We propose a novel method to reuse panels from existing architectural structures by rearranging elements from a source structure to cover a given tessellation on a target surface. The method alternates between a sequence of global optimization steps, which determine the optimal panel assignment, and smooth deformation stages, which adapt the panels that cannot be directly reused to satisfy the new constraints. During the rearrangement process, adjacent panels on the resulting surface may exhibit limited mismatches, and the reconstructed surface may deviate from the target shape. Both effects are explicitly controlled by user-specified bounds on the allowable panel discrepancy and geometric deviation. We demonstrate the effectiveness of the proposed pipeline on several practical examples, including triangular, quadrilateral, and hexagonal tessellations.

We propose a novel method to automatically approximate a free-form surface using a set of near developable patches that form a tensile-like structure when anchored at a sparse set of points. These structures are appealing for their ability to span large areas with low material cost and structural weight, while also offering strong aesthetic potential. Our algorithm strikes a balance between approximation accuracy, patch simplicity, and visual quality, while ensuring manufacturability and structural feasibility. The layout is guided by a curvature field and refined through a combinatorial process that incrementally adds patches until performance and fabrication constraints are met. Redundant elements are then removed to improve clarity and elegance.

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.

We present a method to approximate free-form surfaces using assemblies of rotational patches for architectural rationalization. Rotational surface patches inherently allow for the simultaneous repetition of multiple building elements along the arc direction. By assembling multiple patches, we can create diverse free-form-like geometries to satisfy broad design intents, while preserving local symmetry to enable cost-effective element fabrication. The main challenge lies in the strict constraint of maintaining local rotational symmetry, while ensuring the final tessellated form is seamless, smooth, and closely resembles the target surface. To address this, we propose a patch layout creation approach that segments the input surface into patches, resembling untrimmed rotational patches within a prescribed error threshold. Additionally, we develop a B-spline-based optimization framework to refine the fitted rotational patches for smooth connections and faithful surface approximation. To facilitate practical architectural applications, we provide a post-processing tool that converts the discrete patch assembly into a seamless, smooth quad mesh composed of locally repeated elements. We demonstrate that our approach is applicable to a variety of free-form surfaces, including those that mimic iconic architectural designs, and can address various practical requirements for a wide range of application scenarios.

Free-form structures are highly valued for their aesthetic appeal in architecture, but they typically comprise panels of many different shapes, which can pose great challenges for building construction. In this study, we aim to address this issue by proposing a novel clustering-optimization method to reduce the number of different n-gonal faces in free-form surface approximations. The method partitions the faces into several groups of similar shapes through clustering and transforms the ones within each group toward congruent forms through optimization. By utilizing this approach, the number of geometrically different panels can be reduced while also satisfying a user-specified error threshold. The potential practical application of this method is demonstrated by redesigning the façade of a real architectural project to achieve cost-effective solutions.

Abstract Garment alteration is a practical technique to adapt an existing garment to fit a target body shape. Typically executed by skilled tailors, this process involves a series of strategic fabric operations—removing or adding material—to achieve the desired fit on a target body. We propose an innovative approach to automate this process by computing a set of practically feasible modifications that adapt an existing garment to fit a different body shape. We first assess the garment's fit on a reference body; then, we replicate this fit on the target by deriving a set of pattern modifications via a linear program. We compute these alterations by employing an iterative process that alternates between global geometric optimization and physical simulation. Our method utilizes geometry‐based simulation of woven fabric's anisotropic behavior, accounts for tailoring details like seam matching, and incorporates elements such as darts or gussets. We validate our technique by producing digital and physical garments, demonstrating practical and achievable alterations.

We propose a novel, cost-effective soft sensor capable of detecting contact force, multiple touch points, and reflecting sensor interaction in real-time with a 3D virtual surface representation. Our fabrication process has been optimized for cost efficiency through careful material selection, utilization of automated machinery, and low-cost hardware. The sensor can be easily replicated without the need for complex laboratory equipment. The sensor employs trained neural network models for real-time signal translation into localization, force measurement, and deformation mapping. We have also developed an efficient data collection system that captures accurate 2D localization, force measurement, and 3D surface data to generate a high-quality pre-validated data set. This data set is filtered using prior knowledge before being fed to two neural network models. Our interactive prototype demonstrates the stability and accuracy of the low-cost soft sensor, delivering reliable results in both single-point and multi-point contact scenarios.

