We present a method to automatically approximate a given surface with a small set of patches, each being a developable ruled surface featuring long-ruling lines. These construction primitives are attractive for their inherent ease of fabrication by cutting and folding inextensible materials and for their favo rable structural properties. Our algorithm strikes a good tradeoff between the simplicity of produced designs (in terms of the number and shapes of the patches) and approximation quality. To this end, it is guided by a smooth curvature-aligned cross-field. Compared to traditional methods, we rely on final discretization steps to ensure the developability of the ruled surfaces and produce a fabricable layout, bypassing the need to enforce that the strips are strictly developable in continuous settings (which requires difficulty in enforcing geometric conditions). We demonstrate the effectiveness of the proposed algorithm by producing several viable designs and using them to physically fabricate various physical objects.

Abstract In this short paper, we analyze the problem of finding the triangular barycentric coordinates of an interpolated ray hitting a given point. This task, which we term theinverse barycentric displacement problem, is general and useful in geometry processing and computer graphics. Concrete applications of the solution include the construction of displacement maps and texture baking. We derive the set of complete, closed-form solutions and discuss the number and existence of solutions. We close with a discussion of implementation-oriented optimizations and a few example applications.

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.

We present an efficient algorithm to approximate the Automatic Color Equalization (ACE) of an input color image, with an upper-bound on the introduced approximation error. The computation is based on Summed Area Tables and a carefully optimized partitioning of the plane into rectangular regions, resulting in a pseudo-linear asymptotic complexity with the number of pixels (against a quadratic straightforward computation of ACE). Our experimental evaluation confirms both the speedups and high accuracy, reaching lower approximation errors than existing approaches. We provide a publicly available reference implementation of our algorithm.

Micro-meshes (μ-meshes) are a new structured graphics primitive supporting a large increase in geometric fidelity, without commensurate memory and run-time processing costs, consisting of a base mesh enriched by a displacement map. A new generation of GPUs supports this structure with native hardware μ-mesh ray-tracing, that leverages a self-bounding, compressed displacement mapping scheme to achieve these efficiencies. In this paper, we present anautomatic method to convert an existing multi-million triangle mesh into this compact format, unlocking the advantages of the data representation for a large number of scenarios. We identify the requirements for high-quality μ-meshes, and show how existing re-meshing and displacement-map baking tools are ill-suited for their generation. Our method is based on a simplification scheme tailored to the generation of high-quality base meshes , optimized for tessellation and displacement sampling, in conjunction with algorithms for determining displacement vectors to control the direction and range of displacements. We also explore the optimization of μ-meshes for texture maps and the representation of boundaries. We demonstrate our method with extensive batch processing, converting an existing collection of high-resolution scanned models to the micro-mesh representation, providing an open-source reference implementation, and, as additional material, the data and an inspection tool.

Abstract Volumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. Still, their construction bears several additional challenges compared to boundary‐based representations. Tetrahedral meshes and (pure) hex‐meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hex‐meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. Hex‐dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. In this work, we introduce a strict subset of general hex‐dominant meshes, which we term ‘at‐most‐hexa meshes’, in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. We exemplify the ease of construction of at‐most‐hexa meshes by proposing a frugal and straightforward method to generate high‐quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre‐computations and can start directly from surfaces or samples. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We introduce specialized operations on the three‐dimensional graph structure to enforce consistency during the relaxation. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes.

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.

Knitting can efficiently fabricate stretchable and durable soft surfaces. These surfaces are often designed to be worn on solid objects as covers, garments, and accessories. Given a 3D model, we consider a knit for it wearable if the knit not only reproduces the shape of the 3D model but also can be put on and taken off from the model without deforming the model. This "wearability" places additional constraints on surface design and fabrication, which existing machine knitting approaches do not take into account. We introduce the first practical automatic pipeline to generate knit designs that are both wearable and machine knittable. Our pipeline handles knittability and wearability with two separate modules that run in parallel. Specifically, given a 3D object and its corresponding 3D garment surface, our approach first converts the garment surface into a topological disc by introducing a set of cuts. The resulting cut surface is then fed into a physically-based unclothing simulation module to ensure the garment's wearability over the object. The unclothing simulation determines which of the previously introduced cuts could be sewn permanently without impacting wearability. Concurrently, the cut surface is converted into an anisotropic stitch mesh. Then, our novel, stochastic, any-time flat-knitting scheduler generates fabrication instructions for an industrial knitting machine. Finally, we fabricate the garment and manually assemble it into one complete covering worn by the target object. We demonstrate our method's robustness and knitting efficiency by fabricating models with various topological and geometric complexities. Further, we show that our method can be incorporated into a knitting design tool for creating knitted garments with customized patterns.

