This is an erratum for the article “Lifted Surfacing of Generalized Sweep Volumes” published in ACM Trans. Graph. 44, 6, Article 249 (December 2025), 17 pages.

Computing the boundary surface of the 3D volume swept by a rigid or deforming solid remains a challenging problem in geometric modeling. Existing approaches are often limited to sweeping rigid shapes, cannot guarantee a watertight surface, or struggle with modeling the intricate geometric features (e.g., sharp creases and narrow gaps) and topological features (e.g., interior voids). We make the observation that the sweep boundary is a subset of the projection of the intersection of two implicit surfaces in a higher dimension, and we derive a characterization of the subset using winding numbers. These insights lead to a general algorithm for any sweep represented as a smooth time-varying implicit function satisfying a genericity assumption, and it produces a watertight and intersection-free surface that better approximates the geometric and topological features than existing methods.

We present a method for generating a simplicial (e.g., triangular or tetrahedral) grid to enable adaptive discretization of implicit shapes defined by a vector function. Such shapes, which we call implicit complexes, are generalizations of implicit surfaces and useful for representing non-smooth and non-manifold structures. While adaptive grid generation has been extensively studied for polygonizing implicit surfaces, few methods are designed for implicit complexes. Our method can generate adaptive grids for several implicit complexes, including arrangements of implicit surfaces, CSG shapes, material interfaces, and curve networks. Importantly, our method adapts the grid to the geometry of not only the implicit surfaces but also their lower-dimensional intersections. We demonstrate how our method enables efficient and detail-preserving discretization of non-trivial implicit shapes.

Clothes undergo complex geometric deformations, which lead to appearance changes. To edit human videos in a physically plausible way, a texture map must take into account not only the garment transformation induced by the body movements and clothes fitting, but also its 3D fine-grained surface geometry. This poses, however, a new challenge of 3D reconstruction of dynamic clothes from an image or a video. In this paper, we show that it is possible to edit dressed human images and videos without 3D reconstruction. We estimate a geometry aware texture map between the garment region in an image and the texture space, a.k.a, UV map. Our UV map is designed to preserve isometry with respect to the underlying 3D surface by making use of the 3D surface normals predicted from the image. Our approach captures the underlying geometry of the garment in a self-supervised way, requiring no ground truth annotation of UV maps and can be readily extended to predict temporally coherent UV maps. We demonstrate that our method outperforms the state-of-the-art human UV map estimation approaches on both real and synthetic data.

Three-dimensional curve drawing in Augmented Reality (AR) enables users to create 3D curves that fit within the real-world scene. It has applications in 3D design, sculpting, and animation. However, the task complexity increases when the desirable path for the curve is obstructed by the physical environment or by what the camera can see. For example, it is difficult to draw a curve that wraps around an object or scales to out-of-reach places. We propose WARPY, an environment-aware 3D curve drawing tool for mobile AR. Our system enables users to draw freeform curves from a distance in AR by combining 2D-to-3D sketch inference with geometric proxies. Geometric Proxies can be obtained via 3D scanning or from a list of pre-defined primitives. WARPY also provides a multi-view mode to enable users to sketch a curve from multiple viewpoints, which is useful if the target curve cannot fit within the camera's field of view. We conducted two user studies and found that WARPY can be a viable tool to help users create complex and large curves in AR.

Abstract Artist generated clip‐art images typically consist of a small number of distinct, uniformly colored regions with clear boundaries. Legacy artist created images are often stored in low‐resolution (100x100px or less) anti‐aliased raster form. Compared to anti‐aliasing free rasterization, anti‐aliasing blurs inter‐region boundaries and obscures the artist's intended region topology and color palette; at the same time, it better preserves subpixel details. Recovering the underlying artist‐intended images from their low‐resolution anti‐aliased rasterizations can facilitate resolution independent rendering, lossless vectorization, and other image processing applications. Unfortunately, while human observers can mentally deblur these low‐resolution images and reconstruct region topology, color and subpixel details, existing algorithms applicable to this task fail to produce outputs consistent with human expectations when presented with such images. We recover these viewer perceived blur‐free images at subpixel resolution, producing outputs where each input pixel is replaced by four corresponding (sub)pixels. Performing this task requires computing the size of the output image color palette, generating the palette itself, and associating each pixel in the output with one of the colors in the palette. We obtain these desired output components by leveraging a combination of perceptual and domain priors, and real world data. We use readily available data to train a network that predicts, for each anti‐aliased image, a low‐blur approximation of the blur‐free double‐resolution outputs we seek. The images obtained at this stage are perceptually closer to the desired outputs but typically still have hundreds of redundant differently colored regions with fuzzy boundaries. We convert these low‐blur intermediate images into blur‐free outputs consistent with viewer expectations using a discrete partitioning procedure guided by the characteristic properties of clip‐art images, observations about the antialiasing process, and human perception of anti‐aliased clip‐art. This step dramatically reduces the size of the output color palettes, and the region counts bringing them in line with viewer expectations and enabling the image processing applications we target. We demonstrate the utility of our method by using our outputs for a number of image processing tasks, and validate it via extensive comparisons to prior art. In our comparative study, participants preferred our deblurred outputs over those produced by the best‐performing alternative by a ratio of 75 to 8.5.

