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Image customization is a fundamental image editing task that synthesizes an instruction-following image of a specific subject conditioned on reference images. However, most existing methods rely on a single reference image, which makes it difficult to preserve the subject’s underlying 3D structure and maintain multi-view consistency. We therefore study 3D-aware image customization: given an arbitrary multi-view reference set, the model generates an instruction-following image from a user-specified target camera viewpoint, while preserving both subject identity and 3D geometry. This formulation enables a practical “capture-then-customize” workflow and reduces the viewpoint drift commonly observed in 2D-conditioned editors. We propose ViewWeaver, a geometry-grounded generative rendering framework that anchors synthesis with explicit target-view rendering cues aligned with camera geometry, and aggregates multi-view evidence through a lightweight Mixture-of-Views module inside a rectified-flow DiT generator. To facilitate scalable training and systematic evaluation, we build a large-scale data engine and introduce GSO12, a comprehensive benchmark assessing visual fidelity, instruction adherence, and 3D consistency across different reference-view budgets and diverse scene contexts. Extensive experiments show that ViewWeaver significantly improves 3D consistency and viewpoint controllability while maintaining strong identity preservation, enabling accurate and flexible view-controllable customization.
As instruction-based editing models and multimodal large language models continue to advance, a wide range of image editing tasks have become feasible. However, achieving precise and consistent geometric image editing, such as translating, scaling and rotating in 3D space, remains a major challenge. In this work, we introduce BoxCtrl, a 3D-aware visual prompting framework to address this problem. Unlike text-only or coarse 2D-guided approaches, our method introduces informative RGB 3D bounding boxes projected onto 2D images as a visual prompting. Each box is outlined and its three orthogonal faces are individually painted with different RGB colors, which simultaneously encode its position, size and orientation, providing a compact and intuitive in-context visual example. The key to BoxCtrl’s success lies in its well-designed bounding boxes, which serve as visual prompting that decouple geometric control from appearance control. This design enables the model to learn consistent correspondences between faces with the same color in the latent space, leading to a more precise understanding of geometric intention and more accurate editing result. We introduce a two-stage training paradigm comprising Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL). To address the scarcity of paired training data, we first construct a large-scale synthetic dataset for the SFT stage, which equips the model with fundamental editing capabilities. However, the generalization of the SFT model is constrained by the synthetic-to-real domain gap. To bridge this, we incorporate an online RL stage leveraging unpaired real-world data. Guided by a comprehensive reward function evaluating both geometric accuracy and visual fidelity, our SFT-RL strategy significantly enhances geometric precision while maintaining photorealistic quality. Extensive experiments demonstrate that BoxCtrl achieves state-of-the-art performance across translation, rotation, scaling, and composite editing tasks. Our code is available at https://github.com/beaglew/BoxCtrl.
Transfinite interpolation is a fundamental theme in geometric modeling. The most well-known transfinite interpolation volume is the Coons volume. However, the topology of Coons volumes is restricted to hexahedra, which significantly limits their applications. In this paper, we generalize the Coons volume from hexahedral topology to arbitrary polyhedral topologies via generalized barycentric coordinates. We prove that the proposed generalized Coons volume possesses several desirable geometric properties and demonstrate its applications in computer graphics.
Representing complex geometry as a displacement function defined over a coarse base mesh enables compact storage and accelerated rendering. The core challenge in converting detailed triangle meshes into this representation is computing base meshes that have as few triangles as possible, while also supporting displacement functions that accurately approximate the input. Accurate approximation requires the supported displacement functions to bijectively map the input surface onto the base with low parametric distortion. We observe that this distortion can be measured by evaluating the pointwise Jacobian of the displacement functions. Our new DJM (Displacement Jacobian Metric)-based base-mesh construction method uses the Jacobian of the displacement functions to guide base mesh computation, enabling us to outperform prior approaches in terms of accuracy to size trade-off. We achieve this goal by proposing a variant of the QEM-based simplification scheme that constrains the displacement mapping between the input and the base to be bijective and low distortion (defined as satisfying a lower bound on the mapping Jacobian). When evaluating and encoding the displacement maps, we avoid unreliable ray-mesh intersections by explicitly storing the mapping between the input mesh and the base throughout the construction process, and use this mapping within a robust inverse barycentric displacement solver to obtain dense base-to-mesh correspondences to assist all computations. We demonstrate DJM to outperform alternative schemes in terms of reconstruction accuracy to size trade-off, and demonstrate its robustness and usability for micromesh based rendering and neural encoding.