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.

Abstract Secondary animation effects are essential for liveliness. We propose a simple, real‐time solution for adding them on top of standard skinning, enabling artist‐driven stylization of skeletal motion. Our method takes a standard skeleton animation as input, along with a skin mesh and rig weights. It then derives per‐vertex deformations from the different linear and angular velocities along the skeletal hierarchy. We highlight two specific applications of this general framework, namely the cartoon‐like “squashy” and “floppy” effects, achieved from specific combinations of velocity terms. As our results show, combining these effects enables to mimic, enhance and stylize physical‐looking behaviours within a standard animation pipeline, for arbitrary skinned characters. Interactive on CPU, our method allows for GPU implementation, yielding real‐time performances even on large meshes. Animator control is supported through a simple interface toolkit, enabling to refine the desired type and magnitude of deformation at relevant vertices by simply painting weights. The resulting rigged character automatically responds to new skeletal animation, without further input.

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 The intrinsic problems of texture mapping, regarding its difficulties in content creation and the visual artifacts it causes in rendering, are well‐known, but often considered unavoidable. In this state of the art report, we discuss various radically different ways to rethink texture mapping that have been proposed over the decades, each offering different advantages and trade‐offs. We provide a brief description of each alternative texturing method along with an evaluation of its strengths and weaknesses in terms of applicability, usability, filtering quality, performance, and potential implementation related challenges.

We introduce a practical pipeline to create UV T-layouts for real-world quad dominant semi-regular meshes. Our algorithm creates large rectangular patches by relaxing the notion of motorcycle graphs and making it insensitive to local irregularities in the mesh structure such as non-quad elements, redundant irregular vertices, T-junctions, and others. Each surface patch, which can contain multiple singularities and/or polygonal elements, is mapped to an axis-aligned rectangle, leading to a simple and efficient UV layout, which is ideal for texture mapping (allowing for mipmapping and artifact-free bilinear interpolation). We demonstrate that our algorithm is an ideal solution for both recent semi-regular, quad-dominant meshing methods, and for the low-poly meshes typically used in games and movies.

Implicit models can be combined by using composition operators; functions that determine the resulting shape. Recently, gradient-based composition operators have been used to express a variety of behaviours including smooth transitions, sharp edges, contact surfaces, bulging, or any combinations. The problem for designers is that building new operators is a complex task that requires specialized technical knowledge. In this work, we introduce an automatic method for deriving a gradient-based implicit operator from 2D drawings that prototype the intended visual behaviour. To solve this inverse problem, in which a shape defines a function, we introduce a general template for implicit operators. A user's sketch is interpreted as samples in the 3D operator's domain. We fit the template to the samples with a non-rigid registration approach. The process works at interactive rates and can accommodate successive refinements by the user. The final result can be applied to 3D surfaces as well as to 2D shapes. Our method is able to replicate the effect of any blending operator presented in the literature, as well as generating new ones such as non-commutative operators. We demonstrate the usability of our method with examples in font-design, collision-response modeling, implicit skinning, and complex shape design.

We propose a robust and efficient field-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding fields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The field design phase of our method relies on a compact quaternionic representation of volumetric octa-fields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses field-guided mesh simplification to convert the optimized fields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the benefits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results.

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.

We propose a UV mapping algorithm that jointly optimizes for cuts and distortion, sidestepping heuristics for placing the cuts. The energy we minimize is a state-of-the-art geometric distortion measure, generalized to take seams into account. Our algorithm is designed to support an interactive workflow: it optimizes UV maps on the fly, while the user can interactively move vertices, cut mesh parts, join seams, separate overlapping regions, and control the placement of the parameterization patches in the UV space. Our UV maps are of high quality in terms of both geometric distortion and cut placement, and compare favorably to those designed with traditional modeling tools. The UV maps can be created in a fraction of the time as existing methods, since our algorithm drastically alleviates the trial-and-error, iterative procedures that plague traditional UV mapping approaches.

