Showing papers in "Computer Graphics Forum in 2002"
TL;DR: This paper presents new theoretical and practical results on the parameterization of triangulated surface patches and proposes robust, efficient and tunable tools to obtain least‐distorted parameterizations automatically.
Abstract: Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.
684 citations
IBM1
TL;DR: There is potentially an opportunity to consider new virtual reality applications as diverse as cultural heritage and retail sales that will allow people to view realistic 3D objects on home computers.
Abstract: Three-dimensional (3D) image acquisition systems are rapidly becoming more affordable, especially systems based on commodity electronic cameras. At the same time, personal computers with graphics hardware capable of displaying complex 3D models are also becoming inexpensive enough to be available to a large population. As a result, there is potentially an opportunity to consider new virtual reality applications as diverse as cultural heritage and retail sales that will allow people to view realistic 3D objects on home computers. Although there are many physical techniques for acquiring 3D data—including laser scanners, structured light and time-of-flight—there is a basic pipeline of operations for taking the acquired data and producing a usable numerical model. We look at the fundamental problems of range image registration, line-of-sight errors, mesh integration, surface detail and color, and texture mapping. In the area of registration we consider both the problems of finding an initial global alignment using manual and automatic means, and refining this alignment with variations of the Iterative Closest Point methods. To account for scanner line-of-sight errors we compare several averaging approaches. In the area of mesh integration, that is finding a single mesh joining the data from all scans, we compare various methods for computing interpolating and approximating surfaces. We then look at various ways in which surface properties such as color (more properly, spectral reflectance) can be extracted from acquired imagery. Finally, we examine techniques for producing a final model representation that can be efficiently rendered using graphics hardware.
492 citations
TL;DR: It is shown that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects.
Abstract: STRANDS are thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric non-linearity due to large changes in shape. We introduce Cosserat-type physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results.
324 citations
TL;DR: This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies that can robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities.
Abstract: This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities. The method is valid for general objects (polygon soups), handles multiple moving objects and acyclic articulated bodies, and is efficient in low and high coherency situations. Moreover, the method can be used to speed up existent continuous collision detection methods for parametric or implicit rigid surfaces. The collision detection algorithms have been successfully coupled to a real-time dynamics simulator. Various experiments are conducted that show the method's ability to produce high-quality interaction (precise objects positioning for example) between models up to tens of thousands of triangles, which couldn't have been performed with previous continuous methods.
281 citations
TL;DR: A new algorithm for decomposing surfaces into patches based on their decompositions into patches is presented and a new projection scheme that handles topologically cylinder‐like polyhedral surfaces is presented.
Abstract: This paper describes an algorithm for morphing polyhedral surfaces based on their decompositions into patches. The given surfaces need neither be genus-zero nor two-manifolds. We present a new algorithm for decomposing surfaces into patches. We also present a new projection scheme that handles topologically cylinder-like polyhedral surfaces. We show how these two new techniques can be used within a general framework and result with morph sequences that maintain the distinctive features of the input models.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Boundary representations I.3.7 [Three-Dimensional Graphics and Realism]: Animation
275 citations
TL;DR: Meshes have become a widespread and popular representation of models in computer graphics and morphing techniques for meshes have received a lot of interest lately.
Abstract: Meshes have become a widespread and popular representation of models in computer graphics. Morphing techniques aim at transforming a given source shape into a target shape. Morphing techniques have various applications ranging from special effects in television and movies to medical imaging and scientific visualization. Not surprisingly, morphing techniques for meshes have received a lot of interest lately. Thiswork sums up recent developments in the area of mesh morphing. It presents a consistent framework to classify and compare various techniques approaching the same underlying problems from different angles.
273 citations
TL;DR: Extensions to the previous watermarking algorithm are presented so that much larger meshes can be watermarked within a reasonable time, and the watermark is robust against connectivity alteration and attacks that combine similarity transformation with such other attacks as cropping, mesh simplification, and smoothing.
Abstract: This paper presents a robust watermarking algorithm with informed detection for 3D polygonal meshes. The algorithm is based on our previous algorithm [22] that employs mesh-spectral analysis to modify mesh shapes in their transformed domain. This paper presents extensions to our previous algorithm so that (1) much larger meshes can be watermarked within a reasonable time, and that (2) the watermark is robust against connectivity alteration (e.g., mesh simplification), and that (3) the watermark is robust against attacks that combine similarity transformation with such other attacks as cropping, mesh simplification, and smoothing. Experiment showed that our new watermarks are resistant against mesh simplification and remeshing combined with resection, similarity transformation, and other operations..
