International audience

Texture synthesis remains challenging due to the complex and varied nature of texture characteristics. To address this issue, this paper introduces a feature-enhanced diffusion network, FEDNet, which achieves both fidelity and diversity through two core technical innovations: (i) a frequency-aware residual block which enhances feature extraction during the down-sampling step of the UNet architecture, and (ii) a feature fusion connection process which integrates spatial histogram layers into skip connections. By effectively capturing the global structure and intrinsic texture attributes of the input example, FEDNet can expand the input and its sub blocks after training. Additionally, our model supports continuous texture extension via a cascading mechanism, enhancing its practical applicability. Extensive experiments demonstrate our method's improvements over state-of-the-art approaches in both stationary and non-stationary texture synthesis tasks.

Multi-axis fused filament fabrication (FFF) reduces staircase artifacts and support material by adapting nozzle orientation. However, reliable and highly customizable printing requires layers and toolpaths combining a number of challenging properties: following prescribed fields, preserving constant bead geometry, avoiding stops, retractions, and collisions. We present AtomSlicer, which takes a 3D tool-orientation field and perlayer 2-RoSy tangent direction fields, to generate field-aligned non-planar layers of near-constant thickness. It then computes collision-free deposition toolpaths that are continuous within each layer, and as continuous as possible across layers. AtomSlicer encodes geometry with three orthogonal phase fields sampled into oriented atoms, partitions them into fabricable layers, reconstructs layer meshes, and synthesizes 2-RoSy-aligned toolpaths. Unlike prior methods it treats user- or optimizer-defined fields as constraints, producing a feasible toolpath or reporting non-fabricability rather than modifying the specification. We validate on varied shapes, including a large Thingi10k study, and 13 printed models using constant extrusion per unit path length under a fixed bead profile. AtomSlicer reduces non-extruding travel to a few percent, cuts travel moves by one to two orders of magnitude versus planar and Atomizer baselines, and is 9×-60× faster than Atomizer.

Cloaking objects with metamaterials has been extensively studied to hide internal objects across various physical properties, including optical, acoustic, and thermal. We explore a new direction in mechanical cloaking: halftoning an image using a porous structure that behaves like a uniform, linear, isotropic material and visually matches a target image. For an external observer, this creates the surprising effect where the object appears mechanically isotropic and homogeneous while its porous structure resembles a target image. We introduce a parametric class of porous structures suitable for this problem, as demonstrated by numerical experiments. The structures we define offer a wide range of visual contrasts, enabling effective halftoning while maintaining near isotropic effective mechanical properties.

We introduce a divergence-free nD vector noise defined as the n-dimensional cross product of the gradients of n − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension n. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D.

Abstract We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: We modify the input shape until it admits an overlap‐free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.

Abstract Fused filament fabrication (FFF) enables users to quickly design and fabricate parts with unprecedented geometric complexity, fine‐tuning both the structural and aesthetic properties of each object. Nevertheless, the full potential of this technology has yet to be realized, as current slicing methods fail to fully exploit the deposition freedom offered by modern 3D printers. In this work, we introduce a novel approach to toolpath generation that moves beyond the traditional layer‐based concept. We use frames, referred to as atoms , as solid elements instead of slices. We optimize the distribution of atoms within the part volume to ensure even spacing and smooth orientation while accurately capturing the part's geometry. Although these atoms collectively represent the complete object, they do not inherently define a fabrication plan. To address this, we compute an extrusion toolpath as an ordered sequence of atoms that, when followed, provides a collision‐free fabrication strategy. This general approach is robust, requires minimal user intervention compared to existing techniques, and integrates many of the best features into a unified framework: precise deposition conforming to non‐planar surfaces, effective filling of narrow features – down to a single path – and the capability to locally print vertical structures before transitioning elsewhere. Additionally, it enables entirely new capabilities, such as anisotropic appearance fabrication on curved surfaces.

We present a method to 3D print surfaces exhibiting a prescribed varying field of anisotropic appearance using only standard fused filament fabrication printers. This enables the fabrication of patterns triggering reflections similar to that of brushed metal with direct control over the directionality of the reflections. Our key insight, on which we ground the method, is that the direction of the deposition paths leads to a certain degree of surface roughness, which yields a visual anisotropic appearance. Therefore, generating dense cyclic infills aligned with a line field allows us to grade the anisotropic appearance of the printed surface. To achieve this, we introduce a highly parallelizable algorithm for optimizing oriented, cyclic paths. Our algorithm outperforms existing approaches regarding efficiency, robustness, and result quality. We demonstrate the effectiveness of our technique in conveying an anisotropic appearance on several challenging test cases, ranging from patterns to photographs reinterpreted as anisotropic appearances.

We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of established PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. Our approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved. Our technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs. The code and data for this paper are available at https://github.com/mfremer/pcbend.

While 3D printing enables the customization and home fabrication of a wide range of shapes, fabricating freeform thin-shells remains challenging. As layers misalign with the curvature, they incur structural deficiencies, while the curved shells require large support structures, typically using more material than the part itself. We present a computational framework for optimizing the internal structure of 3D printed plates such that they morph into a desired freeform shell when heated. This exploits the shrinkage effect of thermoplastics such as PLA, which store internal stresses along the deposition directions. These stresses get released when the material is heated again above its glass transition temperature, causing an anisotropic deformation that induces curvature. Our inverse design method takes as input a freeform surface and finds an optimized set of deposition trajectories in each layer such that their anisotropic shrinkage deforms the plate into the prescribed surface geometry. We optimize for a continuous vector field that varies across the plate and within its thickness. The algorithm then extracts a set of deposition trajectories from the vector field in order to fabricate the flat plates on standard FFF printers. We validate our algorithm on freeform, doubly-curved surfaces.

Abstract We explore the optimization of closed space‐filling curves under orientation objectives. By solidifying material along the closed curve, solid layers of 3D prints can be manufactured in a single continuous extrusion motion. The control over orientation enables the deposition to align with specific directions in different areas, or to produce a locally uniform distribution of orientations, patterning the solidified volume in a precisely controlled manner. Our optimization framework proceeds in two steps. First, we cast a combinatorial problem, optimizing Hamiltonian cycles within a specially constructed graph. We rely on a stochastic optimization process based on local operators that modify a cycle while preserving its Hamiltonian property. Second, we use the result to initialize a geometric optimizer that improves the smoothness and uniform coverage of the cycle while further optimizing for alignment and orientation objectives.

