3d modeling teams

Abstract: Procrustes-Wasserstein alignment jointly estimates a matching and rotation without supplied correspondences, but alternating minimization can stop at suboptimal solutions. Rubix solves the equally weighted planar problem globally under squared Euclidean loss. Each matching $σ$ of two centered $n$-point sets defines a complex correlation $z_σ=\sum_i\bar x_i y_{σ(i)}$. Their convex hull is the permutation polygon: supporting vertices give optimal matchings at fixed rotations, and the farthest vertex gives the global alignment. We prove the sharp bound of $n(n-1)$ vertices for $n\ge2$, answering Rote's rotation-assignment open problem. In exact arithmetic, assignment queries recover the polygon in $\mathcal O(n^5)$ operations. Assignment-based bounds extend the approach to three-dimensional rotations and partial matching at a supplied translation through branch-and-bound. On timed MPEG-7 shape pairs, Rubix attains every numerical reference value in 12 ms on average, 50 times faster than a rotation grid at the same accuracy. Its distances improve gravity-aligned matching of real 3D scans, shape retrieval and noisy crystal classification over alternating minimization.

Abstract: Engineering design often starts from a 2D sketch that fixes style and proportions, yet the subsequent 3D shape optimization relies on learned generative priors to keep the geometry valid. However, these priors are agnostic to the sketch: while they admit a valid design by correcting a drifted proposal back to its training distribution, they often correct it towards the high-density region, ignoring the specified design. We introduce \emph{AnchorGen}, a rectified-flow framework trained unconditionally on the concatenated shape and sketch latents of paired data. The learned manifold represents the joint distribution of shape-sketch pairs, so constraining the sketch component restricts the iterate to the sub-manifold of shapes consistent with a target style. Since training employs no conditioning signal, the constraint is imposed at inference: gradient descent optimizes the shape latent to minimize a differentiable drag surrogate, while constraining the sketch latent to remain close to the target sketch via a token-wise cosine penalty. A single model thereby supports design-preserving optimization, dimensionally explicit design edits, and sketch-only synthesis.

Abstract: Part-level 3D assets are essential for editing, reassembly, and interaction, yet recovering such structure from a single image remains challenging due to occlusion, ambiguous boundaries, and the need for coherent multi-part reasoning. Existing approaches struggle to achieve both controllable part-level generation and coherent multi-part structure, as part identity and spatial allocation are typically inferred implicitly. We present Seg3DParts, a segmentation-grounded framework for controllable part-level 3D generation from a single image. By treating segmentation as an explicit grounding signal, our method defines part identity during generation, enabling each component to be anchored to a corresponding image region. To ensure coherent assemblies, we introduce structured cross-part interaction that allows components to exchange global context throughout the generative process. As a result, Seg3DParts directly generates well-aligned part meshes in a shared canonical space without post-hoc alignment, supporting flexible and controllable decomposition. We further introduce PartObjectNet, a large-scale dataset with over 200K objects and 1M annotated parts. Experiments demonstrate that Seg3DParts achieves superior geometry quality, cross-part coherence, and part-level controllability over existing methods.

Abstract: The decomposition of 3D point clouds into interpretable geometric primitives remains a longstanding challenge in Computer Vision and Computer Graphics. Among the available representations, superquadrics offer a compact and expressive model capable of capturing a wide range of shapes. However, their estimation is inherently challenging, as it requires solving a non-linear optimization problem and is particularly sensitive to noise, outliers, and overlapping structures. While robust estimation methods such as RANSAC and its variants achieve strong performance, they rely primarily on spatial proximity and residual-based criteria, often leading to incorrect inlier assignments across adjacent or complex arrangements of primitives. In this work, we introduce a geometric-aware framework for primitive decomposition that explicitly incorporates local surface properties into the fitting process. Specifically, we propose an inlier refinement step formulated as an energy minimization problem and solved via graph-cut optimization. Our formulation integrates geometric priors, such as normal consistency, enabling more reliable inlier selection beyond purely residual-based criteria. The approach naturally applies to both single-model estimation and multi-model decomposition. By leveraging geometric information beyond point-wise residuals, our method reduces erroneous inlier propagation and stabilizes parameter estimation. Experiments on synthetic and real datasets show consistent improvements in geometric accuracy, robustness to noise and outliers, and convergence efficiency compared to state-of-the-art RANSAC-based methods.

Abstract: The use of B-splines and Non-Uniform Rational B-Splines surfaces constitutes the mathematical foundation of contemporary computer-aided design (CAD) systems. Despite long-term progress, geometric kernels in traditional CAD still rely heavily on predetermined heuristic initialization for surface fitting and parameterization. Meanwhile, the procedural semantics and design intent encoded in modeling histories are largely ignored during geometry generation. This disconnect creates a gap between high-level design intent and solver-executable geometric configuration, often leading to suboptimal and semantically inconsistent fitting results. To bridge this gap, we introduce LASP, a Language-Augmented Semantic Priors framework that leverages large language models (LLMs) to infer structured, solver-usable B-spline priors from procedural modeling histories. Rather than modifying the geometric kernel itself, LASP operates as a semantic reasoning layer above existing solvers. It first translates modeling histories into rich textual descriptions that capture design intent, geometric context, and functional relationships, and then uses a fine-tuned LLM to predict structured B-spline prior parameters. LASP is trained through a two-stage scheme that combines local geometric regularities with long-range contextual dependencies, producing priors that are both interpretable and semantically coherent. This approach furnishes inductive signals that direct the conventional B-spline fitting process toward solutions that more accurately encapsulate the intended design objectives and demonstrate heightened semantic coherence. Compared to traditional machine learning schemes, the experiments demonstrate that language-driven reasoning can serve as a powerful inductive bias for geometric solving, establishing a new paradigm of language-guided geometric optimization in modern CAD systems.