245 citations
TL;DR: A new mutation strategy for the Metropolis light transport algorithm, which works in the unit cube of pseudo‐random numbers instead of mutating in the path space, which makes the integrand have lower variation and thus increases the acceptance probability of the mutated samples.
Abstract: The paper presents a new mutation strategy for the Metropolis light transport algorithm, which works in the space of uniform random numbers used to build up paths. Thus instead of mutating directly in the path space, mutations are realized in the infinite dimensional unit cube of pseudo-random numbers and these points are transformed to the path space according to BRDF sampling, light source sampling and Russian roulette. This transformation makes the integrand and the importance function flatter and thus increases the acceptance probability of the new samples in the Metropolis algorithm. Higher acceptance ratio, in turn, reduces the correlation of the samples, which increases the speed of convergence. When mutations are calculated, a new random point is selected usually in the neighborhood of the previous one, but according to our proposition called “large steps”, sometimes an independent point is obtained. Large steps greatly reduce the start-up bias and guarantee the ergodicity of the process. Due to the fact that some samples are generated independently of the previous sample, this method can also be considered as a combination of the Metropolis algorithm with a classical random walk. Metropolis light transport is good in rendering bright image areas but poor in rendering dark sections since it allocates samples proportionally to the pixel luminance. Conventional random walks, on the other hand, have the same performace everywhere, thus they are poorer than Metropolis method in bright areas, but are better at dark sections. In order to keep the merits of both approaches, we use multiple importance sampling to combine their results, that is, the combined method will be as good at bright regions as Metropolis and at dark regions as random walks. The resulting scheme is robust, efficient, but most importantly, is easy to implement and to combine with an available random-walk algorithm.
194 citations
TL;DR: This paper derives an object space formulation of the EWA filter, which is amenable for acceleration by conventional triangle‐based graphics hardware, and implements the algorithm using programmable vertex and pixel shaders, fully exploiting the capabilities of today's graphics processing units (GPUs).
Abstract: Elliptical weighted average (EWA) surface splatting is a technique for high quality rendering of point-sampled 3D objects. EWA surface splatting renders water-tight surfaces of complex point models with high quality, anisotropic texture filtering. In this paper we introduce a new multi-pass approach to perform EWA surface splatting on modern PC graphics hardware, called object space EWA splatting. We derive an object space formulation of the EWA filter, which is amenable for acceleration by conventional triangle-based graphics hardware. We describe how to implement the object space EWA filter using a two pass rendering algorithm. In the first rendering pass, visibility splatting is performed by shifting opaque surfel polygons backward along the viewing rays, while in the second rendering pass view-dependent EWA prefiltering is performed by deforming texture mapped surfel polygons. We use texture mapping and alpha blending to facilitate the splatting process. We implement our algorithm using programmable vertex and pixel shaders, fully exploiting the capabilities of today’s graphics processing units (GPUs). Our implementation renders up to 3 million points per second on recent PC graphics hardware, an order of magnitude more than a pure software implementation of screen space EWA surface splatting.
185 citations
TL;DR: With the advent of sketch‐based methods for shape construction, there's a new degree of power available in the rapid creation of approximate shapes, and Teddy extended this to more free‐form models.
Abstract: With the advent of sketch-based methods for shape construction, there’s a new degree of power available in the rapid creation of approximate shapes. Sketch [Zeleznik, 1996] showed how a gesture-based modeler could be used to simplify conventional CSG-like shape creation. Teddy [Igarashi, 1999] extended this to more free-form models, getting much of its power from its "inflation" operation (which converted a simple closed curve in the plane into a 3D shape whose silhouette, from the current point of view, was that curve on the view plane) and from an elegant collection of gestures for attaching additional parts to a shape, cutting a shape, and deforming it. But despite the powerful collection of tools in Teddy, the underlying polygonal representation of shapes intrudes on the results in many places. In this paper, we discuss our preliminary efforts at using variational implicit surfaces [Turk, 2000] as a representation in a free-form modeler. We also discuss the implementation of several operations within this context, and a collection of user-interaction elements that work well together to make modeling interesting hierarchies simple. These include “stroke inflation” via implicit functions, blob-merging, automatic hierarchy construction, and local surface modification via silhouette oversketching. We demonstrate our results by creating several models.