Anisotropic friction is a critical source of propulsion for efficient locomotion of many terrestrial animals. The interplay between animal morphology, control, and anisotropically frictional contact makes designing optimal anisotropic friction for terrestrial locomotion intriguing and challenging. We propose a computational pipeline for co-designing anisotropic friction and controllers of terrestrial robots with diverse morphologies. Our pipeline presents a co-design algorithm that alternates between optimizing direction of anisotropic friction and training a neural network controller to improve the locomotion performance of a given robot morphology. Based on the intuition that controller’s performance does not change significantly when the frictional force differs slightly, we introduce the concept of trust-region into robot co-design, allowing the controller network to continue training from the previous iteration. Our evaluation on various morphologies show that anisotropic friction is critical for terrestrial robot locomotion, and our pipeline is statistically better than current state-of-the-art methods. Furthermore, we reveal that large language models (LLM) constitute a strong baseline for this kind of co-design problems, worth receiving more attention. We demonstrate that co-designing anisotropic friction and control unlocks effective locomotion in various downstream tasks, including locomotion on uneven terrain, navigation in a maze, and object manipulation. To validate our pipeline in the real world, we design and 3D print a variety of scales and systematically measure their anisotropic friction coefficients. Then we construct a multi-link robot with anisotropic scales designed by our pipeline and compare its performance with isotropic scales. Our real-world experiments confirm that isotropic scales are insufficient to support terrestrial robots’ locomotion abilities, and computationally co-designing friction and control enables robots to perform tasks including turning, slithering, and other non-trivial locomotion tasks.
Coordinate-motion assemblies can only be disassembled by the simultaneous motion of multiple parts along distinct paths, providing high structural stability and enabling efficient robotic assembly. Existing examples are largely limited to architectural structures using joint-based connections, or puzzles created through trial-and-error, as the relationship between part geometry and coordinate motion remains poorly understood. Computationally designing such assemblies is challenging because it requires jointly achieving distributed contacts across the entire assembly and a unique coordinate motion for disassembly that rules out other feasible motions. We address this challenge by establishing a theoretical connection between part geometry and unique coordinate motion, enabling us to rigorously verify whether a given assembly admits a unique coordinate motion. Building on this theory, we introduce a two-stage algorithm that optimizes contact interfaces for a target motion and constructs physically feasible part geometries that conform to a user-specified global shape. We demonstrate our approach on models with complex geometries and topologies, including assemblies with large part counts, and validate it through physical fabrication and experiments.
We introduce Kinematic Kitbashing, an optimization framework that synthesizes articulated 3D objects by assembling reusable parts conditioned on an abstract kinematic graph. Given the graph and a library of articulated parts, our method optimizes per-part similarity transformations that place, orient, and scale each component into a coherent articulated object; optional graph edits further enable novel assemblies beyond the prescribed connectivity. Central to our method is an exemplar-based analogy for part placement: each reused component is paired with a single source asset that exemplifies how it attaches to its parent. We capture this attachment context using vector distance fields and measure consistency by integrating the matching error over the joint’s full motion range. This yields a kinematics-aware attachment energy that favors placements that preserve the exemplar’s local attachment neighborhood throughout articulation. To incorporate task-level functionality, we use this attachment energy as a prior in an annealed Langevin sampling framework, enabling gradient-free optimization of black-box functionality objectives. We demonstrate the versatility of kinematic kitbashing across diverse applications, including instantiating kinematic graphs from user-selected or automatically retrieved parts, synthesizing assemblies with user-defined functionality, and re-targeting articulations via graph edits.
Gears transmit rotary motion via meshing teeth, with circular gears commonly used to produce constant-speed rotation and non-circular gears enabling variable-speed rotation. In order to generate complex motion, gears are typically combined with other mechanical parts such as linkages, cam-followers, and belts, which often leads to complex structures and reduced transmission efficiency. To address these limitations, recent research has been investigating non-conventional gears that can transfer complex motion while preserving key properties of gears, such as compactness, high transmission efficiency, and load-bearing capability. In this paper, we present a new gear mechanism called the multi-point conjugation gear mechanism for exactly generating a user-specified 3D motion under external loads. The mechanism contains a single pair of gears modeled by a pair of conjugate surfaces with multiple conjugation points. We introduce an optimization-based approach that designs this new gear mechanism by modeling multiple sub-gear pairs that satisfy multi-point conjugation and fabricability requirements, whose load-bearing performance is quantified using a measure of dynamic form closure. We demonstrate the effectiveness of our approach by modeling various multi-point conjugation gear mechanisms that generate different kinds of motions, evaluating their kinematic performance and load-bearing performance using 3D printed prototypes, and presenting two application examples.
We present Diceplay, a modular physical display for abstract visual composition built from a grid of identical dice. Each die has six faces with distinct geometric primitives, and images emerge through the placement and orientation of the dice. While this medium enables reusable and reconfigurable physical imagery, it poses a challenging design problem: images must be expressed through discrete, extremely low-resolution abstractions, making manual authoring difficult. To address this challenge, we introduce a computational design system that automatically generates Diceplay configurations from text prompts. Our key technical contribution is a grammar-based formulation that relaxes this discrete design space into a smooth optimization landscape, enabling gradient-based optimization using score distillation sampling. We show that our approach consistently produces meaningful abstractions for this medium, whereas state-of-the-art smoothing techniques fail in this extremely challenging regime. We demonstrate our method across a range of prompts and fabricated examples, showing how computationally generated abstractions can be realized as physical visual artifacts.