Multi-axis motion introduces more degrees of freedom into the process of 3D printing to enable different objectives of fabrication by accumulating materials layers upon curved layers. An existing challenge is how to effectively generate the curved layers satisfying multiple objectives simultaneously. This paper presents a general slicing framework for achieving multiple fabrication objectives including support free, strength reinforcement and surface quality. These objectives are formulated as local printing directions varied in the volume of a solid, which are achieved by computing the rotation-driven deformation for the input model. The height field of a deformed model is mapped into a scalar field on its original shape, the isosurfaces of which give the curved layers of multi-axis 3D printing. The deformation can be effectively optimized with the help of quaternion fields to achieve the fabrication objectives. The effectiveness of our method has been verified on a variety of models.

Abstract We propose a method to simultaneously decompose a 3D object into power diagram cells and to integrate given functions in each of the obtained simple regions. We offer a novel, highly parallel algorithm that lends itself to an efficient GPU implementation. It is optimized for algorithms that need to compute many decompositions, for instance, centroidal Voronoi tesselation algorithms and incompressible fluid dynamics simulations. We propose an efficient solution that directly evaluates the integrals over every cell without computing the power diagram explicitly and without intersecting it with a tetrahedralization of the domain. Most computations are performed on the fly, without storing the power diagram. We manipulate a triangulation of the boundary of the domain (instead of tetrahedralizing the domain) to speed up the process. Moreover, the cells are treated independently one from another, making it possible to trivially scale up on a parallel architecture. Despite recent Voronoi diagram generation methods optimized for the GPU, computing integrals over restricted power diagrams still poses significant challenges; the restriction to a complex simulation domain is difficult and likely to be slow. It is not trivial to determine when a cell of a power diagram is completely computed, and the resulting integrals (e.g. the weighted Laplacian operator matrix) do not fit into fast (shared) GPU memory. We address all these issues and boost the performance of the state‐of‐the‐art algorithms by a factor 2 to 3 for (unrestricted) Voronoi diagrams and a ×50 speed‐up with respect to CPU implementations for restricted power diagrams. An essential ingredient to achieve this is our new scheduling strategy that allows us to treat each Voronoi/power diagram cell with optimal settings and to benefit from the fast memory.

We seek to cover a parametric domain with a set of evenly spaced bands which number and width varies according to a density field. We propose an implicit procedural algorithm, that generates the band pattern from a pixel shader and adapts to changes to the control fields in real time. Each band is uniquely identified by an integer. This allows a wide range of texturing effects, including specifying a different appearance in each individual bands. Our technique also affords for progressive gradations of scales, avoiding the abrupt doubling of the number of lines of typical subdivision approaches. This leads to a general approach for drawing bands, drawing splitting and merging curves, and drawing evenly spaced streamlines. Using these base ingredients, we demonstrate a wide variety of texturing effects.

Abstract Additive manufacturing techniques form an object by accumulating layers of material on top of one another. Each layer has to be supported by the one below for the fabrication process to succeed. To reduce print time and material usage, especially in the context of prototyping, it is often desirable to fabricate hollow objects. This exacerbates the requirement of support between consecutive layers: standard hollowing produces surfaces in overhang that cannot be directly fabricated anymore. Therefore, these surfaces require internal support structures. These are similar to external supports for overhangs, with the key difference that internal supports remain invisible within the object after fabrication. A fundamental challenge is to generate structures that provide a dense support while using little material. In this paper, we propose a novel type of support inspired by rib structures. Our approach guarantees that any point in a layer is supported by a point below, within a given threshold distance. Despite providing strong guarantees for printability, our supports remain lightweight and reliable to print. We propose a greedy support generation algorithm that creates compact hierarchies of rib‐like walls. The walls are progressively eroded away and straightened, eventually merging with the interior object walls. We demonstrate our technique on a variety of models and provide performance figures in the context of fused filament fabrication 3D printing.

We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool paths of which are usually complex and have a large number of discrete time constraints as waypoints. Kinematic redundancy also exists in these robotic systems. The jerk of motion is optimized in our trajectory planning method at the meanwhile of fabrication process to improve the quality of fabrication. Our method is based on a sampling strategy and consists of two major parts. After determining an initial path by graph search, a greedy algorithm is adopted to optimize a path by locally applying adaptive filers in the regions with large jerks. The filtered result is obtained by numerical optimization. In order to achieve efficient computation, an adaptive sampling method is developed for learning a collision-indication function that is represented as a support-vector machine. Applications in robot-assisted 3-D printing are given in this article to demonstrate the functionality of our approach. Note to Practitioners-In robot-assisted manufacturing applications, robotic arms are employed to realize the motion of workpieces (or machining tools) specified as a sequence of waypoints with the positions of tool tip and the tool orientations constrained. The required degree of freedom (DOF) is often less than the robotic hardware system (e.g., a robotic arm has six-DOF). Specifically, rotations of the workpiece around the axis of a tool can be arbitrary (see Fig. 1 for an example). By using this redundancy, i.e., there are many possible poses of a robotic arm to realize a given waypoint, the trajectory of robots can be optimized to consider the performance of motion in velocity, acceleration, and jerk in the joint space. In addition, when fabricating complex models, each tool path can have a large amount of waypoints. It is crucial for a motion planning algorithm to compute a smooth and collision-free trajectory of robot to improve the fabrication quality. The time taken by the planning algorithm should not significantly lengthen the total manufacturing time; ideally, it would remain hidden as computing motions for a layer can be done while the previous layer is printing. The method presented in this article provides an efficient framework to tackle this problem. The framework has been well tested on our robot-assisted additive manufacturing system to demonstrate its effectiveness and can be generally applied to other robot-assisted manufacturing systems.

In most layered additive manufacturing processes, a tool solidifies or deposits material while following pre-planned trajectories to form solid beads. Many interesting problems arise in this context, among which one concerns the planning of trajectories for filling a planar shape as densely as possible. This is the problem we tackle in the present paper. Recent works have shown that allowing the bead width to vary along the trajectories helps increase the filling density. We present a novel technique that, given a deposition width range, constructs a set of closed beads whose width varies within the prescribed range and fill the input shape. The technique outperforms the state of the art in important metrics: filling density (while still guaranteeing the absence of bead overlap) and trajectories smoothness. We give a detailed geometric description of our algorithm, explore its behavior on example inputs and provide a statistical comparison with the state of the art. We show that it is possible to obtain high quality fabricated layers on commodity FDM printers.