Implicit surface networks, such as arrangements of implicit surfaces and materials interfaces, are used for modeling piecewise smooth or partitioned shapes. However, accurate and numerically robust algorithms for discretizing either structure on a grid are still lacking. We present a unified approach for computing both types of surface networks for piecewise linear functions defined on a tetrahedral grid. Both algorithms are guaranteed to produce a correct combinatorial structure for any number of functions. Our main contribution is an exact and efficient method for partitioning a tetrahedron using the level sets of linear functions defined by barycentric interpolation. To further improve performance, we designed look-up tables to speed up processing of tetrahedra involving few functions and introduced an efficient algorithm for identifying nested 3D regions.

We introduce a modeling tool which can evolve a set of 3D objects in a functionality-aware manner. Our goal is for the evolution to generate large and diverse sets of plausible 3D objects for data augmentation, constrained modeling, as well as open-ended exploration to possibly inspire new designs. Starting with an initial population of 3D objects belonging to one or more functional categories, we evolve the shapes through part recombination to produce generations of hybrids or crossbreeds between parents from the heterogeneous shape collection. Evolutionary selection of offsprings is guided both by a functional plausibility score derived from functionality analysis of shapes in the initial population and user preference, as in a design gallery. Since cross-category hybridization may result in offsprings not belonging to any of the known functional categories, we develop a means for functionality partial matching to evaluate functional plausibility on partial shapes. We show a variety of plausible hybrid shapes generated by our functionality-aware model evolution, which can complement existing datasets as training data and boost the performance of contemporary data-driven segmentation schemes, especially in challenging cases. Our tool supports constrained modeling, allowing users to restrict or steer the model evolution with functionality labels. At the same time, unexpected yet functional object prototypes can emerge during open-ended exploration owing to structure breaking when evolving a heterogeneous collection.

To render higher quality images from the samples generated by path tracing with a low sample count, we propose a novel path reuse approach that processes a fixed collection of paths to iteratively refine and improve radiance estimates throughout the scene. Our method operates on a path graph consisting of the union of the traced paths with additional neighbor edges inserted among clustered nearby vertices. Our approach refines the initial noisy radiance estimates via an aggregation operator, treating vertices within clusters as independent sampling techniques that can be combined using MIS. In a novel step, we also introduce a propagation operator to forward the refined estimates along the paths to successive bounces. We apply the aggregation and propagation operations to the graph iteratively, progressively refining the radiance values, converging to fixed-point radiance estimates with lower variance than the original ones. We also introduce a decorrelation (final gather) step, which uses information already in the graph and is cheap to compute, allowing us to combine the method with standard denoisers. Our approach is lightweight, in the sense that it can be easily plugged into any standard path tracer and neural final image denoiser. Furthermore, it is independent of scene complexity, as the graph size only depends on image resolution and average path depth. We demonstrate that our technique leads to realistic rendering results starting from as low as 1 path per pixel, even in complex indoor scenes dominated by multi-bounce indirect illumination.

We present a novel representation of solid models for shape design. Like Constructive Solid Geometry (CSG), the solid shape is constructed from a set of halfspaces without the need for an explicit boundary structure. Instead of using Boolean expressions as in CSG, the shape is defined by sparsely placed samples on the boundary of each halfspace. This representation, called Boundary-Sampled Halfspaces (BSH), affords greater agility and expressiveness than CSG while simplifying the reverse engineering process. We discuss theoretical properties of the representation and present practical algorithms for boundary extraction and conversion from other representations. Our algorithms are demonstrated on both 2D and 3D examples.