160 citations
TL;DR: A geometric snake is proposed as an interactive tool for feature detection on a 3D triangular mesh that slithers from its initial position specified by the user to a nearby feature while minimizing an energy functional.
Abstract: Feature detection is important in various mesh processing techniques, such as mesh editing, mesh morphing, mesh compression, and mesh signal processing. In spite of much research in computer vision, automatic feature detection even for images still remains a difficult problem. To avoid this difficulty, semi-automatic or interactive techniques for image feature detection have been investigated. In this paper, we propose a geometric snake as an interactive tool for feature detection on a 3D triangular mesh. A geometric snake is an extension of an image snake, which is an active contour model that slithers from its initial position specified by the user to a nearby feature while minimizing an energy functional. To constrain the movement of a geometric snake onto the surface of a mesh, we use the parameterization of the surrounding region of a geometric snake. Although the definition of a feature may vary among applications, we use the normal changes of faces to detect features on a mesh. Experimental results demonstrate that geometric snakes can successfully capture nearby features from user-specified initial positions.
TL;DR: A modular behavioural architecture of a multi‐agent system allowing autonomous and scripted behaviour of agents supporting variety is defined, and the concept of levels of variety is introduced.
Abstract: While virtual crowds are becoming common in non-real-time applications, the real-time domain is still relatively unexplored. In this paper we discuss the challenges involved in creating such simulations, especially the need to efficiently manage variety. We introduce the concept of levels of variety, then present our work on crowd behaviour simulation aimed at interactive real-time applications such as computer games or virtual environments. We define a modular behavioural architecture of a multi-agent system allowing autonomous and scripted behaviour of agents supporting variety. Finally we show applications of our system in a virtual reality training system and virtual heritage reconstruction
TL;DR: A method for cloth animation in real‐time exploiting the merits of both the physical‐based and geometric deformations and avoiding complex collision detection and physical deformations wherever possible is described.
Abstract: In this paper, we describe a method for cloth animation in real-time. The algorithm works in a hybrid manner exploiting the merits of both the physical-based and geometric deformations. It makes use of predetermined conditions between the cloth and the body model, avoiding complex collision detection and physical deformations wherever possible. Garments are segmented into pieces that are simulated by various algorithms, depending on how they are laid on the body surface and whether they stick or flow on it. Tests show that the method is well suited to fully dressed virtual human models, achieving real-time performance compared to ordinary cloth-simulations.
TL;DR: Angle‐Analyzer, a new single‐rate compression algorithm for triangle‐quad hybrid meshes using a carefully‐designed geometry‐driven mesh traversal and an efficient encoding of intrinsic mesh properties produces compression ratios 40% better in connectivity and 20%better in geometry than the leading Touma and Gotsman technique for the same level of geometric distortion.
Abstract: Theme 2 — Genie logicielet calcul symboliqueProjet PrismeRapport de recherche n° 4584 — Octobre 2002 — 29 pagesAbstract: We present Angle-Analyzer, a new single-rate compression algorithm for triangle-quad hybrid meshes. Using a carefully-designed geometry-driven mesh traversal and an ef-ficient encoding of intrinsic mesh properties, Angle-Analyzer produces compression ratios40% better in connectivity and 20% better in geometry than the leading Touma and Gotsmantechnique for the same level of geometric distortion. The simplicity and performance of thisnew technique is demonstrated, and we provide extensive comparative tests to contrast ourresults with the current state-of-the-art techniques.Key-words: Compression algorithms, hybrid meshes, Surface mesh compression, connec-tivity coding, geometry coding.
TL;DR: A hardware‐accelerated depth sorting algorithm in image‐space which specifically meets the requirements of the transparency model is proposed, and real‐time rendering of semi‐transparent technical illustrations is achieved.
Abstract: This paper describes how technical illustrations containing opaque and non-opaque objects can be automatically generated. Traditional methods to show transparency in manual drawings are evaluated to extract a small and effective set of rules for computer-based rendering of technical illustrations, leading to a novel view-dependent transparency model. We propose a hardware-accelerated depth sorting algorithm in image-space which specifically meets the requirements of our transparency model. In this way, real-time rendering of semi-transparent technical illustrations is achieved. Finally, it is described how our approach can be combined with other methods in the field of non-photorealistic rendering in order to enhance the visual perception of technical illustrations.