Today's 3D scanning pipelines can be classified into two overarching categories: offline, high accuracy methods that rely on global optimization to reconstruct complex scenes with hundreds of millions of samples, and online methods that produce real-time but low-quality output, usually from structure-from-motion or depth sensors. The method proposed in this paper is the first to combine the benefits of both approaches, supporting online reconstruction of scenes with hundreds of millions of samples from high-resolution sensing modalities such as structured light or laser scanners. The key property of our algorithm is that it sidesteps the signed-distance computation of classical reconstruction techniques in favor of direct filtering, parametrization, and mesh and texture extraction. All of these steps can be realized using only weak notions of spatial neighborhoods, which allows for an implementation that scales approximately linearly with the size of each dataset that is integrated into a partial reconstruction. Combined, these algorithmic differences enable a drastically more efficient output-driven interactive scanning and reconstruction workflow, where the user is able to see the final quality field-aligned textured mesh during the entirety of the scanning procedure. Holes or parts with registration problems are displayed in real-time to the user and can be easily resolved by adding further localized scans, or by adjusting the input point cloud using our interactive editing tools with immediate visual feedback on the output mesh. We demonstrate the effectiveness of our algorithm in conjunction with a state-of-the-art structured light scanner and optical tracking system and test it on a large variety of challenging models.

Collaborative systems are well established solutions for sharing work among people. In computer graphics these workflows are still not well established, compared to what is done for text writing or software development. Usually artists work alone and share their final models by sending files. In this paper we present a system for collaborative 3D digital sculpting. In our prototype, multiple artists concurrently sculpt a polygonal mesh on their local machines by changing its vertex properties, such as positions and material BRDFs. Our system shares the artists' edits automatically and seamlessly merges these edits even when they happen on the same region of the surface. We propose a merge algorithm that is fast-enough for seamless collaboration, respects users' edits as much as possible, can support any sculpting operation, and works for both geometry and appearance modifications. Since in sculpting artists alternatively perform fine adjustments and large scale modifications, our algorithm is based on a multiresolution edit representation that handles concurrent overlapping edits at different scales. We tested our algorithm by modeling meshes collaboratively in different sculpting sessions and found that our algorithm outperforms prior works on collaborative mesh editing in all cases.

UV-maps are required in order to apply a 2D texture over a 3D model. Conventional UV-maps are defined by an assignment of uv positions to mesh vertices. We present an alternative representation, volume-encoded UV-maps, in which each point on the surface is mapped to a uv position which is solely a function of its 3D position. This function is tailored for a target surface: its restriction to the surface is a parametrization exhibiting high quality, e.g. in terms of angle and area preservation; and, near the surface, it is almost constant for small orthogonal displacements. The representation is applicable to a wide range of shapes and UV-maps, and unlocks several key advantages: it removes the need to duplicate vertices in the mesh to encode cuts in the map; it makes the UV-map representation independent from the meshing of the surface; the same texture, and even the same UV-map, can be shared by multiple geometrically similar models (e.g. all levels of a LoD pyramid); UV-maps can be applied to representations other than polygonal meshes, like point clouds or set of registered range-maps. Our schema is cheap on GPU computational and memory resources, requiring only a single, cache-coherent indirection to a small volumetric texture per fragment. We also provide an algorithm to construct a volume-encoded UV-map given a target surface.

Abstract In the digital world, assigning arbitrary colors to an object is a simple operation thanks to texture mapping. However, in the real world, the same basic function of applying colors onto an object is far from trivial. One can specify colors during the fabrication process using a color 3D printer, but this does not apply to already existing objects. Paint and decals can be used during post‐fabrication, but they are challenging to apply on complex shapes. In this paper, we develop a method to enable texture mapping of physical objects, that is, we allow one to map an arbitrary color image onto a three‐dimensional object. Our approach builds upon hydrographics, a technique to transfer pigments printed on a sheet of polymer onto curved surfaces. We first describe a setup that makes the traditional water transfer printing process more accurate and consistent across prints. We then simulate the transfer process using a specialized parameterization to estimate the mapping between the planar color map and the object surface. We demonstrate that our approach enables the application of detailed color maps onto complex shapes such as 3D models of faces and anatomical casts.