Displacement mapping is a powerful mechanism for adding fine to medium geometric details over a 3D surface using a 2D map encoding them. While GPU rasterization supports it through the hardware tessellation unit, ray tracing surface meshes textured with high quality displacement requires a significant amount of memory. More precisely, the input surface needs to be pre-tessellated at the displacement map resolution before being enriched with its mandatory acceleration data structure. Consequently, designing displacement maps interactively while enjoying a full physically-based rendering is often impossible, as simply tiling multiple times the map quickly saturates the graphics memory. In this work we introduce a new tessellation-free displacement mapping approach for ray tracing. Our key insight is to decouple the displacement from its base domain by mapping a displacement-specific acceleration structures directly on the mesh. As a result, our method shows low memory footprint and fast high resolution displacement rendering, making interactive displacement editing possible.

Procedural modeling has produced amazing results, yet fundamental issues such as controllability and limited user guidance persist. We introduce a novel procedural model called PICO (Procedural Iterative Constrained Optimizer) and PICO-Graph that is the underlying procedural model designed with optimization in mind. The key novelty of PICO is that it enables the exploration of generative designs by combining both user and environmental constraints into a single framework by using optimization without the need to write procedural rules. The PICO-Graph procedural model consists of a set of geometry generating operations and a set of axioms connected in a directed cyclic graph. The forward generation is initiated by a set of axioms that use the connections to send coordinate systems and geometric objects through the PICO-Graph, which in turn generates more objects. This allows for fast generation of complex and varied geometries. Moreover, we combine PICO-Graph with efficient optimization that allows for quick exploration of the generated models and the generation of variants. The user defines the rules, the axioms, and the set of constraints; for example, whether an existing object should be supported by the generated model, whether symmetries exist, whether the object should spin, etc. PICO then generates a class of geometric models and optimizes them so that they fulfill the constraints. The generation and the optimization in our implementation provides interactive user control during model execution providing continuous feedback. For example, the user can sketch the constraints and guide the geometry to meet these specified goals. We show PICO on a variety of examples such as the generation of procedural chairs with multiple supports, generation of support structures for 3D printing, generation of spinning objects, or generation of procedural terrains matching a given input. Our framework could be used as a component in a larger design workflow; its strongest application is in the early rapid ideation and prototyping phases.

We present a generative model to synthesize 3D shapes as sets of handles -- lightweight proxies that approximate the original 3D shape -- for applications in interactive editing, shape parsing, and building compact 3D representations. Our model can generate handle sets with varying cardinality and different types of handles. Key to our approach is a deep architecture that predicts both the parameters and existence of shape handles and a novel similarity measure that can easily accommodate different types of handles, such as cuboids or sphere-meshes. We leverage the recent advances in semantic 3D annotation as well as automatic shape summarization techniques to supervise our approach. We show that the resulting shape representations are not only intuitive, but achieve superior quality than previous state-of-the-art. Finally, we demonstrate how our method can be used in applications such as interactive shape editing and completion, leveraging the latent space learned by our model to guide these tasks.

We propose a real-time method to estimate spatially-varying indoor lighting from a single RGB image. Given an image and a 2D location in that image, our CNN estimates a 5th order spherical harmonic representation of the lighting at the given location in less than 20ms on a laptop mobile graphics card. While existing approaches estimate a single, global lighting representation or require depth as input, our method reasons about local lighting without requiring any geometry information. We demonstrate, through quantitative experiments including a user study, that our results achieve lower lighting estimation errors and are preferred by users over the state-of-the-art. Our approach can be used directly for augmented reality applications, where a virtual object is relit realistically at any position in the scene in real-time.

Delivering rich, high quality 3D scenes over the internet is challenged by the size of the 3D objects in terms of geometry and textures. This paper proposes a new method for the delivery of textures, which are encoded and delivered as a video sequence, rather than independently. Implemented on the existing video delivery infrastructure, our method provides a fine-grained control on the quality of the resulting video sequence.