TL;DR: Methods to deal with various aspects of crowd visualization, ranging from collision detection and behaviour modeling to fast rendering with shadows and quality shading are looked at, to suggest that simulations of reasonably complex environments populated with thousands of animated characters are possible in real‐time.
Abstract: Real-time crowd visualization has recently attracted quite an interest from the graphics community and, as interactive applications become even more complex, there is a natural demand for new and unexplored application scenarios. However, the interactive simulation of complex environments populated by large numbers of virtual characters is a composite problem which poses serious difficulties even on modern computer hardware. In this paper we look at methods to deal with various aspects of crowd visualization, ranging from collision detection and behaviour modeling to fast rendering with shadows and quality shading. These methods make extensive use of current graphics hardware capabilities with the aim of providing scalability without compromising run-time speed. Results from a system employing these techniques seem to suggest that simulations of reasonably complex environments populated with thousands of animated characters are possible in real-time.
TL;DR: This work presents an automatic method of integrating facade textures from ground view images into 3D building models for urban site modeling, which combines global feature extraction with Hough transform on an adaptively tessellated Gaussian Sphere and local region segmentation.
Abstract: Visualization of city scenes is important for many applications including entertainment and urban mission planning. Models covering wide areas can be efficiently constructed from aerial images. However, only roof details are visible from aerial views; ground views are needed to provide details of the building facades for high quality ’fly-through’ visualization or simulation applications. We present an automatic method of integrating facade textures from ground view images into 3D building models for urban site modeling. We first segment the input image into building facade regions using a hybrid feature extraction method, which combines global feature extraction with Hough transform on an adaptively tessellated Gaussian Sphere and local region segmentation. We estimate the external camera parameters by using the corner points of the extracted facade regions to integrate the facade textures into the 3D building models. We validate our approach with a set of experiments on some urban sites.
TL;DR: The approach described in this paper proposes the combination of two commonly known concepts: on the one hand level detail (LoD) for those object classes, that require high computational cost for the automated generalization process (e.g. buildings, road network); on the other hand an on‐the‐fly generalization for thoseobject classes which can be generalized by less complex methods and algorithms ( e.g., rivers, lakes).
Abstract: Beyond any doubt much of the current web mapping and web GIS applications lack cartographic quality. Thereasons aren't only the technical limitations related to Internet delivery, but also the neglect of one of the maincartographic principles of digital mapping, namely adaptive zooming. Adaptive zooming describes the adjustmentof a map, its contents and the symbolization to target scale in consequence of a zooming operation. The approachdescribed in this paper proposes the combination of two commonly known concepts: on the one hand levelsof detail (LoD) for those object classes, that require high computational cost for the automated generalizationprocess (e.g. buildings, road network); on the other hand an on-the-fly generalization for those object classeswhich can be generalized by less complex methods and algorithms (e.g. rivers, lakes). Realizing such interactiveand dynamic concept for web mapping requires the use of vector based visualization tools. The data format bestmeeting the criteria is the W3C standard Scalable Vector Graphics (SVG). Thus, it has been used to implementthe presented ideas in a prototype application for topographic web mapping based on the landscape modelVECTOR25 of the Swiss Federal Office of Topography.
TL;DR: In this paper, a method for improving subdivision schemes for subdivision surfaces is presented, which can correct distortion from the base mesh caused by prior art subdivision and smoothing schemes, and adjust positions of the smoothed vertices.
Abstract: A method, computer readable storage, and apparatus for improving subdivision schemes for subdivision surfaces. The present method can correct distortion from the base mesh caused by prior art subdivision and smoothing schemes. In one embodiment, the method includes: (a) subdividing a curve having original vertices producing additional vertices; (b) smoothing the curve into smoothed vertices comprising smoothed original vertices and smoothed additional vertices; and (c) adjusting positions of the smoothed vertices.
TL;DR: An algorithm is introduced that takes a set of silhouette edges originating from polygonal meshes and efficiently computes the visible parts of the edges before connecting them to form long smooth silhouette strokes to which stylization algorithms may be effectively applied.
