Abstract We present a robust and scalable method for generating field‐aligned surface‐filling curves on general manifolds. Building upon prior work on stripe pattern generation and field‐aligned surface‐filling curves, our approach introduces a novel stitching strategy that operates directly in the implicit domain. Unlike previous methods that extract and stitch isolines post hoc, we perform stitching by manipulating the scalar field itself, enabling an efficient and robust solution that generalizes beyond planar surfaces. We demonstrate more than an order of magnitude speed‐up and improved alignment with input direction fields when compared to state‐of‐the‐art geometric flow methods. Robustness is validated on the Thingi10K dataset. Moreover, the method integrates with Blender 4.5 for interactive curve generation on small models, and scales to massive meshes – producing surface‐filling curves with over ten million vertices in under twenty‐five minutes.

Abstract We present a constructive method for generating field‐aligned, volume‐filling curves in watertight 3D volumes. Existing approaches rely on slow gradient‐based optimization and often struggle to simultaneously achieve good field alignment, regular spacing, and scalability. To overcome this limitation, we adopt a constructive strategy: a set of well‐spaced, aligned curves is constructed and then stitched together to form a single closed curve. Our core idea is to represent the intermediate curves as the intersection of two 3D wavefronts orthogonal to the tangent field. The wavefronts are the isosurfaces of two wave fields that can be optimized efficiently. This formulation enables the generation of high‐quality volume‐filling curves with improved alignment and spacing compared to prior work, while scaling to outputs with more than 10 million vertices. We further demonstrate robustness on 4398 solids from the Thingi10K dataset. Our current method assumes watertight inputs whose smallest geometric feature exceeds twice the target curve spacing.

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.

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.

Abstract Anisotropic specular appearances are ubiquitous in the environment: brushed stainless steel pans, kettles, elevator walls, fur, or scratched plastics. Real‐time rendering of these materials with image‐based lighting is challenging due to the complex shape of the bidirectional reflectance distribution function (BRDF). We propose an anisotropic specular image‐based lighting method that can serve as a drop‐in replacement for the standard bent normal technique [Rev11]. Our method yields more realistic results with a 50% increase in computation time of the previous technique, using the same high dynamic range (HDR) preintegrated environment image. We use several environment samples positioned along the major axis of the specular microfacet BRDF. We derive an analytic formula to determine the two closest and two farthest points from the reflected direction on an approximation of the BRDF confidence region boundary. The two farthest points define the BRDF major axis, while the two closest points are used to approximate the BRDF width. The environment level of detail is derived from the BRDF width and the distance between the samples. We extensively compare our method with the bent normal technique and the ground truth using the GGX specular BRDF.

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.

Abstract Physically based rendering of glittering surfaces is a challenging problem in computer graphics. Several methods have proposed off‐line solutions, but none is dedicated to high‐performance graphics. In this work, we propose a novel physically based BRDF for real‐time rendering of glints. Our model can reproduce the appearance of sparkling materials (rocks, rough plastics, glitter fabrics, etc.). Compared to the previous real‐time method [ZK16], which is not physically based, our BRDF uses normalized NDFs and converges to the standard microfacet BRDF [CT82] for a large number of microfacets. Our method procedurally computes NDFs with hundreds of sharp lobes. It relies on a dictionary of 1D marginal distributions: at each location two of them are randomly picked and multiplied (to obtain a NDF), rotated (to increase the variety), and scaled (to control standard deviation/roughness). The dictionary is multiscale, does not depend on roughness, and has a low memory footprint (less than 1 MiB).

Abstract Rendering materials such as metallic paints, scratched metals and rough plastics requires glint integrators that can capture all micro‐specular highlights falling into a pixel footprint, faithfully replicating surface appearance. Specular normal maps can be used to represent a wide range of arbitrary micro‐structures. The use of normal maps comes with important drawbacks though: the appearance is dark overall due to back‐facing normals and importance sampling is suboptimal, especially when the micro‐surface is very rough. We propose a new glint integrator relying on a multiple‐scattering patch‐based BRDF addressing these issues. To do so, our method uses a modified version of microfacet‐based normal mapping [SHHD17] designed for glint rendering, leveraging symmetric microfacets. To model multiple‐scattering, we re‐introduce the lost energy caused by a perfectly specular, single‐scattering formulation instead of using expensive random walks. This reflectance model is the basis of our patch‐based BRDF, enabling robust sampling and artifact‐free rendering with a natural appearance. Additional calculation costs amount to about 40% in the worst cases compared to previous methods [YHMR16, CCM18].