Abstract We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box‐model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non‐conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally‐provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid‐based meshing, such as mixing of 3‐refinement, 2‐refinement, and face‐refinement, and using templated topological bridges to enforce on‐the‐fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques.

In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post-processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.

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.

We propose a method for computing a sewing pattern of a given 3D garment model. Our algorithm segments an input 3D garment shape into patches and computes their 2D parameterization, resulting in pattern pieces that can be cut out of fabric and sewn together to manufacture the garment. Unlike the general state-of-the-art approaches for surface cutting and flattening, our method explicitly targets garment fabrication. It accounts for the unique properties and constraints of tailoring, such as seam symmetry, the usage of darts, fabric grain alignment, and a flattening distortion measure that models woven fabric deformation, respecting its anisotropic behavior. We bootstrap a recent patch layout approach developed for quadrilateral remeshing and adapt it to the purpose of computational pattern making, ensuring that the deformation of each pattern piece stays within prescribed bounds of cloth stress. While our algorithm can automatically produce the sewing patterns, it is fast enough to admit user input to creatively iterate on the pattern design. Our method can take several target poses of the 3D garment into account and integrate them into the sewing pattern design. We demonstrate results on both skintight and loose garments, showcasing the versatile application possibilities of our approach.

Abstract We introduce a novel geometry‐processing pipeline to guide the fabrication of complex shapes from a single block of material using 4‐axis CNC milling machines. This setup extends classical 3‐axis CNC machining with an extra degree of freedom to rotate the object around a fixed axis. The first step of our pipeline identifies the rotation axis that maximizes the overall fabrication accuracy. Then we identify two height‐field regions at the rotation axis's extremes used to secure the block on the rotation tool. We segment the remaining portion of the mesh into a set of height‐fields whose principal directions are orthogonal to the rotation axis. The segmentation balances the approximation quality, the boundary smoothness, and the total number of patches. Additionally, the segmentation process takes into account the object's geometric features, as well as saliency information. The output is a set of meshes ready to be processed by off‐the‐shelf software for the 3‐axis tool‐path generation. We present several results to demonstrate the quality and efficiency of our approach to a range of inputs.

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 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.

We introduce an efficient method for designing shell reinforcements of minimal weight. Inspired by classical Michell trusses, we create a reinforcement layout whose members are aligned with optimal stress directions, then optimize their shape minimizing the volume while keeping stresses bounded. We exploit two predominant techniques for reinforcing shells: adding ribs aligned with stress directions and using thicker walls on regions of high stress. Most previous work can generate either only ribs or only variable-thickness walls. However, in the general case, neither approach by itself will provide optimal solutions. By using a more precise volume model, our method is capable of producing optimized structures with the full range of qualitative behaviors: from ribs to walls and smoothly transitioning in between. Our method includes new algorithms for determining the layout of reinforcement structure elements, and an efficient algorithm to optimize their shape, minimizing a non-linear non-convex functional at a fraction of the cost and with better optimality compared to standard solvers. We demonstrate the optimization results for a variety of shapes and the improvements it yields in the strength of 3D-printed objects.

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.

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.

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 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.

We present a robust method for computing locally bijective global parametrizations aligned with a given cross-field. The singularities of the parametrization in general agree with singularities of the field, except in a small number of cases when several additional cones need to be added in a controlled way. Parametric lines can be constrained to follow an arbitrary set of feature lines on the surface. Our method is based on constructing an initial quad patch partition using robust cross-field integral line tracing. This process is followed by an algorithm modifying the quad layout structure to ensure that consistent parametric lengths can be assigned to the edges. For most meshes, the layout modification algorithm does not add new singularities; a small number of singularities may be added to resolve an explicitly described set of layouts. We demonstrate that our algorithm succeeds on a test data set of over a hundred meshes.