We propose a new method for reconstructing an implicit surface from an un-oriented point set. While existing methods often involve non-trivial heuristics and require additional constraints, such as normals or labelled points, we introduce a direct definition of the function from the points as the solution to a constrained quadratic optimization problem. The definition has a number of appealing features: it uses a single parameter (parameter-free for exact interpolation), applies to any dimensions, commutes with similarity transformations, and can be easily implemented without discretizing the space. More importantly, the use of a global smoothness energy allows our definition to be much more resilient to sampling imperfections than existing methods, making it particularly suited for sparse and non-uniform inputs.

Discovering 3D arrangements of objects from single indoor images is important given its many applications such as interior design and content creation for virtual environments. Although heavily researched in the recent years, existing approaches break down under medium to heavy occlusion as the core image-space region detection module fails in absence of directly visible cues. Instead, we take into account holistic contextual 3D information, exploiting the fact that objects in indoor scenes co-occur mostly in typical configurations. First, we use a neural network trained on real indoor annotated images to extract 2D keypoints, and feed them to a 3D candidate object generation stage. Then, we solve a global selection problem among these candidates using pairwise co-occurrence statistics discovered from a large 3D scene database. We iterate the process allowing for candidates with low keypoint response to be incrementally detected based on the location of the already discovered nearby objects. We demonstrate significant performance improvement over combinations of state-of-the-art methods, especially for scenes with moderately to severely occluded objects.

Abstract In this work we present the first algorithm for restoring consistency between curve networks on non‐parallel cross‐sections. Our method addresses a critical but overlooked challenge in the reconstruction process from cross‐sections that stems from the fact that cross‐sectional slices are often generated independently of one another, such as in interactive volume segmentation. As a result, the curve networks on two non‐parallel slices may disagree where the slices intersect, which makes these cross‐sections an invalid input for surfacing. We propose a method that takes as input an arbitrary number of non‐parallel slices, each partitioned into two or more labels by a curve network, and outputs a modified set of curve networks on these slices that are guaranteed to be consistent. We formulate the task of restoring consistency while preserving the shape of input curves as a constrained optimization problem, and we propose an effective solution framework. We demonstrate our method on a data‐set of complex multi‐labeled input cross‐sections. Our technique efficiently produces consistent curve networks even in the presence of large errors.

Artist-drawn images with distinctly colored, piecewise continuous boundaries, which we refer to as semi-structured imagery , are very common in online raster databases and typically allow for a perceptually unambiguous mental vector interpretation. Yet, perhaps surprisingly, existing vectorization algorithms frequently fail to generate these viewer-expected interpretations on such imagery. In particular, the vectorized region boundaries they produce frequently diverge from those anticipated by viewers. We propose a new approach to region boundary vectorization that targets semi-structured inputs and leverages observations about human perception of shapes to generate vector images consistent with viewer expectations. When viewing raster imagery observers expect the vector output to be an accurate representation of the raster input. However, perception studies suggest that viewers implicitly account for the lossy nature of the rasterization process and mentally smooth and simplify the observed boundaries. Our core algorithmic challenge is to balance these conflicting cues and obtain a piecewise continuous vectorization whose discontinuities, or corners, are aligned with human expectations. Our framework centers around a simultaneous spline fitting and corner detection method that combines a learned metric, that approximates human perception of boundary discontinuities on raster inputs, with perception-driven algorithmic discontinuity analysis. The resulting method balances local cues provided by the learned metric with global cues obtained by balancing simplicity and continuity expectations. Given the finalized set of corners, our framework connects those using simple, continuous curves that capture input regularities. We demonstrate our method on a range of inputs and validate its superiority over existing alternatives via an extensive comparative user study.

We present an algorithm for segmenting a mesh into patches whose boundaries are aligned with prominent ridge and valley lines of the shape. Our key insight is that this problem can be formulated as correlation clustering (CC), a graph partitioning problem originating from the data mining community. The formulation lends two unique advantages to our method over existing segmentation methods. First, since CC is non-parametric, our method has few parameters to tune. Second, as CC is governed by edge weights in the graph, our method offers users direct and local control over the segmentation result. Our technical contributions include the construction of the weighted graph on which CC is defined, a strategy for rapidly computing CC on this graph, and an interactive tool for editing the segmentation. Our experiments show that our method produces qualitatively better segmentations than existing methods on a wide range of inputs.

