Breast cancer is the leading cause of cancer death in women worldwide, emphasizing the need for prevention and early detection. Mammography screening plays a crucial role in secondary prevention, but large datasets of referred mammograms from hospital databases are hard to access due to privacy concerns, and publicly available datasets are often unreliable and unbalanced. We propose a novel workflow using a statistical generative model based on generative adversarial networks to generate high-resolution synthetic mammograms. Utilizing a unique 2D parametric model of the compressed breast in craniocaudal projection and image-to-image translation techniques, our approach allows full and precise control over breast features and the generation of both normal and tumor cases. Quality assessment was conducted through visual analysis, and statistical analysis using the first five statistical moments. Additionally a questionnaire was administered to 45 medical experts (radiologists and radiology residents). The results showed that the features of the real mammograms were accurately replicated in the synthetic ones, the image statistics overall correspond reasonably well, and the two groups of images were statistically indistinguishable in almost all cases according to the experts. The proposed workflow generates realistic synthetic mammograms with fine-tuned features. Synthetic mammograms are powerful tools that can create new or balance existing datasets, allowing for the training of machine learning and deep learning algorithms. These algorithms can then assist radiologists in tasks like classification and segmentation, improving diagnostic performance.

Abstract We propose a method for designing 3D architectural free‐form surfaces, represented as grid shells with beams sourced from inventories of reclaimed elements from dismantled buildings. In inventory‐constrained design, the reused elements must be paired with elements in the target design. Traditional solutions to this assignment problem often result in cuts and material waste or geometric distortions that affect the surface aesthetics and buildability. Our method for inventory‐constrained assisted design blends the traditional assignment problem with differentiable geometry optimization to reduce cut‐off waste while preserving the design intent. Additionally, we extend our approach to incorporate strain energy minimization for structural efficiency. We design differentiable losses that account for inventory, geometry, and structural constraints, and streamline them into a complete pipeline, demonstrated through several case studies. Our approach enables the reuse of existing elements for new designs, reducing the need for sourcing new materials and disposing of waste. Consequently, it can serve as an initial step towards mitigating the significant environmental impact of the construction sector.

This paper addresses the design of surface shells as assemblies of tileable, flat geometric patterns with predictable performance in response to mechanical stimuli. We design a family of tileable and fabricable patterns represented as triangle meshes, which can be assembled for creating surface tessellations. First, a regular recursive subdivision of the planar space generates different geometric configurations for candidate patterns, having interesting and varied aesthetic properties. Then, a refinement step addresses manufacturability by solving for non-manifold configurations and sharp angles that would produce disconnected or weak patterns. We devise a strategy for creating continuous variations on the geometry of individual patterns, in both aesthetics and behavior, to enrich the catalog of available designs. Finally, we simulate our patterns to evaluate their mechanical response when loaded in different scenarios targeting out-of-plane bending. Through a simple browsing interface, we show that our patterns span a variety of different bending behaviors. The result is a catalog of patterns with varied aesthetics and predefined mechanical behavior, to use for the direct design of mechanical metamaterials. To assess the feasibility of our design-to-fabricate approach, we show fabricated 3D objects with different curvatures, and compare physical and simulated experiments.

Mutual-capacitive sensing is the most common technology for detecting multi-touch, especially on flat and simple curvature surfaces. Its extension to a more complex shape is still challenging, as a uniform distribution of sensing electrodes is required for consistent touch sensitivity across the surface. To overcome this problem, we propose a method to adapt the sensor layout of common capacitive multi-touch sensors to more complex 3D surfaces, ensuring high-resolution, robust multi-touch detection. The method automatically computes a grid of transmitter and receiver electrodes with as regular distribution as possible over a general 3D shape. It starts with the computation of a proxy geometry by quad meshing used to place the electrodes through the dual-edge graph. It then arranges electrodes on the surface to minimize the number of touch controllers required for capacitive sensing and the number of input/output pins to connect the electrodes with the controllers. We reach these objectives using a new simplification and clustering algorithm for a regular quad-patch layout. The reduced patch layout is used to optimize the routing of all the structures (surface grooves and internal pipes) needed to host all electrodes on the surface and inside the object's volume, considering the geometric constraints of the 3D shape. Finally, we print the 3D object prototype ready to be equipped with the electrodes. We analyze the performance of the proposed quad layout simplification and clustering algorithm using different quad meshing and characterize the signal quality and accuracy of the capacitive touch sensor for different non-planar geometries. The tested prototypes show precise and robust multi-touch detection with good Signal-to-Noise Ratio and spatial accuracy of about 1mm.

Abstract We devise a technique designed to remove the texturing artefacts that are typical of 3D models representing real‐world objects, acquired by photogrammetric techniques. Our technique leverages the recent advancements in inpainting of natural colour images, adapting them to the specific context. A neural network, modified and trained for our purposes, replaces the texture areas containing the defects, substituting them with new plausible patches of texels, reconstructed from the surrounding surface texture. We train and apply the network model on locally reparametrized texture patches, so to provide an input that simplifies the learning process, because it avoids any texture seams, unused texture areas, background, depth jumps and so on. We automatically extract appropriate training data from real‐world datasets. We show two applications of the resulting method: one, as a fully automatic tool, addressing all problems that can be detected by analysing the UV‐map of the input model; and another, as an interactive semi‐automatic tool, presented to the user as a 3D ‘fixing’ brush that has the effect of removing artefacts from any zone the users paints on. We demonstrate our method on a variety of real‐world inputs and provide a reference usable implementation.

The computational fabrication community is developing an increasing interest in the use of patterned surfaces, which can be designed to show ornamental and unconventional aesthetics or to perform as a proper structural material with a wide range of features. Geometrically designing and controlling the deformation capabilities of these patterns in response to external stimuli is a complex task due to the large number of variables involved. This paper introduces a method for generating sets of tileable and exchangeable flat patterns as well as a model-reduction strategy that enables their mechanical simulation at interactive rates. This method is included in a design pipeline that aims to turn any general flat surface into a pattern tessellation, which is able to deform under a given loading scenario. To validate our approach, we apply it to different contexts, including real-scale 3D printed specimens, for which we compare our results with the ones provided by a ground-truth solver.

Abstract Moulding refers to a set of manufacturing techniques in which a mould, usually a cavity or a solid frame, is used to shape a liquid or pliable material into an object of the desired shape. The popularity of moulding comes from its effectiveness, scalability and versatility in terms of employed materials. Its relevance as a fabrication process is demonstrated by the extensive literature covering different aspects related to mould design, from material flow simulation to the automation of mould geometry design. In this state‐of‐the‐art report, we provide an extensive review of the automatic methods for the design of moulds, focusing on contributions from a geometric perspective. We classify existing mould design methods based on their computational approach and the nature of their target moulding process. We summarize the relationships between computational approaches and moulding techniques, highlighting their strengths and limitations. Finally, we discuss potential future research directions.