Nature offers a marvel of astonishing and rich deformation behaviors. Yet, most of the objects we fabricate are comparatively rather inexpressive, either rigid or exhibiting simple homogeneous deformations when interacted with. We explore the synthesis and fabrication of novel microstructures that mimic the effects of having oriented rigid fibers in an otherwise flexible material: the result is extremely rigid along a transverse direction while being comparatively very flexible in the locally orthogonal plane. By allowing free gradation of the rigidity direction orientation within the object, the microstructures can be designed such that, under deformation, distances along fibers in the volume are preserved while others freely change. Through a simple painting tool, this allows a designer to influence the way the volume reshapes when deformed, and results in a wide range of novel possibilities. Many gradations are possible: local free orientation of the fibers; local control of the overall material rigidity (structure density); local canceling of the effect of the fibers, obtaining a more isotropic material. Our algorithm to synthesize the structures builds upon procedural texturing. It produces a cellular geometry that can be fabricated reliably despite 3D printing walls at a minimal thickness, allowing prints to be very flexible. The synthesis algorithm is efficient and scales to large volumes.

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.

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.

Most additive manufacturing processes fabricate objects by stacking planar layers of solidified material. As a result, produced parts exhibit a so-called staircase effect, which results from sampling slanted surfaces with parallel planes. Using thinner slices reduces this effect, but it always remains visible where layers almost align with the input surfaces. In this research we exploit the ability of some additive manufacturing processes to deposit material slightly out of plane to dramatically reduce these artifacts. We focus in particular on the widespread Fused Filament Fabrication (FFF) technology, since most printers in this category can deposit along slightly curved paths, under deposition slope and thickness constraints. Our algorithm curves the layers, making them either follow the natural slope of the input surface or on the contrary, make them intersect the surfaces at a steeper angle thereby improving the sampling quality. Rather than directly computing curved layers, our algorithm optimizes for a deformation of the model which is then sliced with a standard planar approach. We demonstrate that this approach enables us to encode all fabrication constraints, including the guarantee of generating collision-free toolpaths, in a convex optimization that can be solved using a QP solver. We produce a variety of models and compare print quality between curved deposition and planar slicing.

We propose a method for integrated tool path planning and support structure generation tailored to the specific constraints of extrusion-based ceramics printing. Existing path generation methods for thermoplastic materials rely on transfer moves to navigate between different print paths in a given layer. However, when printing with clay, these transfer moves can lead to severe artifacts and failure. Our method eliminates transfer moves altogether by generating deposition paths that are continuous within and across layers. Our algorithm is implemented as a sequential top-down pass through the layer stack. In each layer, we detect points that require support, connect support points and model paths, and optimize the shape of the resulting continuous path with respect to length, smoothness, and distance to the model. For each of these subproblems, we propose dedicated solutions that take into account the fabrication constraints imposed by printable clay. We evaluate our method on a set of examples with multiple disconnected components and challenging support requirements. Comparisons to existing path generation methods designed for thermoplastic materials show that our method substantially improves print quality and often makes the difference between success and failure.

We present a method for designing mechanical metamaterials based on the novel concept of Voronoi diagrams induced by star-shaped metrics. As one of its central advantages, our approach supports interpolation between arbitrary metrics. This capability opens up a rich space of structures with interesting aesthetics and a wide range of mechanical properties, including isotropic, tetragonal, orthotropic, as well as smoothly graded materials. We evaluate our method by creating large sets of example structures, provided as accompanying material. We validate the mechanical properties predicted by simulation through tensile tests on a set of physical prototypes.

Fused filament fabrication is the method of choice for printing 3D models at low cost and is the de facto standard for hobbyists, makers, and schools. Unfortunately, filament printers cannot truly reproduce colored objects. The best current techniques rely on a form of dithering exploiting occlusion, which was only demonstrated for shades of two base colors and behaves differently depending on surface slope. We explore a novel approach for 3D-printing colored objects, capable of creating controlled gradients of varying sharpness. Our technique exploits off-the-shelf nozzles that are designed to mix multiple filaments in a small melting chamber, obtaining intermediate colors once the mix is stabilized. We apply this property to produce color gradients. We divide each input layer into a set of strata, each having a different constant color. By locally changing the thickness of the stratum, we change the perceived color at a given location. By optimizing the choice of colors of each stratum, we further improve quality and allow the use of different numbers of input filaments. We demonstrate our results by building a functional color printer using low-cost, off-the-shelf components. Using our tool, a user can paint a 3D model and directly produce its physical counterpart using any material and color available for fused filament fabrication.

Procedural pattern synthesis is a fundamental tool of Computer Graphics, ubiquitous in games and special effects. By calling a single procedure in every pixel - or voxel - large quantities of details are generated at low cost, enhancing textures, producing complex structures within and along surfaces. Such procedures are typically implemented as pixel shaders. We propose a novel procedural pattern synthesis technique that exhibits desirable properties for modeling highly contrasted patterns, that are especially well suited to produce surface and microstructure details. In particular, our synthesizer affords for a precise control over the profile, orientation and distribution of the produced stochastic patterns, while allowing to grade all these parameters spatially. Our technique defines a stochastic smooth phase field - a phasor noise - that is then fed into a periodic function (e.g. a sine wave), producing an oscillating field with prescribed main frequencies and preserved contrast oscillations. In addition, the profile of each oscillation is directly controllable (e.g. sine wave, sawtooth, rectangular or any 1D profile). Our technique builds upon a reformulation of Gabor noise in terms of a phasor field that affords for a clear separation between local intensity and phase. Applications range from texturing to modeling surface displacements, as well as multi-material microstructures in the context of additive manufacturing.

This paper presents a new method to fabricate 3D models on a robotic printing system equipped with multi-axis motion. Materials are accumulated inside the volume along curved tool-paths so that the need of supporting structures can be tremendously reduced - if not completely abandoned - on all models. Our strategy to tackle the challenge of tool-path planning for multi-axis 3D printing is to perform two successive decompositions, first volume-to-surfaces and then surfaces-to-curves. The volume-to-surfaces decomposition is achieved by optimizing a scalar field within the volume that represents the fabrication sequence. The field is constrained such that its iso-values represent curved layers that are supported from below, and present a convex surface affording for collision-free navigation of the printer head. After extracting all curved layers, the surfaces-to-curves decomposition covers them with tool-paths while taking into account constraints from the robotic printing system. Our method successfully generates tool-paths for 3D printing models with large overhangs and high-genus topology. We fabricated several challenging cases on our robotic platform to verify and demonstrate its capabilities.