We present a novel approach to remesh a surface into an isotropic triangular or quad-dominant mesh using a unified local smoothing operator that optimizes both the edge orientations and vertex positions in the output mesh. Our algorithm produces meshes with high isotropy while naturally aligning and snapping edges to sharp features. The method is simple to implement and parallelize, and it can process a variety of input surface representations, such as point clouds, range scans and triangle meshes. Our full pipeline executes instantly (less than a second) on meshes with hundreds of thousands of faces, enabling new types of interactive workflows. Since our algorithm avoids any global optimization, and its key steps scale linearly with input size, we are able to process extremely large meshes and point clouds, with sizes exceeding several hundred million elements. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexity and provide our cross-platform reference implementation in the supplemental material.

The usability of hexahedral meshes depends on the degree to which the shape of their elements deviates from a perfect cube; a single concave, or inverted element makes a mesh unusable. While a range of methods exist for discretizing 3D objects with an initial topologically suitable hex mesh, their output meshes frequently contain poorly shaped and even inverted elements, requiring a further quality optimization step. We introduce a novel framework for optimizing hex-mesh quality capable of generating inversion-free high-quality meshes from such poor initial inputs. We recast hex quality improvement as an optimization of the shape of overlapping cones, or unions, of tetrahedra surrounding every directed edge in the hex mesh, and show the two to be equivalent. We then formulate cone shape optimization as a sequence of convex quadratic optimization problems, where hex convexity is encoded via simple linear inequality constraints. As this solution space may be empty, we therefore present an alternate formulation which allows the solver to proceed even when constraints cannot be satisfied exactly. We iteratively improve mesh element quality by solving at each step a set of local, per-cone, convex constrained optimization problems, followed by a global energy minimization step which reconciles these local solutions. This latter method provides no theoretical guarantees on the solution but produces inversion-free, high quality meshes in practice. We demonstrate the robustness of our framework by optimizing numerous poor quality input meshes generated using a variety of initial meshing methods and producing high-quality inversion-free meshes in each case. We further validate our algorithm by comparing it against previous work, and demonstrate a significant improvement in both worst and average element quality.

Starting from the triangle mesh of a digital shape, that is, mainly an articulated object, we produce a coarse quad layout that can be used in character modeling and animation. Our quad layout follows the intrinsic object structure described by its curve skeleton; it contains few irregular vertices of low degree; it can be immediately refined into a semiregular quad mesh; it provides a structured domain for UV mapping and parametrization. Our method is fast, one-click, and does not require any parameter setting. The user can steer and refine the process through simple interactive tools during the construction of the quad layout.

Abstract In the context of real‐time, GPU‐based rendering of animated skinned meshes, we propose a new algorithm to compute surface normals with minimal overhead both in terms of the memory footprint and the required per‐vertex operations. By accounting for the variation of the skinning weights over the surface, we achieve a higher visual quality compared to the standard approximation ubiquitously used in video‐game engines and other real‐time applications. Our method supports Linear Blend Skinning and Dual Quaternion Skinning. We demonstrate the advantages of our technique on a variety of datasets and provide a complete open‐source implementation, including GLSL shaders.

We introduce frame fields, which are a non-orthogonal and non-unit-length generalization of cross fields. Frame fields represent smoothly varying linear transformations on tangent spaces of a surface. We propose an algorithm to create discrete, dense frame fields that satisfy a sparse set of constraints. By computing a surface deformation that warps a frame field into a cross field, we generalize existing quadrangulation algorithms to generate anisotropic and non-uniform quad meshes whose elements shapes match the frame field. With this, our framework enables users to control not only the alignment but also the density and anisotropy of the elements' distribution, resulting in high-quality adaptive quad meshing.

Abstract Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.

We present a method to globally parameterize a surface represented by height maps over a set of planes (range images). In contrast to other parametrization techniques, we do not start with a manifold mesh. The parametrization we compute defines a manifold structure, it is seamless and globally smooth, can be aligned to geometric features and shows good quality in terms of angle and area preservation, comparable to current parametrization techniques for meshes. Computing such global seamless parametrization makes it possible to perform quad remeshing, texture mapping and texture synthesis and many other types of geometry processing operations. Our approach is based on a formulation of the Poisson equation on a manifold structure defined for the surface by the range images. Construction of such global parametrization requires only a way to project surface data onto a set of planes, and can be applied directly to implicit surfaces, nonmanifold surfaces, very large meshes, and collections of range scans. We demonstrate application of our technique to all these geometry types.

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.

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.

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.

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.

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 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.

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.