Abstract: A way to create effective stylized line drawings is to draw strokes that start and stop at visible portions along the silhouette of an object to be portrayed. In computer graphics to date, algorithms to extract silhouette edges are many, although putting these edges into a form such that stylized strokes may be applied to them has not been greatly covered, so that existing methods are either time-consuming or presented vaguely. In this paper, we introduce an algorithm that takes a set of silhouette edges originating from polygonal meshes and efficiently computes the visible parts of the edges before connecting them to form long smooth silhouette strokes to which stylization algorithms may be effectively applied. Features of our algorithm that gain efficiency and accuracy over existing methods is that we directly exploit the analytic connectivity information of the mesh in combination with the available z-buffer information during rendering, and filter artifacts in connected edges during the process to improve the visual quality of strokes after stylization.
TL;DR: The detailed modeling of the hairy brush used typically in Chinese calligraphy is presented, which includes also a model for the ink and the paper, and is found to be nearly indistinguishable from the real artwork.
Abstract: We present the detailed modeling of the hairy brush used typically in Chinese calligraphy. The complex model, which includes also a model for the ink and the paper, covers the various stages of the brush going through a calligraphy process. The model relies on the concept of writing primitives, which are the smallest units of hair clusters, to reduce the load on the simulation. Each such primitive is constructed through the general sweeping operation in CAD and described by a NURBS surface. The writing primitives dynamically adjust themselves during the virtual writing process, leaving an imprint on the virtual paper as they move. The behavior of the brush is an aggregation of the behavior of all the writing primitives. A software system based on the model has been built and tested. Samples of imitation artwork from using the system were obtained and found to be nearly indistinguishable from the real artwork.
TL;DR: A memory model based on ``stage theory'', an influential concept of memory from the field of cognitive psychology, is presented for application to autonomous virtual humans for use in training, entertainment, ergonomics and military simulations.
Abstract: A memory model based on “stage theory”, an influential concept of memory from the field of cognitive psychology, is presented for application to autonomous virtual humans. The virtual human senses external stimuli through a synthetic vision system. The vision system incorporates multiple modes of vision in order to accommodate a perceptual attention approach. The memory model is used to store perceived and attended object information at different stages in a filtering process. The methods outlined in this paper have applications in any area where simulation-based agents are used: training, entertainment, ergonomics and military simulations to name but a few.
TL;DR: This work introduces a novel sampling and stratification algorithm to efficiently generate suitable point sample sets for moving triangle meshes to render highly complex keyframe animations like crowd scenes in real‐time.
Abstract: We present a novel multi-resolution point sample rendering algorithm for keyframe animations. The algorithm accepts triangle meshes of arbitrary topology as input which are animated by specifying different sets of vertices at keyframe positions. A multi-resolution representation consisting of prefiltered point samples and triangles is built to represent the animated mesh at different levels of detail. We introduce a novel sampling and stratification algorithm to efficiently generate suitable point sample sets for moving triangle meshes. Experimental results demonstrate that the new data structure can be used to render highly complex keyframe animations like crowd scenes in real-time.
TL;DR: The approach explores the singularity theory for ridge and ravine detection, combines several filtering methods for skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysis of the skeleton for detection of salient shape regions.
Abstract: The paper presents a skeleton-based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three-dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [3]. Shape creases, ridges and ravines, are detected as curvescorresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches.The approach explores the singularity theory for ridge and ravine detection, combines several filtering methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions.
ACM CSS: I.3.5 Computational Geometry and Object Modeling
TL;DR: In this article, the authors describe an adaptive level of detail for human animation, which includes a complexity gradient for natural behaviour, both conversational and social, and describe the ongoing development of a framework for Adaptive Level Of Detail for Human Animation (ALOHA).
Abstract: Work on levels of detail for human simulation has occurred mainly on a geometrical level, either by reducing the numbers of polygons representing a virtual human, or replacing them with a two-dimensional imposter. Approaches that reduce the complexity of motions generated have also been proposed. In this paper, we describe ongoing development of a framework for Adaptive Level Of Detail for Human Animation (ALOHA), which incorporates levels of detail for not only geometry and motion, but also includes a complexity gradient for natural behaviour, both conversational and social.
TL;DR: An efficient algorithm is presented that computes a manifold triangular mesh from a set of unorganized sample points in to provide a two‐dimensional surface description which can be easily turned into a manifold.