A critical advantage of additive manufacturing is its ability to fabricate complex small-scale structures. These microstructures can be understood as a metamaterial : they exist at a much smaller scale than the volume they fill, and are collectively responsible for an average elastic behavior different from that of the base printing material making the fabricated object lighter and/or flexible along specific directions. In addition, the average behavior can be graded spatially by progressively modifying the micro structure geometry. The definition of a microstructure is a careful trade-off between the geometric requirements of manufacturing and the properties one seeks to obtain within a shape: in our case a wide range of elastic behaviors. Most existing microstructures are designed for stereolithography (SLA) and laser sintering (SLS) processes. The requirements are however different than those of continuous deposition systems such as fused filament fabrication (FFF), for which there is currently a lack of microstructures enabling graded elastic behaviors. In this work we introduce a novel type of microstructures that strictly enforce all the requirements of FFF-like processes: continuity, self-support and overhang angles. They offer a range of orthotropic elastic responses that can be graded spatially. This allows to fabricate parts usually reserved to the most advanced technologies on widely available inexpensive printers that also benefit from a continuously expanding range of materials.

We propose a GPU algorithm that computes a 3 D Voronoi diagram. Our algorithm is tailored for applications that solely make use of the geometry of the Voronoi cells, such as Lloyd's relaxation used in meshing, or some numerical schemes used in fluid simulations and astrophysics. Since these applications only require the geometry of the Voronoi cells, they do not need the combinatorial mesh data structure computed by the classical algorithms (Bowyer-Watson). Thus, by exploiting the specific spatial distribution of the point-sets used in this type of applications, our algorithm computes each cell independently, in parallel, based on its nearest neighbors. In addition, we show how to compute integrals over the Voronoi cells by decomposing them on the fly into tetrahedra, without needing to compute any global combinatorial information. The advantages of our algorithm is that it is fast, very simple to implement, has constant memory usage per thread and does not need any synchronization primitive. These specificities make it particularly efficient on the GPU: it gains one order of magnitude as compared to the fastest state-of-the-art multi-core CPU implementations. To ease the reproducibility of our results, the full documented source code is included in the supplemental material.

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step along the processing pipeline that prepares the 3D model for fabrication can now count on dozens of methods, that analyse and optimize geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during model preparation – a process globally refereed to as Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.

Recent advances in 3D printing have made it easier to manufacture customized objects by ordinary users in an affordable manner, and therefore spurred high demand for more accessible methods for designing and fabricating 3D objects of various shapes and functionalities. In this paper we present a novel approach to model and fabricate surface-like objects composed of connected tiles, which can be used as objects in daily life, such as ornaments, covers, shades or handbags.

Slicing is the procedure necessary to prepare a shape for layered manufacturing. There are degrees of freedom in this process, such as the starting point of the slicing sequence and the thickness of each slice. The choice of these parameters influences the manufacturing process and its result: The number of slices significantly affects the time needed for manufacturing, while their thickness affects the error. Assuming a discrete setting, we measure the error as the number of voxels that are incorrectly assigned due to slicing. We provide an algorithm that generates, for a given set of available slice heights and a shape, a slicing that is provably optimal. By optimal, we mean that the algorithm generates sequences with minimal error for any possible number of slices. The algorithm is fast and flexible, that is, it can accommodate a user driven importance modulation of the error function and allows the interactive exploration of the desired quality/time tradeoff. We demonstrate the practical importance of our optimization on several three-dimensional-printed results.

Additive manufacturing enables the fabrication of objects embedding meta-materials. By creating fine-scale structures, the object's physical properties can be graded (e.g. elasticity, porosity), even though a single base material is used for fabrication. Designing the fine and detailed geometry of a metamaterial while attempting to achieve specific properties is difficult. In addition, the structures are intended to fill comparatively large volumes, which quickly leads to large data structures and intractable simulation costs. Thus, most metamaterials are defined as periodic structures repeated in regular lattices. The periodicity simplifies modeling, simulation, and reduces memory costs - however it limits the possibility to smoothly grade properties along free directions. In this work, we propose a novel metamaterial with controllable, freely orientable, orthotropic elastic behavior - orthotropy means that elasticity is controlled independently along three orthogonal axes, which leads to materials that better adapt to uneven, directional load scenarios, and offer a more versatile material design primitive. The fine-scale structures are generated procedurally by a stochastic process, and resemble a foam. The absence of global organization and periodicity allows the free gradation of density, orientation, and stretch, leading to the controllable orthotropic behavior. The procedural nature of the synthesis process allows it to scale to arbitrarily large volumes at low memory costs. We detail the foam structure synthesis, analyze and discuss its properties through numerical and experimental verifications, and finally demonstrate the use of orthotropic materials for the design of 3D printed objects.

In traditional design, shapes are first conceived, and then fabricated. While this decoupling simplifies the design process, it can result in unwanted material wastage, especially where off-cut pieces are hard to reuse. In absence of explicit feedback on material usage, the designer remains helpless to effectively adapt the design - even when design variabilities exist. We investigate waste minimizing furniture design wherein based on the current design, the user is presented with design variations that result in less wastage of materials. Technically, we dynamically analyze material space layout to determine which parts to change and how , while maintaining original design intent specified in the form of design constraints. We evaluate the approach on various design scenarios, and demonstrate effective material usage that is difficult, if not impossible, to achieve without computational support.

Filigrees are thin patterns found in jewelry, ornaments and lace fabrics. They are often formed of repeated base elements manually composed into larger, delicate patterns. Digital fabrication simplifies the process of turning a virtual model of a filigree into a physical object. However, designing a virtual model of a filigree remains a time consuming and challenging task. The difficulty lies in tightly packing together the base elements while covering a target surface. In addition, the filigree has to be well connected and sufficiently robust to be fabricated. We propose a novel approach automating this task. Our technique covers a target surface with a set of input base elements, forming a filigree strong enough to be fabricated. We exploit two properties of filigrees to make this possible. First, as filigrees form delicate traceries they are well captured by their skeleton. This affords for a simpler definition of operators such as matching and deformation. Second, instead of seeking for a perfect packing of the base elements we relax the problem by allowing appearance preserving partial overlaps. We optimize a filigree by a stochastic search, further improved by a novel boosting algorithm that records and reuses good configurations discovered during the process. We illustrate our technique on a number of challenging examples reproducing filigrees on large objects, which we manufacture by 3D printing. Our technique affords for several user controls, such as the scale and orientation of the elements.