We propose a novel technique to compose new 3D animated models, such as videogame characters, by combining pieces from existing ones. Our method works on production-ready rigged, skinned, and animated 3D models to reassemble new ones. We exploit mix-and-match operations on the skeletons to trigger the automatic creation of a new mesh, linked to the new skeleton by a set of skinning weights and complete with a set of animations. The resulting model preserves the quality of the input meshings (which can be quad-dominant and semi-regular), skinning weights (inducing believable deformation), and animations, featuring coherent movements of the new skeleton. Our method enables content creators to reuse valuable, carefully designed assets by assembling new ready-to-use characters while preserving most of the hand-crafted subtleties of models authored by digital artists. As shown in the accompanying video, it allows for drastically cutting the time needed to obtain the final result.

Structure-from-Motion (SfM) using the frames of a video sequence can be a challenging task because there is a lot of redundant information, the computational time increases quadratically with the number of frames, there would be low-quality images (e.g., blurred frames) that can decrease the final quality of the reconstruction, etc. To overcome all these issues, we present a novel deep-learning architecture that is meant for speeding up SfM by selecting frames using predicted sub-sampling frequency. This architecture is general and can learn/distill the knowledge of any algorithm for selecting frames from a video for generating high-quality reconstructions. One key advantage is that we can run our architecture in real-time saving computations while keeping high-quality results.

Abstract We propose a method to improve an existing parametrization (UV‐map layout) of a textured 3D model, targeted explicitly at alleviating typical defects afflicting models generated with automatic photo‐reconstruction tools from real‐world objects. This class of 3D data is becoming increasingly important thanks to the growing popularity of reliable, ready‐to‐use photogrammetry software packages. The resulting textured models are richly detailed, but their underlying parametrization typically falls short of many practical requirements, particularly exhibiting excessive fragmentation and consequent problems. Producing a completely new UV‐map, with standard parametrization techniques, and then resampling a new texture image, is often neither practical nor desirable for at least two reasons: first, these models have characteristics (such as inconsistencies, high resolution) that make them unfit for automatic or manual parametrization; second, the required resampling leads to unnecessary signal degradation because this process is unaware of the original texel densities. In contrast, our method improves the existing UV‐map instead of replacing it, balancing the reduction of the map fragmentation with signal degradation due to resampling, while also avoiding oversampling of the original signal. The proposed approach is fully automatic and extensively tested on a large benchmark of photo‐reconstructed models; quantitative evaluation evidences a drastic and consistent improvement of the mappings.

We introduce a novel technique to automatically decompose an input object's volume into a set of parts that can be represented by two opposite height fields. Such decomposition enables the manufacturing of individual parts using two-piece reusable rigid molds. Our decomposition strategy relies on a new energy formulation that utilizes a pre-computed signal on the mesh volume representing the accessibility for a predefined set of extraction directions. Thanks to this novel formulation, our method allows for efficient optimization of a fabrication-aware partitioning of volumes in a completely automatic way. We demonstrate the efficacy of our approach by generating valid volume partitionings for a wide range of complex objects and physically reproducing several of them.

We present a new algorithm for the semi-regular quadrangulation of an input surface, driven by its line features, such as sharp creases. We define a perfectly feature-aligned cross-field and a coarse layout of polygonal-shaped patches where we strictly ensure that all the feature-lines are represented as patch boundaries. To be able to consistently do so, we allow non-quadrilateral patches and T-junctions in the layout; the key is the ability to constrain the layout so that it still admits a globally consistent, T-junction-free, and pure-quad internal tessellation of its patches. This requires the insertion of additional irregular-vertices inside patches, but the regularity of the final-mesh is safeguarded by optimizing for both their number and for their reciprocal alignment. In total, our method guarantees the reproduction of feature-lines by construction, while still producing good quality, isometric, pure-quad, conforming meshes, making it an ideal candidate for CAD models. Moreover, the method is fully automatic, requiring no user intervention, and remarkably reliable, requiring little assumptions on the input mesh, as we demonstrate by batch processing the entire Thingi10K repository, with less than 0.5% of the attempted cases failing to produce a usable mesh.

Abstract We propose a method for the automatic segmentation of 3D objects into parts which can be individually 3D printed and then reassembled by preserving the visual quality of the final object. Our technique focuses on minimizing the surface affected by supports, decomposing the object into multiple parts whose printing orientation is automatically chosen. The segmentation reduces the visual impact on the fabricated model producing non‐planar cuts that adapt to the object shape. This is performed by solving an optimization problem that balances the effects of supports and cuts, while trying to place both in occluded regions of the object surface. To assess the practical impact of the solution, we show a number of segmented, 3D printed and reassembled objects.

Abstract We propose an optimization algorithm for the design of post‐tensioned architectural shell structures, composed of triangular glass panels, in which glass has a load‐bearing function. Due to its brittle nature, glass can fail when it is subject to tensile forces. Hence, we enrich the structure with a cable net, which is specifically designed to post‐tension the shell, relieving the underlying glass structure from tension. We automatically derive an optimized cable layout, together with the appropriate pre‐load of each cable. The method is driven by a physically based static analysis of the shell subject to its service load. We assess our approach by applying non‐linear finite element analysis to several real‐scale application scenarios. Such a method of cable tensioning produces glass shells that are optimized from the material usage viewpoint since they exploit the high compression strength of glass. As a result, they are lightweight and robust. Both aesthetic and static qualities are improved with respect to grid shell competitors.

We present a new fully automatic block-decomposition algorithm for feature-preserving, strongly hex-dominant meshing, that yields results with a drastically larger percentage of hex elements than prior art. Our method is guided by a surface field that conforms to both surface curvature and feature lines, and exploits an ordered set of cutting loops that evenly cover the input surface, defining an arrangement of loops suitable for hex-element generation. We decompose the solid into coarse blocks by iteratively cutting it with surfaces bounded by these loops. The vast majority of the obtained blocks can be turned into hexahedral cells via simple midpoint subdivision. Our method produces pure hexahedral meshes in approximately 80% of the cases, and hex-dominant meshes with less than 2% non-hexahedral cells in the remaining cases. We demonstrate the robustness of our method on 70+ models, including CAD objects with features of various complexity, organic and synthetic shapes, and provide extensive comparisons to prior art, demonstrating its superiority.