We present FlowRep , an algorithm for extracting descriptive compact 3D curve networks from meshes of free-form man-made shapes. We infer the desired compact curve network from complex 3D geometries by using a series of insights derived from perception, computer graphics, and design literature. These sources suggest that visually descriptive networks are cycle-descriptive , i.e their cycles unambiguously describe the geometry of the surface patches they surround. They also indicate that such networks are designed to be projectable , or easy to envision when observed from a static general viewpoint; in other words, 2D projections of the network should be strongly indicative of its 3D geometry. Research suggests that both properties are best achieved by using networks dominated by flowlines , surface curves aligned with principal curvature directions across anisotropic regions and strategically extended across sharp-features and isotropic areas. Our algorithm leverages these observation in the construction of a compact descriptive curve network. Starting with a curvature aligned quad dominant mesh we first extract sequences of mesh edges that form long, well-shaped and reliable flowlines by leveraging directional similarity between nearby meaningful flowline directions We then use a compact subset of the extracted flowlines and the model's sharp-feature, or trim, curves to form a sparse, projectable network which describes the underlying surface. We validate our method by demonstrating a range of networks computed from diverse inputs, using them for surface reconstruction, and showing extensive comparisons with prior work and artist generated networks.

In this work we present the first algorithm for reconstructing multi-labeled material interfaces the allows for explicit topology control. Our algorithm takes in a set of 2D cross-sectional slices (not necessarily parallel), each partitioned by a curve network into labeled regions representing different material types. For each label, the user has the option to constrain the number of connected components and genus. Our algorithm is able to not only produce a material interface that interpolates the curve networks but also simultaneously satisfy the topological requirements. Our key innovation is defining a space of topology-varying material interfaces, which extends the family of level sets in a scalar function, and developing discrete methods for sampling distinct topologies in this space. Besides specifying topological constraints, the user can steer the algorithm interactively, such as by scribbling. We demonstrate, on synthetic and biological shapes, how our algorithm opens up new opportunities for topology-aware modeling in the multi-labeled context.

We introduce Skippy, a novel algorithm for 3D interactive curve modeling from a single view. While positing curves in space can be a tedious task, our rapid sketching algorithm allows users to draw curves in and around existing geometry in a controllable manner. The key insight behind our system is to automatically infer the 3D curve coordinates by enumerating a large set of potential curve trajectories. More specifically, we partition 2D strokes into continuous segments that land both on and off the geometry, duplicating segments that could be placed in front or behind, to form a directed graph. We use distance fields to estimate 3D coordinates for our curve segments and solve for an optimally smooth path that follows the curvature of the scene geometry while avoiding intersections. Using our curve design framework we present a collection of novel editing operations allowing artists to rapidly explore and refine the combinatorial space of solutions. Furthermore, we include the quick placement of transient geometry to aid in guiding the 3D curve. Finally we demonstrate our interactive design curve system on a variety of applications including geometric modeling, and camera motion path planning.

Natural images often exhibit symmetries that should be taken into account when editing them. In this paper we present Nautilus --- a method for automatically identifying symmetric regions in an image along with their corresponding symmetry transformations. We compute dense local similarity symmetry transformations using a novel variant of the Generalised PatchMatch algorithm that uses Metropolis-Hastings sampling. We combine and refine these local symmetries using an extended Lucas-Kanade algorithm to compute regional transformations and their spatial extents. Our approach produces dense estimates of complex symmetries that are combinations of translation, rotation, scale, and reflection under perspective distortion. This enables a number of automatic symmetry-aware image editing applications including inpainting, rectification, beautification, and segmentation, and we demonstrate state-of-the-art applications for each of them.

We present a method for constructing almost-everywhere curvature-continuous, piecewise-quadratic curves that interpolate a list of control points and have local maxima of curvature only at the control points. Our premise is that salient features of the curve should occur only at control points to avoid the creation of features unintended by the artist. While many artists prefer to use interpolated control points, the creation of artifacts, such as loops and cusps, away from control points has limited the use of these types of curves. By enforcing the maximum curvature property, loops and cusps cannot be created unless the artist intends for them to be. To create such curves, we focus on piecewise quadratic curves, which can have only one maximum curvature point. We provide a simple, iterative optimization that creates quadratic curves, one per interior control point, that meet with G 2 continuity everywhere except at inflection points of the curve where the curves are G 1 . Despite the nonlinear nature of curvature, our curves only obtain local maxima of the absolute value of curvature only at interpolated control points.