Microstructures at the scale of tens of microns change the physical properties of objects, making them lighter or more flexible. While traditionally difficult to produce, additive manufacturing now lets us physically realize such microstructures at low cost. In this paper we propose to study procedural, aperiodic microstructures inspired by Voronoi open-cell foams. The absence of regularity affords for a simple approach to grade the foam geometry --- and thus its mechanical properties --- within a target object and its surface. Rather than requiring a global optimization process, the microstructures are directly generated to exhibit a specified elastic behavior. The implicit evaluation is akin to procedural textures in computer graphics, and locally adapts to follow the elasticity field. This allows very detailed structures to be generated in large objects without having to explicitly produce a full representation --- mesh or voxels --- of the complete object: the structures are added on the fly, just before each object slice is manufactured. We study the elastic behavior of the microstructures and provide a complete description of the procedure generating them. We explain how to determine the geometric parameters of the microstructures from a target elasticity, and evaluate the result on printed samples. Finally, we apply our approach to the fabrication of objects with spatially varying elasticity, including the implicit modeling of a frame following the object surface and seamlessly connecting to the microstructures.

Abstract The success of physics sandbox applications and physics‐based puzzle games is a strong indication that casual users and hobbyists enjoy designing mechanisms, for educational or entertainment purposes. In these applications, a variety of mechanisms are designed by assembling two‐dimensional shapes, creating gears, cranks, cams, and racks. The experience is made enjoyable by the fact that the user does not need to worry about the intricate geometric details that would be necessary to produce a real mechanism. In this paper, we propose to start from such casual designs of mechanisms and turn them into a 3D model that can be printed onto widely available, inexpensive filament based 3D printers. Our intent is to empower the users of such tools with the ability to physically realize their mechanisms and see them operate in the real world. To achieve this goal we tackle several challenges. The input 2D mechanism allows for some parts to overlap during simulation. These overlapping parts have to be resolved into non‐intersecting 3D parts in the real mechanism. We introduce a novel scheme based on the idea of including moving parts into one another whenever possible. This reduces bending stresses on axles compared to previous methods. Our approach supports sliding parts and arbitrarily shaped mechanical parts in the 2D input. The exact 3D shape of the parts is inferred from the 2D input and the simulation of the mechanism, using boolean operations between shapes. The input mechanism is often simply attached to the background. We automatically synthesize a chassis by formulating a topology optimization problem, taking into account the stresses exerted by the mechanism on the chassis through time.

Several techniques exist to automatically synthesize a 2D image resembling an input exemplar texture. Most of the approaches optimize a new image so that the color neighborhoods in the output closely match those in the input, across all scales. In this paper we revisit by-example texture synthesis in the context of additive manufacturing. Our goal is to generate not only colors, but also structure along output surfaces: given an exemplar indicating 'solid' and 'empty' pixels, we generate a similar pattern along the output surface. The core challenge is to guarantee that the pattern is not only fully connected, but also structurally sound. To achieve this goal we propose a novel formulation for on-surface by-example texture synthesis that directly works in a voxel shell around the surface. It enables efficient local updates to the pattern, letting our structural optimizer perform changes that improve the overall rigidity of the pattern. We use this technique in an iterative scheme that jointly optimizes for appearance and structural soundness. We consider fabricability constraints and a user-provided description of a force profile that the object has to resist. Our results fully exploit the capabilities of additive manufacturing by letting users design intricate structures along surfaces. The structures are complex, yet they resemble input exemplars, resulting in a modeling tool accessible to casual users.

The field of topology optimization seeks to optimize shapes under structural objectives, such as achieving the most rigid shape using a given quantity of material. Besides optimal shape design, these methods are increasingly popular as design tools, since they automatically produce structures having desirable physical properties, a task hard to perform by hand even for skilled designers. However, there is no simple way to control the appearance of the generated objects. In this paper, we propose to optimize shapes for both their structural properties and their appearance, the latter being controlled by a user-provided pattern example. These two objectives are challenging to combine, as optimal structural properties fully define the shape, leaving no degrees of freedom for appearance. We propose a new formulation where appearance is optimized as an objective while structural properties serve as constraints. This produces shapes with sufficient rigidity while allowing enough freedom for the appearance of the final structure to resemble the input exemplar. Our approach generates rigid shapes using a specified quantity of material while observing optional constraints such as voids, fills, attachment points, and external forces. The appearance is defined by examples, making our technique accessible to casual users. We demonstrate its use in the context of fabrication using a laser cutter to manufacture real objects from optimized shapes.

Abstract Fused Filament Fabrication is an additive manufacturing process by which a 3D object is created from plastic filament. The filament is pushed through a hot nozzle where it melts. The nozzle deposits plastic layer after layer to create the final object. This process has been popularized by the RepRap community. Several printers feature multiple extruders, allowing objects to be formed from multiple materials or colors. The extruders are mounted side by side on the printer carriage. However, the print quality suffers when objects with color patterns are printed – a disappointment for designers interested in 3D printing their colored digital models. The most severe issue is the oozing of plastic from the idle extruders: Plastics of different colors bleed onto each other giving the surface a smudged aspect, excess strings oozing from the extruder deposit on the surface, and holes appear due to this missing plastic. Fixing this issue is difficult: increasing the printing speed reduces oozing but also degrades surface quality – on large prints the required speed level become impractical. Adding a physical mechanism increases cost and print time as extruders travel to a cleaning station. Instead, we rely on software and exploit degrees of freedom of the printing process. We introduce three techniques that complement each other in improving the print quality significantly. We first reduce the impact of oozing plastic by choosing a better azimuth angle for the printed part. We build a disposable rampart in close proximity of the part, giving the extruders the opportunity to wipe oozing strings and refill with hot plastic. We finally introduce a toolpath planner avoiding and hiding most of the defects due to oozing, and seamlessly integrating the rampart. We demonstrate our technique on several challenging multiple color prints, and show that our tool path planner improves the surface finish of single color prints as well.

Abstract The design of video game environments, or levels, aims to control gameplay by steering the player through a sequence of designer‐controlled steps, while simultaneously providing a visually engaging experience. Traditionally these levels are painstakingly designed by hand, often from pre‐existing building blocks, or space templates. In this paper, we propose an algorithmic approach for automatically laying out game levels from user‐specified blocks. Our method allows designers to retain control of the gameplay flow via user‐specified level connectivity graphs, while relieving them from the tedious task of manually assembling the building blocks into a valid, plausible layout. Our method produces sequences of diverse layouts for the same input connectivity, allowing for repeated replay of a given level within a visually different, new environment. We support complex graph connectivities and various building block shapes, and are able to compute complex layouts in seconds. The two key components of our algorithm are the use of configuration spaces defining feasible relative positions of building blocks within a layout and a graph‐decomposition based layout strategy that leverages graph connectivity to speed up convergence and avoid local minima. Together these two tools quickly steer the solution toward feasible layouts. We demonstrate our method on a variety of real‐life inputs, and generate appealing layouts conforming to user specifications.