3-axis milling enables cheap and precise fabrication of target objects from precut slabs of materials such as wood or stone. However, the space of directly millable shapes is limited since a 3-axis mill can only carve a height-field (HF) surface during each milling and their size is bounded by the slab dimensions, one of which, the height , is typically significantly smaller than the other two for many typical materials. Extending 3-axis milling of precut slabs to general arbitrarily-sized shapes requires decomposing them into bounded-height 3-axis millable parts, or slices , which can be individually milled and then assembled to form the target object. We present DHFSlicer , a novel decomposition method that satisfies the above constraints and significantly reduces both milling time and material waste compared to alternative approaches. We satisfy the fabrication constraints by partitioning target objects into double height-field (DHF) slices, which can be fabricated using two milling passes: the HF surface accessible from one side is milled first, the slice is then flipped using appropriate fixtures, and then the second, remaining, HF surface is milled. DHFSlicer uses an efficient coarse-to-fine decomposition process: It first partitions the inputs into maximally coarse blocks that satisfy a local DHF criterion with respect to per-block milling axes, and then cuts each block into well-sized DHF slices. It minimizes milling time and material waste by keeping the slice count small, and maximizing slice height. We validate our method by embedding it within an end-to-end DHF milling pipeline and fabricating objects from slabs of foam, wood, and MDF; demonstrate that using the obtained slices reduces milling time and material waste by 42% on average compared to existing automatic alternatives; and highlight the benefits of DHFSlicer via extensive ablation studies.

Digital fabrication devices are powerful tools for creating tangible reproductions of 3D digital models. Most available printing technologies aim at producing an accurate copy of a tridimensional shape. However, fabrication technologies can also be used to create a stylistic representation of a digital shape. We refer to this class of methods as stylized fabrication methods. These methods abstract geometric and physical features of a given shape to create an unconventional representation, to produce an optical illusion, or to devise a particular interaction with the fabricated model. In this course, we classify and overview this broad and emerging class of approaches and also propose possible directions for future research.

Abstract Acquired 3D point clouds make possible quick modeling of virtual scenes from the real world. With modern 3D capture pipelines, each point sample often comes with additional attributes such as normal vector and color response. Although rendering and processing such data has been extensively studied, little attention has been devoted using the light transport hidden in the recorded per‐sample color response to relight virtual objects in visual effects (VFX) look‐dev or augmented reality (AR) scenarios. Typically, standard relighting environment exploits global environment maps together with a collection of local light probes to reflect the light mood of the real scene on the virtual object. We propose instead a unified spatial approximation of the radiance and visibility relationships present in the scene, in the form of a colored point cloud. To do so, our method relies on two core components: High Dynamic Range (HDR) expansion and real‐time Point‐Based Global Illumination (PBGI). First, since an acquired color point cloud typically comes in Low Dynamic Range (LDR) format, we boost it using a single HDR photo exemplar of the captured scene that can cover part of it. We perform this expansion efficiently by first expanding the dynamic range of a set of renderings of the point cloud and then projecting these renderings on the original cloud. At this stage, we propagate the expansion to the regions not covered by the renderings or with low‐quality dynamic range by solving a Poisson system. Then, at rendering time, we use the resulting HDR point cloud to relight virtual objects, providing a diffuse model of the indirect illumination propagated by the environment. To do so, we design a PBGI algorithm that exploits the GPU's geometry shader stage as well as a new mipmapping operator, tailored for G‐buffers, to achieve real‐time performances. As a result, our method can effectively relight virtual objects exhibiting diffuse and glossy physically‐based materials in real time. Furthermore, it accounts for the spatial embedding of the object within the 3D environment. We evaluate our approach on manufactured scenes to assess the error introduced at every step from the perfect ground truth. We also report experiments with real captured data, covering a range of capture technologies, from active scanning to multiview stereo reconstruction.

We propose a novel technique for the automatic design of molds to cast highly complex shapes. The technique generates composite, two-piece molds. Each mold piece is made up of a hard plastic shell and a flexible silicone part. Thanks to the thin, soft, and smartly shaped silicone part, which is kept in place by a hard plastic shell, we can cast objects of unprecedented complexity. An innovative algorithm based on a volumetric analysis defines the layout of the internal cuts in the silicone mold part. Our approach can robustly handle thin protruding features and intertwined topologies that have caused previous methods to fail. We compare our results with state of the art techniques, and we demonstrate the casting of shapes with extremely complex geometry.

We propose QuadMixer, a novel interactive technique to compose quad mesh components preserving the majority of the original layouts. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. We first perform robust boolean operations on the corresponding triangle meshes. Then we use this result to identify and build new surface patches for small regions neighboring the intersection curves. These blending patches are carefully quadrangulated respecting boundary constraints and stitched back to the untouched parts of the original models. The resulting mesh preserves the designed edge flow that, by construction, is captured and incorporated to the new quads as much as possible. We present our technique in an interactive tool to show its usability and robustness.

Abstract Digital fabrication devices are powerful tools for creating tangible reproductions of 3D digital models. Most available printing technologies aim at producing an accurate copy of a tridimensional shape. However, fabrication technologies can also be used to create a stylistic representation of a digital shape. We refer to this class of methods as ‘stylized fabrication methods’. These methods abstract geometric and physical features of a given shape to create an unconventional representation, to produce an optical illusion or to devise a particular interaction with the fabricated model. In this state‐of‐the‐art report, we classify and overview this broad and emerging class of approaches and also propose possible directions for future research.

Abstract The wide availability of 3D acquisition devices makes viable their use for shape monitoring. The current techniques for the analysis of time‐varying data can efficiently detect actual significant geometric changes and rule out differences due to irrelevant variations (such as sampling, lighting and coverage). On the other hand, the effective visualization of such detected changes can be challenging when we want to show at the same time the original appearance of the 3D model. In this paper, we propose a dynamic technique for the effective visualization of detected differences between two 3D scenes. The presented approach, while retaining the original appearance, allows the user to switch between the two models in a way that enhances the geometric differences that have been detected as significant. Additionally, the same technique is able to visually hides the other negligible, yet visible, variations. The main idea is to use two distinct screen space time‐based interpolation functions for the significant 3D differences and for the small variations to hide. We have validated the proposed approach in a user study on a different class of datasets, proving the objective and subjective effectiveness of the method.

We propose a new method for fabricating digital objects through reusable silicone molds. Molds are generated by casting liquid silicone into custom 3D printed containers called metamolds. Metamolds automatically define the cuts that are needed to extract the cast object from the silicone mold. The shape of metamolds is designed through a novel segmentation technique, which takes into account both geometric and topological constraints involved in the process of mold casting. Our technique is simple, does not require changing the shape or topology of the input objects, and only requires of-the-shelf materials and technologies. We successfully tested our method on a set of challenging examples with complex shapes and rich geometric detail.