In this work, we investigate the problem of automatically inferring the lattice structure of near-regular textures (NRT) in real-world images. Our technique leverages the PatchMatch algorithm for finding k-nearest-neighbor (kNN) correspondences in an image. We use these kNNs to recover an initial estimate of the 2D wallpaper basis vectors, and seed vertices of the texture lattice. We iteratively expand this lattice by solving an MRF optimization problem. We show that we can discretize the space of good solutions for the MRF using the kNNs, allowing us to efficiently and accurately optimize the MRF energy function using the Particle Belief Propagation algorithm. We demonstrate our technique on a benchmark NRT dataset containing a wide range of images with geometric and photometric variations, and show that our method clearly outperforms the state of the art in terms of both texel detection rate and texel localization score.

We propose a novel system to reconstruct a high-quality hair depth map from a single portrait photo with minimal user input. We achieve this by combining depth cues such as occlusions, silhouettes, and shading, with a novel 3D helical structural prior for hair reconstruction. We fit a parametric morphable face model to the input photo and construct a base shape in the face, hair and body regions using occlusion and silhouette constraints. We then estimate the normals in the hair region via a Shape-from-Shading-based optimization that uses the lighting inferred from the face model and enforces an adaptive albedo prior that models the typical color and occlusion variations of hair. We introduce a 3D helical hair prior that captures the geometric structure of hair, and show that it can be robustly recovered from the input photo in an automatic manner. Our system combines the base shape, the normals estimated by Shape from Shading, and the 3D helical hair prior to reconstruct high-quality 3D hair models. Our single-image reconstruction closely matches the results of a state-of-the-art multi-view stereo applied on a multi-view stereo dataset. Our technique can reconstruct a wide variety of hairstyles ranging from short to long and from straight to messy, and we demonstrate the use of our 3D hair models for high-quality portrait relighting, novel view synthesis and 3D-printed portrait reliefs.

In this work we detail the first algorithm that provides topological control during surface reconstruction from an input set of planar cross-sections. Our work has broad application in a number of fields including surface modeling and biomedical image analysis, where surfaces of known topology must be recovered. Given curves on arbitrarily oriented cross-sections, our method produces a manifold interpolating surface that exactly matches a user-specified genus. The key insight behind our approach is to formulate the topological search as a divide-and-conquer optimization process which scores local sets of topologies and combines them to satisfy the global topology constraint. We further extend our method to allow image data to guide the topological search, achieving even better results than relying on the curves alone. By simultaneously satisfying both geometric and topological constraints, we are able to produce accurate reconstructions with fewer input cross-sections, hence reducing the manual time needed to extract the desired shape.

Abstract In this work we detail a method that leverages the two color heads of recent low‐end fused deposition modeling (FDM) 3D printers to produce continuous tone imagery. The challenge behind producing such two‐tone imagery is how to finely interleave the two colors while minimizing the switching between print heads, making each color printed span as long and continuous as possible to avoid artifacts associated with printing short segments. The key insight behind our work is that by applying small geometric offsets, tone can be varied without the need to switch color print heads within a single layer. We can now effectively print (two‐tone) texture mapped models capturing both geometric and color information in our output 3D prints.

Abstract We propose an optimization framework for 3D printing that seeks to save printing time and the support material required to print 3D shapes. Three‐dimensional printing technology is rapidly maturing and may revolutionize how we manufacture objects. The total cost of printing, however, is governed by numerous factors which include not only the price of the printer but also the amount of material and time to fabricate the shape. Our PackMerger framework converts the input 3D watertight mesh into a shell by hollowing its inner parts. The shell is then divided into segments. The location of splits is controlled based on several parameters, including the size of the connection areas or volume of each segment. The pieces are then tightly packed using optimization. The optimization attempts to minimize the amount of support material and the bounding box volume of the packed segments while keeping the number of segments minimal. The final packed configuration can be printed with substantial time and material savings, while also allowing printing of objects that would not fit into the printer volume. We have tested our system on three different printers and it shows a reduction of 5–30% of the printing time while simultaneously saving 15–65% of the support material. The optimization time was approximately 1 min. Once the segments are printed, they need to be assembled.

