Daily Papers

Creating multi-view wire art (MVWA), a static 3D sculpture with diverse interpretations from different viewpoints, is a complex task even for skilled artists. In response, we present DreamWire, an AI system enabling everyone to craft MVWA easily. Users express their vision through text prompts or scribbles, freeing them from intricate 3D wire organisation. Our approach synergises 3D B\'ezier curves, Prim's algorithm, and knowledge distillation from diffusion models or their variants (e.g., ControlNet). This blend enables the system to represent 3D wire art, ensuring spatial continuity and overcoming data scarcity. Extensive evaluation and analysis are conducted to shed insight on the inner workings of the proposed system, including the trade-off between connectivity and visual aesthetics.

This paper introduces a novel approach to post-Optical Character Recognition Correction (POC) for handwritten Cyrillic text, addressing a significant gap in current research methodologies. This gap is due to the lack of large text corporas that provide OCR errors for further training of language-based POC models, which are demanding in terms of corpora size. Our study primarily focuses on the development and application of a synthetic handwriting generation engine based on B\'ezier curves. Such an engine generates highly realistic handwritten text in any amounts, which we utilize to create a substantial dataset by transforming Russian text corpora sourced from the internet. We apply a Handwritten Text Recognition (HTR) model to this dataset to identify OCR errors, forming the basis for our POC model training. The correction model is trained on a 90-symbol input context, utilizing a pre-trained T5 architecture with a seq2seq correction task. We evaluate our approach on HWR200 and School_notebooks_RU datasets as they provide significant challenges in the HTR domain. Furthermore, POC can be used to highlight errors for teachers, evaluating student performance. This can be done simply by comparing sentences before and after correction, displaying differences in text. Our primary contribution lies in the innovative use of B\'ezier curves for Cyrillic text generation and subsequent error correction using a specialized POC model. We validate our approach by presenting Word Accuracy Rate (WAR) and Character Accuracy Rate (CAR) results, both with and without post-OCR correction, using real open corporas of handwritten Cyrillic text. These results, coupled with our methodology, are designed to be reproducible, paving the way for further advancements in the field of OCR and handwritten text analysis. Paper contributions can be found in https://github.com/dbrainio/CyrillicHandwritingPOC

Abstraction is at the heart of sketching due to the simple and minimal nature of line drawings. Abstraction entails identifying the essential visual properties of an object or scene, which requires semantic understanding and prior knowledge of high-level concepts. Abstract depictions are therefore challenging for artists, and even more so for machines. We present CLIPasso, an object sketching method that can achieve different levels of abstraction, guided by geometric and semantic simplifications. While sketch generation methods often rely on explicit sketch datasets for training, we utilize the remarkable ability of CLIP (Contrastive-Language-Image-Pretraining) to distill semantic concepts from sketches and images alike. We define a sketch as a set of B\'ezier curves and use a differentiable rasterizer to optimize the parameters of the curves directly with respect to a CLIP-based perceptual loss. The abstraction degree is controlled by varying the number of strokes. The generated sketches demonstrate multiple levels of abstraction while maintaining recognizability, underlying structure, and essential visual components of the subject drawn.

3D sketches are widely used for visually representing the 3D shape and structure of objects or scenes. However, the creation of 3D sketch often requires users to possess professional artistic skills. Existing research efforts primarily focus on enhancing the ability of interactive sketch generation in 3D virtual systems. In this work, we propose Diff3DS, a novel differentiable rendering framework for generating view-consistent 3D sketch by optimizing 3D parametric curves under various supervisions. Specifically, we perform perspective projection to render the 3D rational B\'ezier curves into 2D curves, which are subsequently converted to a 2D raster image via our customized differentiable rasterizer. Our framework bridges the domains of 3D sketch and raster image, achieving end-toend optimization of 3D sketch through gradients computed in the 2D image domain. Our Diff3DS can enable a series of novel 3D sketch generation tasks, including textto-3D sketch and image-to-3D sketch, supported by the popular distillation-based supervision, such as Score Distillation Sampling (SDS). Extensive experiments have yielded promising results and demonstrated the potential of our framework.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

We present PI3DETR, an end-to-end framework that directly predicts 3D parametric curve instances from raw point clouds, avoiding the intermediate representations and multi-stage processing common in prior work. Extending 3DETR, our model introduces a geometry-aware matching strategy and specialized loss functions that enable unified detection of differently parameterized curve types, including cubic B\'ezier curves, line segments, circles, and arcs, in a single forward pass. Optional post-processing steps further refine predictions without adding complexity. This streamlined design improves robustness to noise and varying sampling densities, addressing critical challenges in real world LiDAR and 3D sensing scenarios. PI3DETR sets a new state-of-the-art on the ABC dataset and generalizes effectively to real sensor data, offering a simple yet powerful solution for 3D edge and curve estimation.