We propose FlexMaps, a novel framework for fabricating smooth shapes out of flat, flexible panels with tailored mechanical properties. We start by mapping the 3D surface onto a 2D domain as in traditional UV mapping to design a set of deformable flat panels called FlexMaps. For these panels, we design and obtain specific mechanical properties such that, once they are assembled, the static equilibrium configuration matches the desired 3D shape. FlexMaps can be fabricated from an almost rigid material, such as wood or plastic, and are made flexible in a controlled way by using computationally designed spiraling microstructures.

Abstract Digital fabrication devices exploit basic technologies in order to create tangible reproductions of 3D digital models. Although current 3D printing pipelines still suffer from several restrictions, accuracy in reproduction has reached an excellent level. The manufacturing industry has been the main domain of 3D printing applications over the last decade. Digital fabrication techniques have also been demonstrated to be effective in many other contexts, including the consumer domain. The Cultural Heritage is one of the new application contexts and is an ideal domain to test the flexibility and quality of this new technology. This survey overviews the various fabrication technologies, discussing their strengths, limitations and costs. Various successful uses of 3D printing in the Cultural Heritage are analysed, which should also be useful for other application contexts. We review works that have attempted to extend fabrication technologies in order to deal with the specific issues in the use of digital fabrication in the Cultural Heritage. Finally, we also propose areas for future research.

We propose a novel framework for the computational design of tensegrity structures, which are constructions made of struts and cables, held rigid by continuous tension between the elements. Tensegrities are known to be difficult to design---existing design methods are often restricted to using symmetric or templated configurations, limiting the design space to simple constructions. We introduce an algorithm to automatically create free-form stable tensegrity designs that satisfy both fabrication and geometric constraints, and faithfully approximate input geometric shapes. Our approach sidesteps the usual force-based approach in favor of a geometric optimization on the positions of the elements. Equipped with this formulation, we provide a design framework to explore the highly constrained space of tensegrity structures. We validate our method with simulations and real-world constructions.

Abstract Detecting geometric changes between two 3D captures of the same location performed at different moments is a critical operation for all systems requiring a precise segmentation between change and no‐change regions. Such application scenarios include 3D surface reconstruction, environment monitoring, natural events management and forensic science. Unfortunately, typical 3D scanning setups cannot provide any one‐to‐one mapping between measured samples in static regions: in particular, both extrinsic and intrinsic sensor parameters may vary over time while sensor noise and outliers additionally corrupt the data. In this paper, we adopt a multi‐scale approach to robustly tackle these issues. Starting from two point clouds, we first remove outliers using a probabilistic operator. Then, we detect the actual change using the implicit surface defined by the point clouds under a Growing Least Square reconstruction that, compared to the classical proximity measure, offers a more robust change/no‐change characterization near the temporal intersection of the scans and in the areas exhibiting different sampling density and direction. The resulting classification is enhanced with a spatial reasoning step to solve critical geometric configurations that are common in man‐made environments. We validate our approach on a synthetic test case and on a collection of real data sets acquired using commodity hardware. Finally, we show how 3D reconstruction benefits from the resulting precise change/no‐change segmentation.

Abstract Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field‐coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t‐junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state‐of‐the‐art methods.

We present FlexMolds, a novel computational approach to automatically design flexible, reusable molds that, once 3D printed, allow us to physically fabricate, by means of liquid casting, multiple copies of complex shapes with rich surface details and complex topology. The approach to design such flexible molds is based on a greedy bottom-up search of possible cuts over an object, evaluating for each possible cut the feasibility of the resulting mold. We use a dynamic simulation approach to evaluate candidate molds, providing a heuristic to generate forces that are able to open, detach, and remove a complex mold from the object it surrounds. We have tested the approach with a number of objects with nontrivial shapes and topologies.

Abstract We introduce a framework for the generation of polygonal gridshell architectural structures, whose topology is designed in order to excel in static performances. We start from the analysis of stress on the input surface and we use the resulting tensor field to induce an anisotropic nonEuclidean metric over it. This metric is derived by studying the relation between the stress tensor over a continuous shell and the optimal shape of polygons in a corresponding gridshell. Polygonal meshes with uniform density and isotropic cells under this metric exhibit variable density and anisotropy in Euclidean space, thus achieving a better distribution of the strain energy over their elements. Meshes are further optimized taking into account symmetry and regularity of cells to improve aesthetics. We experiment with quad meshes and hexdominant meshes, demonstrating that our gridshells achieve better static performances than stateoftheart gridshells.

We propose an interactive quadrangulation method based on a large collection of patterns that are learned from models manually designed by artists. The patterns are distilled into compact quadrangulation rules and stored in a database. At run-time, the user draws strokes to define patches and desired edge flows, and the system queries the database to extract fitting patterns to tessellate the sketches' interiors. The quadrangulation patterns are general and can be applied to tessellate large regions while controlling the positions of the singularities and the edge flow. We demonstrate the effectiveness of our algorithm through a series of live retopology sessions and an informal user study with three professional artists.

We introduce elastic textures: a set of parametric, tileable, printable, cubic patterns achieving a broad range of isotropic elastic material properties: the softest pattern is over a thousand times softer than the stiffest, and the Poisson's ratios range from below zero to nearly 0.5. Using a combinatorial search over topologies followed by shape optimization, we explore a wide space of truss-like, symmetric 3D patterns to obtain a small family. This pattern family can be printed without internal support structure on a single-material 3D printer and can be used to fabricate objects with prescribed mechanical behavior. The family can be extended easily to create anisotropic patterns with target orthotropic properties. We demonstrate that our elastic textures are able to achieve a user-supplied varying material property distribution. We also present a material optimization algorithm to choose material properties at each point within an object to best fit a target deformation under a prescribed scenario. We show that, by fabricating these spatially varying materials with elastic textures, the desired behavior is achieved.

Mesh joinery is an innovative method to produce illustrative shape approximations suitable for fabrication. Mesh joinery is capable of producing complex fabricable structures in an efficient and visually pleasing manner. We represent an input geometry as a set of planar pieces arranged to compose a rigid structure, by exploiting an efficient slit mechanism. Since slices are planar, to fabricate them a standard 2D cutting system is enough. We automatically arrange slices according to a smooth cross-field defined over the surface. Cross-fields allow representing global features that characterize the appearance of the shape. Slice placement conforms to specific manufacturing constraints.