Abstract: We present an efficient algorithm that computes a manifold triangular mesh from a set of unorganized sample points in. The algorithm builds on the observation made by several researchers that the Gabriel graph of the sample points provides a good surface description. However, this surface description is only one-dimensional. We associate the edges of the Gabriel graph with index 1 critical points of a dynamical system induced by the sample points. Exploiting also the information contained in the critical points of index 2 provides a two-dimensional surface description which can be easily turned into a manifold.
TL;DR: Extension of subdivision methods to the volumetric case would enable their use in a broad class of applications including solid modeling, scientific visualization and mesh generation.
Abstract: The efficient representation of volumetric meshes is a central problem in scientific visualization. The difference in performance between most visualization algorithm for rectilinear grids and for unstructured mesh is mostly due to fundamental difference in efficiency of their representations. In Computer Graphics the gap in performance between 2D rectilinear grids and unstructured mesh has been overcome with the development of representation schemes based on the concept of subdivision surfaces. This gap has not been bridged in the volumetric cases which is fundamental interest for Scientific Visualization. In this paper we introduce a slow-growing volumetric subdivision scheme for meshes of any topology, any intrinsic dimension d and composed of a general type of polyhedral cells (topological balls). The main feature of this approach is the ability to split in different stages cells of different dimensions. This allows to increase the resolution of the mesh slowly using small stencils for the smoothing rules. ''Sharp features'' of dimension lower than d are embedded naturally in the subdivision procedure. Automatic adaptation is provided for variable resolution. In the uniform case the slow subdivision doubles the number of vertices in the mesh at each refinement independent of its dimension d. The bisection of all themore » edges in a d-dimensional simplicial mesh requires d subdivision steps. Hence the slow subdivision is a d{radical}2 subdivision scheme. This algorithm generalizes a recently developed {radical}2 subdivision scheme to 3D and higher dimensional meshes where the vertex proliferation becomes increasingly problematic as d grows (the curse of dimensionality). We introduce a smoothing rule for both the domain mesh and for functions defined on it. Empirical evidence demonstrates the smoothness of the scheme directly on the mesh and indirectly on the isosurfaces of the functions.« less
TL;DR: This paper proposes an efficient method for rendering images of scenes within water by using graphics hardware to accelerate the computation and by using a shadow mapping technique to display shafts of light and caustics taking account of shadows due to objects.
Abstract: The display of realistic natural scenes is one of the most important research areas in computer graphics. The rendering of water is one of the essential components. This paper proposes an efficient method for rendering images of scenes within water. For underwater scenery, the shafts of light and caustics are attractive and important elements. However, computing these effects is difficult and time-consuming since light refracts when passing through waves. To address the problem, our method makes use of graphics hardware to accelerate the computation. Our method displays the shafts of light by accumulating the intensities of streaks of light by using hardware color blending functions. Making use of a Z-buffer and a stencil buffer accelerates the rendering of caustics. Moreover, by using a shadow mapping technique, our method can display shafts of light and caustics taking account of shadows due to objects.
TL;DR: Here, a novel reversing process to convert a fine surface into a coarse one plus an error is proposed, which has the property that the subdivision of the resulting coarse surface is locally closest to the original fine surface, in the least squares sense, for two important face geometries.
Abstract: We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models 16. As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In 1 we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here, we construct multiresolution surfaces of arbitrary topologies by locally reversing the Doo subdivision scheme. In a Doo subdivision, a coarse surface is converted into a fine one by the contraction of coarse faces and the addition of new adjoining faces. We propose a novel reversing process to convert a fine surface into a coarse one plus an error. The conversion has the property that the subdivision of the resulting coarse surface is locally closest to the original fine surface, in the least squares sense, for two important face geometries. In this process, we first find those faces of the fine surface which might have been produced by the contraction of a coarse face in a Doo subdivision scheme. Then, we expand these faces. Since the expanded faces are not necessarily joined properly, several candidates are usually at hand for a single vertex of the coarse surface. To identify the set of candidates corresponding to a vertex, we construct a graph in such a way that any set of candidates corresponds to a connected component. The connected components can easily be identified by a depth first search traversal of the graph. Finally, vertices of the coarse surface are set to be the average of their corresponding candidates, and this is shown to be equivalent to local least squares approximation for regular arrangements of triangular and quadrilateral faces.