Abstract We present an interactive method for mesh segmentation that is inspired by the classical live‐wire interaction for image segmentation. The core contribution of the work is the definition and computation of wires on surfaces that are likely to lie at segment boundaries. We define wires as geodesics in a new tensor‐based anisotropic metric, which improves upon previous metrics in stability and feature‐awareness. We further introduce a simple but effective mesh embedding approach that allows geodesic paths in an anisotropic path to be computed efficiently using existing algorithms designed for Euclidean geodesics. Our tool is particularly suited for delineating segmentation boundaries that are aligned with features or curvature directions, and we demonstrate its use in creating artist‐guided segmentations.

We present a user-friendly image editing system that supports a drag-and-drop object insertion (where the user merely drags objects into the image, and the system automatically places them in 3D and relights them appropriately), postprocess illumination editing, and depth-of-field manipulation. Underlying our system is a fully automatic technique for recovering a comprehensive 3D scene model (geometry, illumination, diffuse albedo, and camera parameters) from a single, low dynamic range photograph. This is made possible by two novel contributions: an illumination inference algorithm that recovers a full lighting model of the scene (including light sources that are not directly visible in the photograph), and a depth estimation algorithm that combines data-driven depth transfer with geometric reasoning about the scene layout. A user study shows that our system produces perceptually convincing results, and achieves the same level of realism as techniques that require significant user interaction.

Monte Carlo ray tracing is considered one of the most effective techniques for rendering photo-realistic imagery, but requires a large number of ray samples to produce converged or even visually pleasing images. We develop a novel image-plane adaptive sampling and reconstruction method based on local regression theory. A novel local space estimation process is proposed for employing the local regression, by robustly addressing noisy high-dimensional features. Given the local regression on estimated local space, we provide a novel two-step optimization process for selecting bandwidths of features locally in a data-driven way. Local weighted regression is then applied using the computed bandwidths to produce a smooth image reconstruction with well-preserved details. We derive an error analysis to guide our adaptive sampling process at the local space. We demonstrate that our method produces more accurate and visually pleasing results over the state-of-the-art techniques across a wide range of rendering effects. Our method also allows users to employ an arbitrary set of features, including noisy features, and robustly computes a subset of them by ignoring noisy features and decorrelating them for higher quality.

Abstract We present a method for accelerating the convergence of continuous non‐linear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyse this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace–Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized to arrive at a solution that is optimal across multiple scales. This is in contrast to traditional descent‐based methods, for which the rate of convergence often stalls early once the high frequency components have been optimized. We demonstrate how our method can be easily integrated into existing non‐linear optimization frameworks such as gradient descent, Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the non‐linear conjugate gradient method. We show significant performance improvement for shape optimization in variational shape modelling and parameterization, and we also demonstrate the use of our method for efficient physical simulation.

Abstract We present an algorithm for obtaining a triangulation of multiple, non‐planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a single polygon. The key novelty is a mechanism for avoiding non‐manifold outputs for two and more input polygons without compromising optimality. For better performance on real‐world data, we also propose an approximate solution by feeding the algorithm with a reduced set of triangles. In particular, we demonstrate experimentally that the triangles in the Delaunay tetrahedralization of the polygon vertices offer a reasonable trade off between performance and optimality.

Generating surfaces from 3D curve networks has been a longstanding problem in computer graphics. Recent attention to this area has resurfaced as a result of new sketch based modeling systems. In this work we present a new algorithm for finding cycles that bound surface patches. Unlike prior art in this area, the output of our technique is unrestricted, generating both manifold and non-manifold geometry with arbitrary genus. The novel insight behind our method is to formulate our problem as finding local mappings at the vertices and curves of our network, where each mapping describes how incident curves are grouped into cycles. This approach lends us the efficiency necessary to present our system in an interactive design modeler, whereby the user can adjust patch constraints and change the manifold properties of curves while the system automatically re-optimizes the solution.

The use of 3D printing has rapidly expanded in the past couple of years. It is now possible to produce 3D-printed objects with exceptionally high fidelity and precision. However, although the quality of 3D printing has improved, both the time to print and the material costs have remained high. Moreover, there is no guarantee that a printed model is structurally sound. The printed product often does not survive cleaning, transportation, or handling, or it may even collapse under its own weight. We present a system that addresses this issue by providing automatic detection and correction of the problematic cases. The structural problems are detected by combining a lightweight structural analysis solver with 3D medial axis approximations. After areas with high structural stress are found, the model is corrected by combining three approaches: hollowing, thickening, and strut insertion. Both detection and correction steps are repeated until the problems have been eliminated. Our process is designed to create a model that is visually similar to the original model but possessing greater structural integrity.