Multiview stereo reconstruction methods can provide impressive results in a number of applications. Nevertheless, when trying to apply the state-of-the-art methods in the case of a more structured 3D acquisition, the lack of feedback on the quality of the reconstruction during the photo shooting can be problematic. In this paper we present a framework for the assisted reconstruction from images of real objects. The framework is able to provide, in quasi-real time, a sparse reconstruction of the scene, so that the user is able to spot the missing or problematic parts. Moreover, the framework is able to separate the object of interest from the background and suggests missing points of view to the user, without any previous knowledge of the shape of the scene and the acquisition path. This is obtained by analyzing the sparse reconstruction and the connection between the reconstructed points and the input images. The framework has been tested on a variety of practical cases, and it has proved to be effective not only to obtain more complete reconstructions, but also to reduce the number of images needed and the processing time for dense reconstruction.

Abstract In this work we present a new algorithm for accelerating the colour bilateral filter based on a subsampling strategy working in the spatial domain. The base idea is to use a suitable subset of samples of the entire kernel in order to obtain a good estimation of the exact filter values. The main advantages of the proposed approach are that it has an excellent trade‐off between visual quality and speed‐up, a very low memory overhead is required and it is straightforward to implement on the GPU allowing real‐time filtering. We show different applications of the proposed filter, in particular efficient cross‐bilateral filtering, real‐time edge‐aware image editing and fast video denoising. We compare our method against the state of the art in terms of image quality, time performance and memory usage.

This paper deals with the problem of taking random samples over the surface of a 3D mesh describing and evaluating efficient algorithms for generating different distributions. We discuss first the problem of generating a Monte Carlo distribution in an efficient and practical way avoiding common pitfalls. Then, we propose Constrained Poisson-disk sampling, a new Poisson-disk sampling scheme for polygonal meshes which can be easily tweaked in order to generate customized set of points such as importance sampling or distributions with generic geometric constraints. In particular, two algorithms based on this approach are presented. An in-depth analysis of the frequency characterization and performance of the proposed algorithms are also presented and discussed.

The projection of a photographic data set on a 3D model is a robust and widely applicable way to acquire appearance information of an object. The first step of this procedure is the alignment of the images on the 3D model. While any reconstruction pipeline aims at avoiding misregistration by improving camera calibrations and geometry, in practice a perfect alignment cannot always be reached. Depending on the way multiple camera images are fused on the object surface, remaining misregistrations show up either as ghosting or as discontinuities at transitions from one camera view to another. In this paper we propose a method, based on the computation of Optical Flow between overlapping images, to correct the local misalignment by determining the necessary displacement. The goal is to correct the symptoms of misregistration, instead of searching for a globally consistent mapping, which might not exist. The method scales up well with the size of the data set (both photographic and geometric) and is quite independent of the characteristics of the 3D model (topology cleanliness, parametrization, density). The method is robust and can handle real world cases that have different characteristics: low level geometric details and images that lack enough features for global optimization or manual methods. It can be applied to different mapping strategies, such as texture or per-vertex attribute encoding.

We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing.

We present an automatic method to produce a Catmull-Clark subdivision surface that fits a given input mesh. Its control mesh is coarse and adaptive, and it is obtained by simplifying an initial mesh at high resolution. Simplification occurs progressively via local operators and addresses both quality of surface and faithfulness to the input shape throughout the whole process. The method is robust and performs well on rather complex shapes. Displacement mapping or normal mapping can be applied to approximate the input shape arbitrarily well.

Analyzing either high-frequency shape detail or any other 2D fields (scalar or vector) embedded over a 3D geometry is a complex task, since detaching the detail from the overall shape can be tricky. An alternative approach is to move to the 2D space, resolving shape reasoning to easier image processing techniques. In this paper we propose a novel framework for the analysis of 2D information distributed over 3D geometry, based on a locally smooth parametrization technique that allows us to treat local 3D data in terms of image content. The proposed approach has been implemented as a sketch-based system that allows to design with a few gestures a set of (possibly overlapping) parameterizations of rectangular portions of the surface. We demonstrate that, due to the locality of the parametrization, the distortion is under an acceptable threshold, while discontinuities can be avoided since the parametrized geometry is always homeomorphic to a disk. We show the effectiveness of the proposed technique to solve specific Cultural Heritage (CH) tasks: the analysis of chisel marks over the surface of a unfinished sculpture and the local comparison of multiple photographs mapped over the surface of an artwork. For this very difficult task, we believe that our framework and the corresponding tool are the first steps toward a computer-based shape reasoning system, able to support CH scholars with a medium they are more used to.

Abstract In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle‐to‐Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh.

Conventional browsing of image collections use mechanisms such as thumbnails arranged on a regular grid or on a line, often mounted over a scrollable panel. However, this approach does not scale well with the size of the datasets (number of images). In this paper, we propose a new thumbnail-based interface to browse large collections of images. Our approach is based on weighted centroidal anisotropic Voronoi diagrams. A dynamically changing subset of images is represented by thumbnails and shown on the screen. Thumbnails are shaped like general polygons, to better cover screen space, while still reflecting the original aspect ratios or orientation of the represented images. During the browsing process, thumbnails are dynamically rearranged, reshaped and rescaled. The objective is to devote more screen space (more numerous and larger thumbnails) to the parts of the dataset closer to the current region of interest, and progressively lesser away from it, while still making the dataset visible as a whole. During the entire process, temporal coherence is always maintained. GPU implementation easily guarantees the frame rates needed for fully smooth interactivity.

In this paper, we propose a robust, automatic technique to build a global hi-quality parameterization of a two-manifold triangular mesh. An adaptively chosen 2D domain of the parameterization is built as part of the process. The produced parameterization exhibits very low isometric distortion, because it is globally optimized to preserve both areas and angles. The domain is a collection of equilateral triangular 2D regions enriched with explicit adjacency relationships (it is abstract in the sense that no 3D embedding is necessary). It is tailored to minimize isometric distortion, resulting in excellent parameterization qualities, even when meshes with complex shape and topology are mapped into domains composed of a small number of large continuous regions. Moreover, this domain is, in turn, remapped into a collection of 2D square regions, unlocking many advantages found in quad-based domains (e.g., ease of packing). The technique is tested on a variety of cases, including challenging ones, and compares very favorably with known approaches. An open-source implementation is made available.

Abstract In this paper we present a practical, simple and robust method to acquire the spatially‐varying illumination of a real‐world scene. The basic idea of the proposed method is to acquire the radiance distribution of the scene using high‐dynamic range images of two reflective balls. The use of two light probes instead of a single one allows to estimate, not only the direction and intensity of the light sources, but also the actual position in space of the light sources. To robustly achieve this goal we first rectify the two input spherical images, then, using a region‐based stereo matching algorithm, we establish correspondences and compute the position of each light. The radiance distribution so obtained can be used for augmented reality applications, photo‐realistic rendering and accurate reflectance properties estimation. The accuracy and the effectiveness of the method have been tested by measuring the computed light position and rendering synthetic version of a real object in the same scene. The comparison with standard method that uses a simple spherical lighting environment is also shown.

