction is intuitively controlled. Optionally, simple user masking can be incorporated into the algorithm to selectively control the abstraction speed and to protect particular regions. Experimental results show that our method effectively produces highly abstract yet feature‐preserving illustrations from photographs.     

Hierarchical Deformation of Locally Rigid Meshes

We propose a method for calculating deformations of models by deforming a low‐resolution mesh and adding details while ensuring that the details we add satisfy a set of constraints. Our method builds a low‐resolution representation of a mesh by using edge collapses and performs an as‐rigid‐as‐possible deformation on the simplified mesh. We then add back details by reversing edge‐collapses so that the shape of the mesh is locally preserved. While adding details, we deform the mesh to match the predicted positions of constraints so that constraints on the full‐resolution mesh are met. Our method operates on meshes with arbitrary triangulations, satisfies constraints over the full‐resolution mesh and converges quickly.