We present a global, discrete optimization framework for quad-dominant mesh reduction that formulates simplification as an edge selection problem under coupled topological and geometric constraints. Unlike greedy edge-collapse heuristics, which make irreversible local decisions, and rigid poly-chord removal schemes, which over-constrain global structure, our method casts quad-dominant reduction as an Integer Linear Programming (ILP) problem that jointly optimizes edge flow continuity and geometric fidelity in a single global optimization. To make this formulation both tractable and adaptive, we segment poly-chords at geometrically meaningful breakpoints to relax otherwise rigid topological constraints, and introduce geometry-aware soft constraints that steer the optimization toward preserving high-curvature and deformation-critical regions. Extensive experiments demonstrate that our approach consistently outperforms state-of-the-art methods in preserving quad structure and edge flow, while achieving competitive geometric accuracy and significantly benefiting downstream editing applications.
A variety of problems in geometry processing boil down to finding the most parallel field relative to a connection. Instances of this prototypical problem show up in computing direction fields and stripe patterns, quadrilateral meshing, and visualization of fluid flows. When the class of allowed fields includes those with topological defects, a relaxation is required to make the problem well-posed. We observe that these problems can be viewed as synchronization problems, which admit a natural semidefinite relaxation. We propose a unified method of solving all these problems via the efficient Burer-Monteiro factorization method. Geometrically, this amounts to lifting the field values to a higher-dimensional manifold, naturally resolving the singular nature of defects. Practically, we show that our convex relaxation method achieves better and more reliable optima than previous work employing alternative relaxations.
The low-poly style is a popular genre of vector graphics that depicts objects and scenes as flat-shaded meshes of low polygon count, often with a limited palette. In this paper, we propose a method to generate 2D low-poly meshes to abstract images. While it has been possible to achieve this look with general-purpose image generators and vector-based diffusion models, the resulting images are not guaranteed to be valid polygonal meshes. A key problem is that polygons overlap or intersect and, in the case of pixel-based image generators, the shapes are often not polygons. Moreover, the colors are not guaranteed to be constrained to a fixed palette. Aside from aesthetic considerations, this has practical consequences: it complicates editing and fabricating the results. We solve this problem by representing an image as a 2D polygonal mesh and optimizing the topology, geometry and coloring of the mesh using score distillation sampling, while enforcing geometric constraints, such as manifoldness and bijectivity. This presents unique challenges due to the discrete nature of the topology, which we handle using a fine-to-coarse strategy based on mesh simplification. By also constraining the colors to a fixed palette, we are able to produce various fabrications such as mosaics, embroidery, crocheting, patchwork and stencils from the resulting vector images. Code is at https://github.com/rubenwiersma/alps.
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Artistic styles often embed abstraction beyond surface appearance, involving deliberate reinterpretation of structure rather than mere changes in texture or color. Conventional style transfer methods typically preserve the input geometry and therefore struggle to capture this deeper abstraction behavior, especially for illustrative and non-photorealistic styles. In this work, we introduce Abstraction in Style (AiS), a generative framework that separates structural abstraction from visual stylization. Given a target image and a small set of style exemplars, AiS first derives an intermediate abstraction proxy that reinterprets the target’s structure in accordance with the abstraction logic exhibited by the style. The proxy captures semantic structure while relaxing geometric fidelity, enabling subsequent stylization to operate on an abstracted representation rather than the original image. In a second stage, the abstraction proxy is rendered to produce the final stylized output, preserving visual coherence with the reference style. Both stages are implemented using a shared image-space analogy, enabling transformations to be learned from visual exemplars without explicit geometric supervision. By decoupling abstraction from appearance and treating abstraction as an explicit, transferable process, AiS supports a wider range of stylistic transformations, improves controllability, and enables more expressive stylization.
Recent radiance-field-based reconstruction methods, such as NeRF and 3DGS, achieve high visual fidelity for indoor scenes, but often break down under scene editing due to baked illumination and the lack of explicit light transport. In contrast, inverse path tracing methods based on mesh representations enforce correct light transport but require highly accurate geometry, making them difficult to apply robustly to real indoor scenes. We present Emission-Aware Gaussians and Path Tracing (EAG-PT), a method for physically based reconstruction and rendering of indoor scenes using a unified 2D Gaussian representation, targeting editable diffuse global illumination. Our approach consists of three key ideas: (1) representing indoor scenes with 2D Gaussians as a transport-friendly geometric proxy that avoids explicit mesh reconstruction; (2) explicitly separating emissive and non-emissive components during reconstruction to support editing; and (3) decoupling reconstruction from final rendering by using efficient single-bounce optimization and high-quality multi-bounce path tracing, respectively. Experiments on synthetic and real indoor scenes show that EAG-PT produces more natural and physically consistent edited renderings than radiance-field reconstructions, while preserving finer geometric detail and avoiding mesh-induced artifacts compared with mesh-based inverse path tracing. These results highlight the potential of our approach for applications such as interior design, XR content creation, and embodied AI.