Abstract We introduce a GPU‐friendly technique that efficiently exploits the highly structured nature of urban environments to ensure rendering quality and interactive performance of city exploration tasks. Central to our approach is a novel discrete representation, called BlockMap, for the efficient encoding and rendering of a small set of textured buildings far from the viewer. A BlockMap compactly represents a set of textured vertical prisms with a bounded on‐screen footprint. BlockMaps are stored into small fixed size texture chunks and efficiently rendered through GPU raycasting. Blockmaps can be seamlessly integrated into hierarchical data structures for interactive rendering of large textured urban models. We illustrate an efficient output‐sensitive framework in which a visibility‐aware traversal of the hierarchy renders components close to the viewer with textured polygons and employs BlockMaps for far away geometry. Our approach provides a bounded size far distance representation of cities, naturally scales with the improving shader technology, and outperforms current state of the art approaches. Its efficiency and generality is demonstrated with the interactive exploration of a large textured model of the city of Paris on a commodity graphics platform.

Abstract We describe a compressed multiresolution representation for supporting interactive rendering of very large planar and spherical terrain surfaces. The technique, called Compressed Batched Dynamic Adaptive Meshes (C‐BDAM), is an extension of the BDAM and P‐BDAM chunked level‐of‐detail hierarchy. In the C‐BDAM approach, all patches share the same regular triangulation connectivity and incrementally encode their vertex attributes using a quantized representation of the difference with respect to values predicted from the coarser level. The structure provides a number of benefits: simplicity of data structures, overall geometric continuity for planar and spherical domains, support for variable resolution input data, management of multiple vertex attributes, efficient compression and fast construction times, ability to support maximum‐error metrics, real‐time decompression and shaded rendering with configurable variable level‐of‐detail extraction, and runtime detail synthesis. The efficiency of the approach and the achieved compression rates are demonstrated on a number of test cases, including the interactive visualization of a 29 gigasample reconstruction of the whole planet Earth created from high resolution SRTM data. Categories and Subject Descriptors (according toACMCCS): I.3.3 [Computer Graphics]: Picture and Image Generation; I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism.

The paper presents a set of combined techniques to enhance the real-time visualization of simple or complex molecules (up to order of 106 atoms) space fill mode. The proposed approach includes an innovative technique for efficient computation and storage of ambient occlusion terms, a small set of GPU accelerated procedural impostors for space-fill and ball-and-stick rendering, and novel edge-cueing techniques. As a result, the user's understanding of the three-dimensional structure under inspection is strongly increased (even for still images), while the rendering still occurs in real time.

The multi triangulation framework (MT) is a very general approach for managing adaptive resolution in triangle meshes. The key idea is arranging mesh fragments at different resolution in a directed acyclic graph (DAG) which encodes the dependencies between fragments, thereby encompassing a wide class of multiresolution approaches that use hierarchies or DAGs with predefined topology. On current architectures, the classic MT is however unfit for real-time rendering, since DAG traversal costs vastly dominate raw rendering costs. In this paper, we redesign the MT framework in a GPU friendly fashion, moving its granularity from triangles to precomputed optimized triangle patches. The patches can be conveniently tri-stripped and stored in secondary memory to be loaded on demand, ready to be sent to the GPU using preferential paths. In this manner, central memory only contains the DAG structure and CPU workload becomes negligible. The major contributions of this work are: a new out-of-core multiresolution framework, that, just like the MT, encompasses a wide class of multiresolution structures; a robust and elegant way to build a well conditioned MT DAG by introducing the concept of V-partitions, that can encompass various state of the art multiresolution algorithms; an efficient multithreaded rendering engine and a general subsystem for the external memory processing and simplification of huge meshes.

Range map registration is still the most time consuming phase in the processing of 3D scanning data. This is because real scanning sets are composed of hundreds of range maps and their registration is still partially manual. We propose a new method to manage complex scan sets acquired by following a regular scanner pose pattern. Our goal is to define an initial adjacency graph by coarsely aligning couples of range maps that we know are partially overlapping thanks to the adopted scanning strategy. For a pair of partially overlapping range maps, our iterative solution locates pairs of correspondent vertices through the computation of a regular n×n kernel which takes into account vertex normals and is defined in the 2D space of the range map (represented in implicit 2D format rather than as a triangle mesh in 3D space). The shape-characterization kernel and the metrics defined give a sufficiently accurate shape matching, which has been proven to fit well the requirements of automatic registration. This initial set of adjacency arcs can then be augmented by the automatic identification of the other significant arcs, by adopting a criterion based on approximate range map overlap computation. With respect to the solutions present in literature, the simplifications and assumptions adopted make our solution specifically oriented to complex 3D scanning campaigns (hundreds of range maps). The proposed method can coarsely register range maps in parallel with the acquisition activity and this is a valuable help in assessing on site the completeness of the sampling of large objects.

We introduce a new texture representation that combines standard sampling, to be bilinearly interpolated in smoothly varying regions, with customizable discontinuities, to model sharp boundaries between these regions. The structure consists of a standard signal texture, plus a second texture we call pinchmap, which encodes discontinuities along generally curved lines; at rendering time the fragment processor efficiently decodes this structure with a single access to each texture. We also present a fully automatic way to compute a pinchmap and signal texture pair, starting from an original high resolution image. The final result on the screen is a comparable visual quality for a fraction of the texture storage and with a negligible impact on performance.

Although in recent years the 3D-scanning field has reached a good level of maturity, it is still far from being perceived by common users as a 3D-photography approach, as simple as standard photography is. The main reason for that is that obtaining good 3D models without human intervention is still very hard. In particular, two problems remain open: automatic registration of single shots and planning of the acquisition session. In this paper we address the second issue and propose a solution to improve the coverage of automatically acquired objects. Rather than searching for the next-best-view in order to minimise the number of acquisitions, we propose a simple and easy-to-implement algorithm limiting our scope to closing gaps (i.e. filling unsampled regions) in roughly acquired models. The idea is very simple: detect holes in the current model and cluster their estimated normals in order to determine new views. Some results are shown to support our approach.

We describe an efficient technique for out-of-core construction and accurate view-dependent visualization of very large surface models. The method uses a regular conformal hierarchy of tetrahedra to spatially partition the model. Each tetrahedral cell contains a precomputed simplified version of the original model, represented using cache coherent indexed strips for fast rendering. The representation is constructed during a fine-to-coarse simplification of the surface contained in diamonds (sets of tetrahedral cells sharing their longest edge). The construction preprocess operates out-of-core and parallelizes nicely. Appropriate boundary constraints are introduced in the simplification to ensure that all conforming selective subdivisions of the tetrahedron hierarchy lead to correctly matching surface patches. For each frame at runtime, the hierarchy is traversed coarse-to-fine to select diamonds of the appropriate resolution given the view parameters. The resulting system can interatively render high quality views of out-of-core models of hundreds of millions of triangles at over 40Hz (or 70M triangles/s) on current commodity graphics platforms.