Fused Filament Fabrication (FFF) is the process of 3D printing objects from melted plastic filament. The hot plastic exits a nozzle and fuses with the part just below, adding a layer of material to the object being formed. However, filament can only be deposited on top of an existing surface. Therefore, overhangs require a disposable support structure to be printed, temporarily supporting the threads of plastic that would otherwise hang in empty space. Existing techniques for support generation fall into two categories: The first allow for very reliable prints by enclosing the bottom of the object in a dense structure, at the expense of increased material usage and build times. The second generate thin hierarchical structures connecting to the surface in a sparse number of points. This uses less material, at the expense of reliability: the part might become unstable, the structure itself may become difficult to print, the bottom surface quality degrades. The user therefore has to correct the structure and its parameters for each new object. We propose to exploit the ability of FFF printers to print bridges across gaps. Since bridges are always supported by pillars at their extremities, they are both stronger and more stable than hierarchical tree structures. Our technique first selects the points to support based on overhang and part stability during the entire print process. It then optimizes for a printable scaffolding composed of bridges and vertical pillars, supporting all points. The result is an automated support generation technique using little material while ensuring fine surface quality and stability during the printing process.

Decorative patterns are observed in many forms of art, typically enriching the visual aspect of otherwise simple shapes. Such patterns are especially difficult to create, as they often exhibit intricate structural details and at the same time have to precisely match the size and shape of the underlying geometry. In the field of Computer Graphics, several approaches have been proposed to automatically synthesize a decorative pattern along a curve, from an example. This empowers non expert users with a simple brush metaphor, allowing them to easily paint complex structured decorations. We extend this idea to the space of design and fabrication. The major challenge is to properly account for the topology of the produced patterns. In particular, our technique ensures that synthesized patterns will be made of exactly one connected component, so that once printed they form a single object. To achieve this goal we propose a two steps synthesis process, first synthesizing the topology of the pattern and later synthesizing its exact geometry. We introduce topology descriptors that efficiently capture the topology of the pattern synthesized so far. We propose several applications of our method, from designing objects using synthesized patterns along curves and within rectangles, to the decoration of surfaces with a dedicated smooth frame interpolation. Using our technique, designers paint structured patterns that can be fabricated into solid, tangible objects, creating unusual and surprising designs of lamps, chairs and laces from examples.

Abstract Many algorithms in Computer Graphics require to synthesize a pattern along a curve. This is for instance the case with line stylization, to decorate objects with elaborate patterns (chains, laces, scratches), or to synthesize curvilinear features such as mountain ridges, rivers or roads. We describe a simple yet effective method for this problem. Our method addresses the main challenge of maintaining the continuity of the pattern while following the curve. It allows some freedom to the synthesized pattern: It may locally diverge from the curve so as to allow for a more natural global result. This also lets the pattern escape areas of overlaps or fold‐overs. This makes our method particularly well suited to structured, detailed patterns following complex curves. Our synthesizer copies tilted pieces of the exemplar along the curve, following its orientation. The result is optimized through a shortest path search, with dynamic programming. We speed up the process by an efficient parallel implementation. Finally, since discontinuities may always remain we propose an optional post‐processing step optimally deforming neighboring pieces to smooth the transitions.

Many natural phenomena consist of geometric elements with dynamic motions characterized by small scale repetitions over large scale structures, such as particles, herds, threads, and sheets. Due to their ubiquity, controlling the appearance and behavior of such phenomena is important for a variety of graphics applications. However, such control is often challenging; the repetitive elements are often too numerous for manual edit, while their overall structures are often too versatile for fully automatic computation. We propose a method that facilitates easy and intuitive controls at both scales: high-level structures through spatial-temporal output constraints (e.g. overall shape and motion of the output domain), and low-level details through small input exemplars (e.g. element arrangements and movements). These controls are suitable for manual specification, while the corresponding geometric and dynamic repetitions are suitable for automatic computation. Our system takes such user controls as inputs, and generates as outputs the corresponding repetitions satisfying the controls. Our method, which we call dynamic element textures , aims to produce such controllable repetitions through a combination of constrained optimization (satisfying controls) and data driven computation (synthesizing details). We use spatial-temporal samples as the core representation for dynamic geometric elements. We propose analysis algorithms for decomposing small scale repetitions from large scale themes, as well as synthesis algorithms for generating outputs satisfying user controls. Our method is general, producing a range of artistic effects that previously required disparate and specialized techniques.

Imbalance suggests a feeling of dynamism and movement in static objects. It is therefore not surprising that many 3D models stand in impossibly balanced configurations. As long as the models remain in a computer this is of no consequence: the laws of physics do not apply. However, fabrication through 3D printing breaks the illusion: printed models topple instead of standing as initially intended. We propose to assist users in producing novel, properly balanced designs by interactively deforming an existing model. We formulate balance optimization as an energy minimization, improving stability by modifying the volume of the object, while preserving its surface details. This takes place during interactive editing: the user cooperates with our optimizer towards the end result. We demonstrate our method on a variety of models. With our technique, users can produce fabricated objects that stand in one or more surprising poses without requiring glue or heavy pedestals.

Abstract Procedural textures usually require spending time testing parameters to realize the diversity of appearances. This paper introduces the idea of a procedural texture preview: A single static image summarizing in a limited pixel space the appearances produced by a given procedure. Unlike grids of thumbnails our previews present a continuous image of appearances, analog to a map. The main challenge is to ensure that most appearances are visible, are allocated a similar pixel area, and are ordered in a smooth manner throughout the preview. To reach this goal, we introduce a new layout algorithm accounting simultaneously for these criteria. After computing a layout of appearances, we rely on by‐example texture synthesis to produce the final preview. We demonstrate our approach on a database of production‐level procedural textures.