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.

Abstract Geometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point‐to‐point correspondence, and we automatically produce a quadrangular mesh that fits well the input animation. We first analyze the local deformation that the surface undergoes at each point, and we initialize a cross field that remains as aligned as possible to the principal directions of deformation throughout the sequence. We then smooth this cross field based on an energy that uses a weighted combination of the initial field and the local amount of stretch. Finally, we compute a field‐aligned quadrangulation with an off‐the‐shelf method. Our technique is fast and very simple to implement, and it significantly improves the quality of the output quad mesh and its suitability for character animation, compared to creating the quad mesh based on a single pose. We present experimental results and comparisons with a state‐of‐the‐art quadrangulation method, on both sequences from 3D scanning and synthetic sequences obtained by a rough animation of a triangulated model.

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.

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.

High-order and regularly sampled surface representations are more efficient and compact than general meshes and considerably simplify many geometric modeling and processing algorithms. A number of recent algorithms for conversion of arbitrary meshes to regularly sampled form (typically quadrangulation) aim to align the resulting mesh with feature lines of the geometry. While resulting in a substantial improvement in mesh quality, feature alignment makes it difficult to obtain coarse regular patch partitions of the mesh. In this paper, we propose an approach to constructing patch layouts consisting of small numbers of quadrilateral patches while maintaining good feature alignment. To achieve this, we use quadrilateral T-meshes, for which the intersection of two faces may not be the whole edge or vertex, but a part of an edge. T-meshes offer more flexibility for reduction of the number of patches and vertices in a base domain while maintaining alignment with geometric features. At the same time, T-meshes retain many desirable features of quadrangulations, allowing construction of high-order representations, easy packing of regularly sampled geometric data into textures, as well as supporting different types of discretizations for physical simulation.

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 Visual fidelity and interactivity are the main goals in Computer Graphics research, but recently also audio is assuming an important role. Binaural rendering can provide extremely pleasing and realistic three‐dimensional sound, but to achieve best results it's necessary either to measure or to estimate individual Head Related Transfer Function (HRTF). This function is strictly related to the peculiar features of ears and face of the listener. Recent sound scattering simulation techniques can calculate HRTF starting from an accurate 3D model of a human head. Hence, the use of binaural rendering on large scale (i.e. video games, entertainment) could depend on the possibility to produce a sufficiently accurate 3D model of a human head, starting from the smallest possible input. In this paper we present a completely automatic system, which produces a 3D model of a head starting from simple input data (five photos and some key‐points indicated by user). The geometry is generated by extracting information from images and accordingly deforming a 3D dummy to reproduce user head features. The system proves to be fast, automatic, robust and reliable: geometric validation and preliminary assessments show that it can be accurate enough for HRTF calculation.

In this paper, we present a physically based model for real-time simulation of thread dynamics. Our model captures all the relevant aspects of the physics of the thread, including quasi-zero elasticity, bending, torsion and self-collision, and it provides output forces for the haptic feedback. The physical properties are modeled in terms of constraints that are iteratively satisfied while the numerical integration is carried out through a Verlet scheme. This approach leads to an unconditionally stable, controllable and computationally light simulation [Müller et al. 2007]. Our results demonstrate the effectiveness of our model, showing the interaction of the thread with other objects in real time and the creation of complex knots.

Abstract We introduce a new appearance‐modeling paradigm for synthesizing the internal structure of a 3D model from photographs of a few cross‐sections of a real object. When the internal surfaces of the 3D model are revealed as it is cut, carved, or simply clipped, we synthesize their texture from the input photographs. Our texture synthesis algorithm is best classified as a morphing technique, which efficiently outputs the texture attributes of each surface point on demand. For determining source points and their weights in the morphing algorithm, we propose an interpolation domain based on BSP trees that naturally resembles planar splitting of real objects. In the context of the interpolation domain, we define efficient warping and morphing operations that allow for real‐time synthesis of textures. Overall, our modeling paradigm, together with its realization through our texture morphing algorithm, allow users to author 3D models that reveal highly realistic internal surfaces in a variety of artistic flavors.