Valuable 3D graphical models, such as high-resolution digital scans of cultural heritage objects, may require protection to prevent piracy or misuse, while still allowing for interactive display and manipulation by a widespread audience. We have investigated techniques for protecting 3D graphics content, and we have developed a remote rendering system suitable for sharing archives of 3D models while protecting the 3D geometry from unauthorized extraction. The system consists of a 3D viewer client that includes low-resolution versions of the 3D models, and a rendering server that renders and returns images of high-resolution models according to client requests. The server implements a number of defenses to guard against 3D reconstruction attacks, such as monitoring and limiting request streams, and slightly perturbing and distorting the rendered images. We consider several possible types of reconstruction attacks on such a rendering server, and we examine how these attacks can be defended against without excessively compromising the interactive experience for non-malicious users.

Standard texture mapping of real-world meshes suffers from the presence of seams that need to be introduced in order to avoid excessive distortions and to make the topology of the mesh compatible to the one of the texture domain. In contrast, cube maps provide a mechanism that could be used for seamless texture mapping with low distortion, but only if the object roughly resembles a cube. We extend this concept to arbitrary meshes by using as texture domain the surface of a polycube whose shape is similar to that of the given mesh. Our approach leads to a seamless texture mapping method that is simple enough to be implemented in currently available graphics hardware.

In this paper, we address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets.

We describe an efficient technique for out-of-core management and interactive rendering of planet sized textured terrain surfaces. The technique, called planet-sized batched dynamic adaptive meshes (P-BDAM), extends the BDAM approach by using as basic primitive a general triangulation of points on a displaced triangle. The proposed framework introduces several advances with respect to the state of the art: thanks to a batched host-to-graphics communication model, we outperform current adaptive tessellation solutions in terms of rendering speed; we guarantee overall geometric continuity, exploiting programmable graphics hardware to cope with the accuracy issues introduced by single precision floating points; we exploit a compressed out of core representation and speculative prefetching for hiding disk latency during rendering of out-of-core data; we efficiently construct high quality simplified representations with a novel distributed out of core simplification algorithm working on a standard PC network.

In this paper we propose a new method for the creation of normal maps for recovering the detail on simplified meshes and a set of objective techniques to metrically evaluate the quality of different recovering techniques. The proposed techniques, that automatically produces a normal-map texture for a simple 3D model that "imitates" the high frequency detail originally present in a second, much higher resolution one, is based on the computation of per-texel visibility and self-occlusion information. This information is used to define a point-to-point correspondence between simplified and hires meshes. Moreover, we introduce a number of criteria for measuring the quality (visual or otherwise) of a given mapping method, and provide efficient algorithms to implement them. Lastly, we apply them to rate different mapping methods, including the widely used ones and the new one proposed here.

Abstract This paper describes an efficient technique for out‐of‐core rendering and management of large textured terrainsurfaces. The technique, called Batched Dynamic Adaptive Meshes (BDAM), is based on a paired tree structure:a tiled quadtree for texture data and a pair of bintrees of small triangular patches for the geometry. These smallpatches are TINs and are constructed and optimized off‐line with high quality simplification and tristrippingalgorithms. Hierarchical view frustum culling and view‐dependent texture and geometry refinement is performedat each frame through a stateless traversal algorithm. Thanks to the batched CPU/GPU communication model,the proposed technique is not processor intensive and fully harnesses the power of current graphics hardware.Both preprocessing and rendering exploit out‐of‐core techniques to be fully scalable and to manage large terraindatasets. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture and Image Generation;I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism.

Very large triangle meshes, i.e., meshes composed of millions of faces, are becoming common in many applications. Obviously, processing, rendering, transmission, and archiving of these meshes are not simple tasks. Mesh simplification and LOD management are a rather mature technology that, in many cases, can efficiently manage complex data. But, only a few available systems can manage meshes characterized by a huge size: RAM size is often a severe bottleneck. In this paper, we present a data structure called Octree-based External Memory Mesh (OEMM). It supports external memory management of complex meshes, loading dynamically in main memory only the selected sections and preserving data consistency during local updates. The functionalities implemented on this data structure (simplification, detail preservation, mesh editing, visualization, and inspection) can be applied to huge triangles meshes on low-cost PC platforms. The time overhead due to the external memory management is affordable. Results of the test of our system on complex meshes are presented.

The paper presents a simple and efficient algorithm for the removal of small topological inconsistencies and high frequency details from surface models. The method, called marching intersections (MI), adopts a volumetric approach and acts as a resampling filter. All the intersection points between the input model and the lines of a user selected 3D reference grid are located and then, beginning from these intersections, an output surface is reconstructed. MI, which presents good characteristics in terms of efficiency, compactness, and quality of the output models, can be also used: for the conversion between different representation schemes; to perform logical operations on geometric models; for the topological simplification of surfaces; and for the simplification of huge meshes, i.e. meshes too large to be allocated in main memory during the simplification process. All these aspects are discussed in the paper and timing and graphic results are presented.

Multi-resolution representations are widely used in many data visualization contexts and applications. The adoption of a multi-resolution approach provides the optimal management of a data representation, using at each instant of time a level of detail that is more adequate for the given action or task to be performed. Recently, multi-resolution has also been introduced into the interactive physically-based simulation of deformable objects (e.g. in virtual surgery applications). In these applications, the processing resources available are often insufficient and pose a critical constraint. The adoption of multi-resolution allows one to improve the accuracy of the simulation in the proximity of the action focus while maintaining computations under a given bound. In this particular context, the user should be able to perform cuts in the object. The problem is that most multi-resolution models need a pre-processing phase in which the data structure is constructed. Such a construction strictly depends on the topology of the object, which is supposed to be invariable. We propose a new approach for the dynamic topological modification of a multi-resolution model, which allows easy updating of the multi-resolution data structure (based on the multi-resolution triangulation framework), and efficient decomposition of the cells intersected by the cut. With respect to previous methods, our solution supports a much lower degree of fragmentation of the decomposition and very short processing times, due to the design of a lookup table (LUT) based splitting solution.