Abstract We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.

We present an algorithm for creating digital micrography images, or micrograms , a special type of calligrams created from minuscule text. These attractive text-art works successfully combine beautiful images with readable meaningful text. Traditional micrograms are created by highly skilled artists and involve a huge amount of tedious manual work. We aim to simplify this process by providing a computerized digital micrography design tool. The main challenge in creating digital micrograms is designing textual layouts that simultaneously convey the input image, are readable and appealing. To generate such layout we use the streamlines of singularity free, low curvature, smooth vector fields, especially designed for our needs. The vector fields are computed using a new approach which controls field properties via a priori boundary condition design that balances the different requirements we aim to satisfy. The optimal boundary conditions are computed using a graph-cut approach balancing local and global design considerations. The generated layouts are further processed to obtain the final micrograms. Our method automatically generates engaging, readable micrograms starting from a vector image and an input text while providing a variety of optional high-level controls to the user.

Abstract Smart deformation and warping tools play an important part in modern day geometric modeling systems. They allow existing content to be stretched or scaled while preserving visually salient information. To date, these techniques have primarily focused on preserving local shape details, not taking into account important global structures such as symmetry and line features. In this work we present a novel framework that can be used to preserve the global structure in images and vector art. Such structures include symmetries and the spatial relations in shapes and line features in an image. Central to our method is a new formulation of preserving structure as an optimization problem. We use novel optimization strategies to achieve the interactive performance required by modern day modeling applications. We demonstrate the effectiveness of our framework by performing structure preservation deformation of images and complex vector art at interactive rates.

Abstract In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a by‐product of the sampling procedure we produce a multi‐resolution representation of the density function as either a spherical mip‐map or Haar wavelet. By exploiting this implicit conversion we can extend the method to distribute samples according to the product of an SH function with a spherical mip‐map or Haar wavelet. This generalization has immediate applicability in rendering, e.g., importance sampling the product of a BRDF and an environment map where the lighting is stored as a single high‐resolution wavelet and the BRDF is represented in spherical harmonics. Since spherical harmonics can be efficiently rotated, this product can be computed on‐the‐fly even if the BRDF is stored in local‐space. Our sampling approach generates over 6 million samples per second while significantly reducing precomputation time and storage requirements compared to previous techniques.

Surface painting is a technique that allows a user to paint a texture directly onto a surface, usually with a texture atlas: a 1:1 mapping between the surface and its texture image. Many good automatic texture atlas generation methods exist that evenly distribute texture samples across a surface based on its area and/or curvature, and some are even sensitive to the frequency spectrum of the input texture. However, during the surface painting process, the texture can change non-uniformly and unpredictably and even the atlases are static and can thus fail to reproduce sections of finely painted detail such as surface illustration.We present a new texture atlas algorithm that distributes initial texture samples evenly according to surface area and texture frequency, and, more importantly, maintains this distribution as the texture signal changes during the surface painting process. The running time is further accelerated with a novel GPU implementation of the surface painting process. The redistribution of samples is transparent to the user, resulting in a surface painting system of seemingly unlimited resolution. The atlas construction is local, making it fast enough to run interactively on models containing over 100K faces.

We describe an implementation of procedural solid texturing that uses the texture atlas, a one-to-one mapping from an object's surface into its texture space. The method uses the graphics hardware to rasterize the solid texture coordinates as colors directly into the atlas. A texturing procedure is applied per-pixel to the texture map, replacing each solid texture coordinate with its corresponding procedural solid texture result. The procedural solid texture is then mapped back onto the object surface using standard texture mapping. The implementation renders procedural solid textures in real time, and the user can design them interactively.The quality of this technique depends greatly on the layout of the texture atlas. A broad survey of texture atlas schemes is used to develop a set of general purpose mesh atlases and tools for measuring their effectiveness at distributing as many available texture samples as evenly across the surface as possible. The main contribution of this paper is a new multiresolution texture atlas. It distributes all available texture samples in a nearly uniform distribution. This multiresolution texture atlas also supports MIP-mapped minification antialiasing and linear magnification filtering.