Classical microfacet theory suffers from energy loss on materials with high roughness due to the single bounce assumption of most microfacet models. When roughness is high, there is a large chance of multiple scattering occurring among the microfacets of the surface. Without explicitly modelling for this behaviour, rough surfaces appear darker than they should. To address this issue, we present a novel method to estimate the multiple scattering contribution from a second light bounce. Our method is inspired by Zipin’s geometric construction approach, which simplifies the calculation of the light transport inside a V-groove cavity. Our experimental results demonstrate that our method is visually pleasing, physically plausible, and artifact-free compared to recent multiple scattering works. Additionally, the low computational cost makes our model suitable for real-time rendering.

Artists often need to reshape 3D models of human-made objects by changing the relative proportions or scales of different model parts or elements while preserving the look and structure of the inputs. Manually reshaping inputs to satisfy these criteria is highly time-consuming; the edit in our teaser took an artist 5 hours to complete. However, existing methods for 3D shape editing are largely designed for other tasks and produce undesirable outputs when repurposed for reshaping. Prior work on 2D curve network reshaping suggests that in 2D settings the user-expected outcome is achieved when the reshaping edit keeps the orientations of the different model elements and when these elements scale as-locally-uniformly-as-possible (ALUP). However, our observations suggest that in 3D viewers are tolerant of non-uniform tangential scaling if and when this scaling preserves slippage and reduces changes in element size, or scale , relative to the input. Slippage preservation requires surfaces which are locally slippable with respect to a given rigid motion to retain this property post-reshaping (a motion is slippable if when applied to the surface, it slides the surface along itself without gaps). We build on these observations by first extending the 2D ALUP framework to 3D and then modifying it to allow non-uniform scaling while promoting slippage and scale preservation. Our 3D ALUP extension produces reshaped outputs better aligned with viewer expectations than prior alternatives; our slippage-aware method further improves the outcome producing results on par with manual reshaping ones. Our method does not require any user input beyond specifying control handles and their target locations. We validate our method by applying it to over one hundred diverse inputs and by comparing our results to those generated by alternative approaches and manually. Comparative study participants preferred our outputs over the best performing traditional deformation method by a 65% margin and over our 3D ALUP extension by a 61% margin; they judged our outputs as at least on par with manually produced ones.

Vector clip-art images consist of regions bounded by a network of vector curves. Users often wish to reshape , or rescale, existing clip-art images by changing the locations, proportions, or scales of different image elements. When reshaping images depicting synthetic content they seek to preserve global and local structures. These structures are best preserved when the gradient of the mapping between the original and the reshaped curve networks is locally as close as possible to a uniform scale; mappings that satisfy this property maximally preserve the input curve orientations and minimally change the shape of the input's geometric details, while allowing changes in the relative scales of the different features. The expectation of approximate scale uniformity is local ; while reshaping operations are typically expected to change the relative proportions of a subset of network regions, users expect the change to be minimal away from the directly impacted regions and expect such changes to be gradual and distributed as evenly as possible. Unfortunately, existing methods for editing 2D curve networks do not satisfy these criteria. We propose a targeted As-Locally-Uniform-as-Possible (ALUP) vector clip-art reshaping method that satisfies the properties above. We formulate the computation of the desired output network as the solution of a constrained variational optimization problem. We effectively compute the desired solution by casting this continuous problem as a minimization of a non-linear discrete energy function, and obtain the desired minimizer by using a custom iterative solver. We validate our method via perceptual studies comparing our results to those created via algorithmic alternatives and manually generated ones. Participants preferred our results over the closest alternative by a ratio of 6 to 1.

Virtual reality drawing applications let users draw 3D shapes using brushes that form ribbon shaped, or ruled-surface, strokes. Each ribbon is uniquely defined by its user-specified ruling length, path, and the ruling directions at each point along this path. Existing brushes use the trajectory of a handheld controller in 3D space as the ribbon path, and compute the ruling directions using a fixed mapping from a specific controller coordinate-frame axis. This fixed mapping forces users to rotate the controller and thus their wrists to change ribbon normal or ruling directions, and requires substantial physical effort to draw even medium complexity ribbons. Since human ability to rotate their wrists continuously is heavily restricted, the space of ribbon geometries users can comfortably draw using these brushes is limited. These brushes can be unpredictable, producing ribbons with unexpectedly varying width or flipped and wobbly normals in response to seemingly natural hand gestures. Our AdaptiBrush ribbon brush system dramatically extends the space of ribbon geometries users can comfortably draw while enabling them to accurately predict the ribbon shape that a given hand motion produces. We achieve this by introducing a novel adaptive ruling direction computation method, enabling users to easily change ribbon ruling and normal orientation using predominantly translational controller, and thus wrist, motion. We facilitate ease-of-use by computing predictable ruling directions that smoothly change in both world and controller coordinate systems, and facilitate ease-of-learning by prioritizing ruling directions which are well-aligned with one of the controller coordinate system axes. Our comparative user studies confirm that our more general and predictable ruling computation leads to significant improvements in brush usability and effectiveness compared to all prior brushes; in a head to head comparison users preferred AdaptiBrush over the next-best brush by a margin of 2 to 1.

Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge through the use of largely unstructured neural networks that effectively distill conditional mapping and priors over 3D shape. In this work, we induce structure and geometric constraints by leveraging three core observations: (1) the surface of most everyday objects is often almost entirely exposed from pairs of typical opposite views; (2) everyday objects often exhibit global reflective symmetries which can be accurately predicted from single views; (3) opposite orthographic views of a 3D shape share consistent silhouettes. Following these observations, we first predict orthographic 2.5D visible surface maps (depth, normal and silhouette) from perspective 2D images, and detect global reflective symmetries in this data; second, we predict the back facing depth and normal maps using as input the front maps and, when available, the symmetric reflections of these maps; and finally, we reconstruct a 3D mesh from the union of these maps using a surface reconstruction method best suited for this data. Our experiments demonstrate that our framework outperforms state-of-the art approaches for 3D shape reconstructions from 2D and 2.5D data in terms of input fidelity and details preservation. Specifically, we achieve 12% better performance on average in ShapeNet benchmark dataset, and up to 19% for certain classes of objects (e.g., chairs and vessels).

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.

Popular Virtual Reality (VR) tools allow users to draw varying-width, ribbonlike 3D brush strokes by moving a hand-held controller in 3D space. Artists frequently use dense collections of such strokes to draw virtual 3D shapes. We propose SurfaceBrush , a surfacing method that converts such VR drawings into user-intended manifold free-form 3D surfaces, providing a novel approach for modeling 3D shapes. The inputs to our method consist of dense collections of artist-drawn stroke ribbons described by the positions and normals of their central polylines, and ribbon widths. These inputs are highly distinct from those handled by existing surfacing frameworks and exhibit different sparsity and error patterns, necessitating a novel surfacing approach. We surface the input stroke drawings by identifying and leveraging local coherence between nearby artist strokes. In particular, we observe that strokes intended to be adjacent on the artist imagined surface often have similar tangent directions along their respective polylines. We leverage this local stroke direction consistency by casting the computation of the user-intended manifold surface as a constrained matching problem on stroke polyline vertices and edges. We first detect and smoothly connect adjacent similarly-directed sequences of stroke edges producing one or more manifold partial surfaces. We then complete the surfacing process by identifying and connecting adjacent similarly directed edges along the borders of these partial surfaces. We confirm the usability of the SurfaceBrush interface and the validity of our drawing analysis via an observational study. We validate our stroke surfacing algorithm by demonstrating an array of manifold surfaces computed by our framework starting from a range of inputs of varying complexity, and by comparing our outputs to reconstructions computed using alternative means.

When creating line drawings, artists frequently depict intended curves using multiple, tightly clustered, or overdrawn, strokes. Given such sketches, human observers can readily envision these intended, aggregate , curves, and mentally assemble the artist's envisioned 2D imagery. Algorithmic stroke consolidation---replacement of overdrawn stroke clusters by corresponding aggregate curves---can benefit a range of sketch processing and sketch-based modeling applications which are designed to operate on consolidated, intended curves. We propose StrokeAggregator , a novel stroke consolidation method that significantly improves on the state of the art, and produces aggregate curve drawings validated to be consistent with viewer expectations. Our framework clusters strokes into groups that jointly define intended aggregate curves by leveraging principles derived from human perception research and observation of artistic practices. We employ these principles within a coarse-to-fine clustering method that starts with an initial clustering based on pairwise stroke compatibility analysis, and then refines it by analyzing interactions both within and in-between clusters of strokes. We facilitate this analysis by computing a common 1D parameterization for groups of strokes via common aggregate curve fitting. We demonstrate our method on a large range of line drawings, and validate its ability to generate consolidated drawings that are consistent with viewer perception via qualitative user evaluation, and comparisons to manually consolidated drawings and algorithmic alternatives.

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.