The techniques for reducing the size of a volume dataset by preserving both the geometrical/topological shape and the information encoded in an attached scalar field are attracting growing interest. Given the framework of incremental 3D mesh simplification based on edge collapse, we propose an approach for the integrated evaluation of the error introduced by both the modification of the domain and the approximation of the field of the original volume dataset. We present and compare various techniques to evaluate the approximation error or to produce a sound prediction. A flexible simplification tool has been implemented, which provides a different degree of accuracy and computational efficiency for the selection of the edge to be collapsed. Techniques for preventing a geometric or topological degeneration of the mesh are also presented.

Performing a really interactive and physically‐based simulation of complex soft objects is still an open problem in computer animation/simulation. Given the application domain of virtual surgery training, a complete model should be quite realistic, interactive and should enable the user to modify the topology of the objects. Recent papers propose the adoption of multiresolution techniques to optimize time performance by representing at high resolution only the object parts considered more important or critical. The speed up obtainable at simulation time are counterbalanced by the need of a preprocessing phase strongly dependent on the topology of the object, with the drawback that performing dynamic topology modification becomes a prohibitive issue. In this paper we present an approach that couples multiresolution and topological modifications, based on the adoption of a particle systems approach to the physical simulation. Our approach is based on a tetrahedral decomposition of the space, chosen both for its suitability to support a particle system and for the ready availability of many techniques recently proposed for the simplification and multiresolution management of 3D simplicial decompositions. The multiresolution simulation system is designed to ensure the required speedup and to support dynamic changes of the topology, e.g. due to cuts or lacerations of the represented tissue.

We present a new technique to render in real time objects which have part of their high frequency geometric detail encoded in bump maps. It is based on the quantization of normal‐maps, and achieves excellent result both in rendering time and rendering quality, with respect to other alternative methods. The method proposed also allows to add many interesting visual effects, even for object with large bumb maps, including non‐s rendering, chrome effects, shading under multiple lights, rendering of different materials within a single object, specular reflections and others. Moreover, the implementation of the method is not complex and can be eased by software reuse.

The paper addresses the problem of the representation of three-dimensional works of art (e.g. sculptures, architectural elements, vases, etc.) in a web-based environment. Specifically, we propose a system for the visual presentation of the 3D results of a standard SQL query to distributed archives. The system solves the general problem of the remote visualization of dynamic result sets on the Internet using standard and low cost processing architectures. It provides the user with an innovative visual metaphor for the analysis and investigation of the objects presented. Moreover, the system has been designed to provide capabilities which go beyond visualization (e.g. manipulation), and further extensions are possible. We describe the methodologies used for the acquisition, storing, and manipulation of 3D artistic objects together with details on the system's implementation in a web environment, using the VRML2.0 specification language.

Many sophisticated solutions have been proposed to reduce the geometric complexity of 3D meshes. A problem studied less often is how to preserve on a simplified mesh the detail (e.g., color, high frequency shape detail, scalar fields, etc.) which is encoded in the original mesh. We present a general approach for preserving detail on simplified meshes. The detail (or high frequency information) lost after simplification is encoded through texture or bump maps. The original contribution is that preservation is performed after simplification, by building set of triangular texture patches that are then packed in a single texture map. Each simplified mesh face is sampled to build the associated triangular texture patch; a new method for storing this set of texture patches into a standard rectangular texture is presented and discussed. Our detail preserving approach makes no assumptions about the simplification process adopted to reduce mesh complexity and allows highly efficient rendering. The solution is very general, allowing preservation of any attribute value defined on the high resolution mesh. We also describe an alternative application: the conversion of 3D models with 3D static procedural textures into standard 3D models with 2D textures.

This paper presents a new tool, Metro, designed to compensate for a deficiency in many simplification methods proposed in literature. Metro allows one to compare the difference between a pair of surfaces (e.g. a triangulated mesh and its simplified representation) by adopting a surface sampling approach. It has been designed as a highly general tool, and it does no assumption on the particular approach used to build the simplified representation. It returns both numerical results (meshes areas and volumes, maximum and mean error, etc.) and visual results, by coloring the input surface according to the approximation error.

The interval tree is an optimally efficient search structure proposed by Edelsbrunner (1980) to retrieve intervals on the real line that contain a given query value. We propose the application of such a data structure to the fast location of cells intersected by an isosurface in a volume dataset. The resulting search method can be applied to both structured and unstructured volume datasets, and it can be applied incrementally to exploit coherence between isosurfaces. We also address issues of storage requirements, and operations other than the location of cells, whose impact is relevant in the whole isosurface extraction task. In the case of unstructured grids, the overhead, due to the search structure, is compatible with the storage cost of the dataset, and local coherence in the computation of isosurface patches is exploited through a hash table. In the case of a structured dataset, a new conceptual organization is adopted, called the chess-board approach, which exploits the regular structure of the dataset to reduce memory usage and to exploit local coherence. In both cases, efficiency in the computation of surface normals on the isosurface is obtained by a precomputation of the gradients at the vertices of the mesh. Experiments on different kinds of input show that the practical performance of the method reflects its theoretical optimality.

A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task and to the performance of a specific hardware platform. Representations at different resolutions can be used together to further enhance interaction and performance through progressive and multiresolution rendering.

Abstract The paper deals with the parallelization of Delaunay triangulation, a widely used space partitioning technique. Two parallel implementations of a three‐dimensional incremental construction algorithm are presented. The first is based on the decomposition of the spatial domain, while the second relies on the master‐slaves approach. Both parallelization strategies are evaluated, stressing practical issues rather than theoretical complexity. We report on the exploitation of two different parallel environments: a tightly coupled distributed memory MIMD architecture and a network of workstations co‐operating under the Linda environment Then, a third hybrid solution is proposed, specifically addressed to the exploitation of higher parallelism. It combines the other two solutions by grouping the processing nodes of the multicomputer into clusters and by exploiting parallelism at two different levels.

Abstract How to render very complex datasets, and yet maintain interactive response times, is a hot topic in computer graphics. The MagicSphere idea originated as a solution to this problem, but its potential goes much further than this original scope. In fact, it has been designed as a very generical 3D widget: it defines a spherical volume of interest in the dataset modeling space. Then, several filters can be associated with the Magicsphere, which apply different visualization modalities to the data contained in the volume of interest. The visualization of multi‐resolution datasets is selected here as a case study and an ad hoc filter has been designed, the MultiRes filter. Some results of a prototipal implementation are presented and discussed.

Abstract The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity. Two parallel implementations are presented. The first one is built on De Wall, an Ed triangulator based on an original interpretation of the divide & conquer paradigm. The second is based on an incremental construction algorithm. The parallelization strategies are presented and evaluated. The target parallel machine is a distributed computing environment, composed of coarse grain processing nodes. Results of first implementations are reported and compared with the performance of the serial versions running on a Unix workstation.