Procedural noise is a fundamental tool in Computer Graphics. However, designing noise patterns is hard. In this paper, we present Gabor noise by example , a method to estimate the parameters of bandwidth-quantized Gabor noise, a procedural noise function that can generate noise with an arbitrary power spectrum, from exemplar Gaussian textures, a class of textures that is completely characterized by their power spectrum. More specifically, we introduce (i) bandwidth-quantized Gabor noise, a generalization of Gabor noise to arbitrary power spectra that enables robust parameter estimation and efficient procedural evaluation; (ii) a robust parameter estimation technique for quantized-bandwidth Gabor noise, that automatically decomposes the noisy power spectrum estimate of an exemplar into a sparse sum of Gaussians using non-negative basis pursuit denoising; and (iii) an efficient procedural evaluation scheme for bandwidth-quantized Gabor noise, that uses multi-grid evaluation and importance sampling of the kernel parameters. Gabor noise by example preserves the traditional advantages of procedural noise, including a compact representation and a fast on-the-fly evaluation, and is mathematically well-founded.

Recent spatial hashing schemes hash millions of keys in parallel, compacting sparse spatial data in small hash tables while still allowing for fast access from the GPU. Unfortunately, available schemes suffer from two drawbacks: Multiple runs of the construction process are often required before success, and the random nature of the hash functions decreases access performance. We introduce a new parallel hashing scheme which reaches high load factor with a very low failure rate. In addition our scheme has the unique advantage to exploit coherence in the data and the access patterns for faster performance. Compared to existing approaches, it exhibits much greater locality of memory accesses and consistent execution paths within groups of threads. This is especially well suited to Computer Graphics applications, where spatial coherence is common. In absence of coherence our scheme performs similarly to previous methods, but does not suffer from construction failures. Our scheme is based on the Robin Hood scheme modified to quickly abort queries of keys that are not in the table, and to preserve coherence. We demonstrate our scheme on a variety of data sets. We analyze construction and access performance, as well as cache and threads behavior.

We present an image-based approach to relighting photographs of tree canopies. Our goal is to minimize capture overhead; thus the only input required is a set of photographs of the tree taken at a single time of day, while allowing relighting at any other time. We first analyze lighting in a tree canopy both theoretically and using simulations. From this analysis, we observe that tree canopy lighting is similar to volumetric illumination. We assume a single-scattering volumetric lighting model for tree canopies, and diffuse leaf reflectance; we validate our assumptions with synthetic renderings. We create a volumetric representation of the tree from 10-12 images taken at a single time of day and use a single-scattering participating media lighting model. An analytical sun and sky illumination model provides consistent representation of lighting for the captured input and unknown target times. We relight the input image by applying a ratio of the target and input time lighting representations. We compute this representation efficiently by simultaneously coding transmittance from the sky and to the eye in spherical harmonics. We validate our method by relighting images of synthetic trees and comparing to path-traced solutions. We also present results for photographs, validating with time-lapse ground truth sequences.

We have recently proposed a new procedural noise function, Gabor noise, which offers a combination of properties not found in the existing noise functions. In this paper, we present three significant improvements to Gabor noise: 1) an isotropic kernel for Gabor noise, which speeds up isotropic Gabor noise with a factor of roughly two, 2) an error analysis of Gabor noise, which relates the kernel truncation radius to the relative error of the noise, and 3) spatially varying Gabor noise, which enables spatial variation of all noise parameters. These improvements make Gabor noise an even more attractive alternative for the existing noise functions.

Virtual environments are typically textured by manually choosing an image to apply on each surface. This implies browsing through large sets of generic textures for each and every surface in the scene.

Abstract We present a new solution for temporal coherence in non‐photorealistic rendering (NPR) of animations. Given the conflicting goals of preserving the 2D aspect of the style and the 3D scene motion, any such solution is a tradeoff. We observe that primitive‐based methods in NPR can be seen as texture‐based methods when using large numbers of primitives, leading to our key insight, namely that this process is similar to sparse convolution noise in procedural texturing. Consequently, we present a new primitive for NPR based on Gabor noise, that preserves the 2D aspect of noise, conveys the 3D motion of the scene, and is temporally continuous. We can thus use standard techniques from procedural texturing to create various styles, which we show for interactive NPR applications. We also present a user study to evaluate this and existing solutions, and to provide more insight in the trade‐off implied by temporal coherence. The results of the study indicate that maintaining coherent motion is important, but also that our new solution provides a good compromise between the 2D aspect of the style and 3D motion.

Abstract Procedural noise functions are widely used in computer graphics, from off‐line rendering in movie production to interactive video games. The ability to add complex and intricate details at low memory and authoring cost is one of its main attractions. This survey is motivated by the inherent importance of noise in graphics, the widespread use of noise in industry and the fact that many recent research developments justify the need for an up‐to‐date survey. Our goal is to provide both a valuable entry point into the field of procedural noise functions, as well as a comprehensive view of the field to the informed reader. In this report, we cover procedural noise functions in all their aspects. We outline recent advances in research on this topic, discussing and comparing recent and well‐established methods. We first formally define procedural noise functions based on stochastic processes and then classify and review existing procedural noise functions. We discuss how procedural noise functions are used for modelling and how they are applied to surfaces. We then introduce analysis tools and apply them to evaluate and compare the major approaches to noise generation. We finally identify several directions for future work.

Abstract Surface materials are commonly described by attributes stored in textures (for instance, color, normal, or displacement). Interpolation during texture lookup provides a continuous value field everywhere on the surface, except at the chart boundaries where visible discontinuities appear. We propose a solution to make these seams invisible, while still outputting a standard texture atlas. Our method relies on recent advances in quad remeshing using global parameterization to produce a set of texture coordinates aligning texel grids across chart boundaries. This property makes it possible to ensure that the interpolated value fields on both sides of a chart boundary precisely match, making all seams invisible. However, this requirement on the uv coordinates needs to be complemented by a set of constraints on the colors stored in the texels. We propose an algorithm solving for all the necessary constraints between texel values, including through different magnification modes (nearest, bilinear, biquadratic and bicubic), and across facets using different texture resolutions. In the typical case of bilinear magnification and uniform resolution, none of the texels appearing on the surface are constrained. Our approach also ensures perfect continuity across several MIP‐mapping levels.

Textures are often reused on different surfaces in large virtual environments. This leads to unpleasing stretch and cropping of features when textures contain architectural elements. Existing retargeting methods could adapt each texture to the size of their support surface, but this would imply storing a different image for each and every surface, saturating memory. Our new texture synthesis approach casts synthesis as a shortest path problem in a graph describing the space of images that can be synthesized. Each path in the graph describes how to form a new image by cutting strips of the source image and reassembling them in a different order. Only the paths describing the result need to be stored in memory: synthesized textures are reconstructed at rendering time. The user can control repetition of features, and may specify positional constraints. We demonstrate our approach on a variety of textures, from facades for large city rendering to structured textures commonly used in video games.

We propose a new approach to efficiently render large volumetric data sets. The system achieves interactive to real-time rendering performance for several billion voxels.

Abstract Modeling large architectural environments is a difficult task due to the intricate nature of these models and the complex dependencies between the structures represented. Moreover, textures are an essential part of architectural models. While the number of geometric primitives is usually relatively low (i.e., many walls are at surfaces), textures actually contain many detailed architectural elements. We present an approach for modeling architectural scenes by reshaping and combining existing textured models, where the manipulation of the geometry and texture are tightly coupled. For geometry, preserving angles such as oor orientation or vertical walls is of key importance. We thus allow the user to interactively modify lengths of edges, while constraining angles. Our texture reshaping solution introduces a measure of directional autosimilarity to focus stretching in areas of stochastic content and to preserve details in such areas. We show results on several challenging models, and show two applications: Building complex road structures from simple initial pieces and creating complex game‐levels from an existing game based on pre‐existing model pieces.

Noise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties. In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design.

Abstract Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.

Abstract The goal of texture synthesis is to generate an arbitrarily large high‐quality texture from a small input sample. Generally, it is assumed that the input image is given as a flat, square piece of texture, thus it has to be carefully prepared from a picture taken under ideal conditions. Instead we would like to extract the input texture from any surface from within an arbitrary photograph. This introduces several challenges: Only parts of the photograph are covered with the texture of interest, perspective and scene geometry introduce distortions, and the texture is non‐uniformly sampled during the capture process. This breaks many of the assumptions used for synthesis. In this paper we combine a simple novel user interface with a generic per‐pixel synthesis algorithm to achieve high‐quality synthesis from a photograph. Our interface lets the user locally describe the geometry supporting the textures by combining rational Bézier patches. These are particularly well suited to describe curved surfaces under projection. Further, we extend per‐pixel synthesis to account for arbitrary texture sparsity and distortion, both in the input image and in the synthesis output. Applications range from synthesizing textures directly from photographs to high‐quality texture completion.

Texture mapping with atlases suffer from several drawbacks: Wasted memory, seams, uniform resolution and no support of implicit surfaces. Texture mapping in a volume solves most of these issues, but unfortunately it induces an important space and time overhead.

The traditional approach in texture synthesis is to compare color neighborhoods with those of an exemplar. We show that quality is greatly improved if pointwise colors are replaced by appearance vectors that incorporate nonlocal information such as feature and radiance-transfer data. We perform dimensionality reduction on these vectors prior to synthesis, to create a new appearance-space exemplar. Unlike a texton space, our appearance space is low-dimensional and Euclidean. Synthesis in this information-rich space lets us reduce runtime neighborhood vectors from 5x5 grids to just 4 locations. Building on this unifying framework, we introduce novel techniques for coherent anisometric synthesis, surface texture synthesis directly in an ordinary atlas, and texture advection. Remarkably, we achieve all these functionalities in real-time, or 3 to 4 orders of magnitude faster than prior work.

We explore using hashing to pack sparse data into a compact table while retaining efficient random access. Specifically, we design a perfect multidimensional hash function -- one that is precomputed on static data to have no hash collisions. Because our hash function makes a single reference to a small offset table, queries always involve exactly two memory accesses and are thus ideally suited for parallel SIMD evaluation on graphics hardware. Whereas prior hashing work strives for pseudorandom mappings, we instead design the hash function to preserve spatial coherence and thereby improve runtime locality of reference. We demonstrate numerous graphics applications including vector images, texture sprites, alpha channel compression, 3D-parameterized textures, 3D painting, simulation, and collision detection.

We present a novel algorithm for the rendering of hard shadows cast by a point light source. The well-known Z-pass method for rasterizing shadow volumes is not always correct. Our algorithm, which we call ZP+, elegantly corrects Z-pass defects. ZP+ takes advantage of triangle strips and the fast culling capabilities of graphics hardware not available to conventional robust methods like Z-fail. While Z-fail can be up to 80% slower than Z-pass, our new method ZP+ is typically less than 10% slower than Z-pass. Finally, we compare the three methods. When a scene is geometry-bound, ZP+ is always faster than Z-fail. We also explain why, in some situations, Z-pass (hence ZP+) is surprisingly slower than Z-fail on more recent graphics hardware.

We present a new interactive method to texture complex geometries at very high resolution, while using little memory and without the need for a global planar parameterization. We rely on small texture elements, the texture sprites, locally splatted onto the surface to define a composite texture. The sprites can be arbitrarily blended to create complex surface appearances. Their attributes (position, size, texture id) can be dynamically updated, thus providing a convenient framework for interactive editing and animated textures. We demonstrate the flexibility of our method by creating new surface aspects difficult to achieve with other methods.Each sprite is described by a small set of attributes which is stored in a hierarchical structure surrounding the object's surface. The patterns supported by the sprites are stored only once. The whole data structure is compactly encoded into GPU memory. At run time, it is accessed by a fragment program which computes the final appearance of a surface point from all the sprites covering it. The overall memory cost of the structure is very low compared to the resulting texturing resolutions. Rendering is done in real-time. The resulting texture is linearly interpolated and filtered.

We present a texture synthesis scheme based on neighborhood matching, with contributions in two areas: parallelism and control. Our scheme defines an infinite, deterministic, aperiodic texture, from which windows can be computed in real-time on a GPU. We attain high-quality synthesis using a new analysis structure called the Gaussian stack, together with a coordinate upsampling step and a subpass correction approach. Texture variation is achieved by multiresolution jittering of exemplar coordinates. Combined with the local support of parallel synthesis, the jitter enables intuitive user controls including multiscale randomness, spatial modulation over both exemplar and output, feature drag-and-drop, and periodicity constraints. We also introduce synthesis magnification, a fast method for amplifying coarse synthesis results to higher resolution.

Numerous real-time applications such computer games or flight simulators require non-repetitive high-resolution texturing on large landscapes. We propose an algorithm which procedurally determines the texture value at any surface location by aperiodically combining provided patterns according to user-defined controls such as a probability distribution (possibly non stationary). Our algorithm can be implemented on programmable hardware by taking advantage of the texture indirection ability of recent graphics boards. We use explicit and virtual indirection tables to determine the pattern to apply at each pixel as well as its attributes (displacement, scaling, time...). This provides the programmer with a very high resolution virtual texture with nice properties: Low memory consumption, no periodicity, control of the statistics, numerous control parameters (which can be edited on the fly). Our representation consists of building blocks that we combine in order to illustrate various convenient texture modalities such as aperiodic tiling, sparse convolution, domain transitions and animated textures.