Vector font synthesis is a challenging and ongoing problem in the fields of Computer Vision and Computer Graphics. The recently-proposed DeepVecFont achieved state-of-the-art performance by exploiting information of both the image and sequence modalities of vector fonts. However, it has limited capability for handling long sequence data and heavily relies on an image-guided outline refinement post-processing. Thus, vector glyphs synthesized by DeepVecFont still often contain some distortions and artifacts and cannot rival human-designed results. To address the above problems, this paper proposes an enhanced version of DeepVecFont mainly by making the following three novel technical contributions. First, we adopt Transformers instead of RNNs to process sequential data and design a relaxation representation for vector outlines, markedly improving the model's capability and stability of synthesizing long and complex outlines. Second, we propose to sample auxiliary points in addition to control points to precisely align the generated and target B\'ezier curves or lines. Finally, to alleviate error accumulation in the sequential generation process, we develop a context-based self-refinement module based on another Transformer-based decoder to remove artifacts in the initially synthesized glyphs. Both qualitative and quantitative results demonstrate that the proposed method effectively resolves those intrinsic problems of the original DeepVecFont and outperforms existing approaches in generating English and Chinese vector fonts with complicated structures and diverse styles.

New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives of rational B\'{e}zier curves of high degrees.

Animating clipart images with seamless motion while maintaining visual fidelity and temporal coherence presents significant challenges. Existing methods, such as AniClipart, effectively model spatial deformations but often fail to ensure smooth temporal transitions, resulting in artifacts like abrupt motions and geometric distortions. Similarly, text-to-video (T2V) and image-to-video (I2V) models struggle to handle clipart due to the mismatch in statistical properties between natural video and clipart styles. This paper introduces FlexiClip, a novel approach designed to overcome these limitations by addressing the intertwined challenges of temporal consistency and geometric integrity. FlexiClip extends traditional B\'ezier curve-based trajectory modeling with key innovations: temporal Jacobians to correct motion dynamics incrementally, continuous-time modeling via probability flow ODEs (pfODEs) to mitigate temporal noise, and a flow matching loss inspired by GFlowNet principles to optimize smooth motion transitions. These enhancements ensure coherent animations across complex scenarios involving rapid movements and non-rigid deformations. Extensive experiments validate the effectiveness of FlexiClip in generating animations that are not only smooth and natural but also structurally consistent across diverse clipart types, including humans and animals. By integrating spatial and temporal modeling with pre-trained video diffusion models, FlexiClip sets a new standard for high-quality clipart animation, offering robust performance across a wide range of visual content. Project Page: https://creative-gen.github.io/flexiclip.github.io/

Clipart, a pre-made graphic art form, offers a convenient and efficient way of illustrating visual content. Traditional workflows to convert static clipart images into motion sequences are laborious and time-consuming, involving numerous intricate steps like rigging, key animation and in-betweening. Recent advancements in text-to-video generation hold great potential in resolving this problem. Nevertheless, direct application of text-to-video generation models often struggles to retain the visual identity of clipart images or generate cartoon-style motions, resulting in unsatisfactory animation outcomes. In this paper, we introduce AniClipart, a system that transforms static clipart images into high-quality motion sequences guided by text-to-video priors. To generate cartoon-style and smooth motion, we first define B\'{e}zier curves over keypoints of the clipart image as a form of motion regularization. We then align the motion trajectories of the keypoints with the provided text prompt by optimizing the Video Score Distillation Sampling (VSDS) loss, which encodes adequate knowledge of natural motion within a pretrained text-to-video diffusion model. With a differentiable As-Rigid-As-Possible shape deformation algorithm, our method can be end-to-end optimized while maintaining deformation rigidity. Experimental results show that the proposed AniClipart consistently outperforms existing image-to-video generation models, in terms of text-video alignment, visual identity preservation, and motion consistency. Furthermore, we showcase the versatility of AniClipart by adapting it to generate a broader array of animation formats, such as layered animation, which allows topological changes.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

Scene text detection and recognition has received increasing research attention. Existing methods can be roughly categorized into two groups: character-based and segmentation-based. These methods either are costly for character annotation or need to maintain a complex pipeline, which is often not suitable for real-time applications. Here we address the problem by proposing the Adaptive Bezier-Curve Network (ABCNet). Our contributions are three-fold: 1) For the first time, we adaptively fit arbitrarily-shaped text by a parameterized Bezier curve. 2) We design a novel BezierAlign layer for extracting accurate convolution features of a text instance with arbitrary shapes, significantly improving the precision compared with previous methods. 3) Compared with standard bounding box detection, our Bezier curve detection introduces negligible computation overhead, resulting in superiority of our method in both efficiency and accuracy. Experiments on arbitrarily-shaped benchmark datasets, namely Total-Text and CTW1500, demonstrate that ABCNet achieves state-of-the-art accuracy, meanwhile significantly improving the speed. In particular, on Total-Text, our realtime version is over 10 times faster than recent state-of-the-art methods with a competitive recognition accuracy. Code is available at https://tinyurl.com/AdelaiDet

Even though trained mainly on images, we discover that pretrained diffusion models show impressive power in guiding sketch synthesis. In this paper, we present DiffSketcher, an innovative algorithm that creates vectorized free-hand sketches using natural language input. DiffSketcher is developed based on a pre-trained text-to-image diffusion model. It performs the task by directly optimizing a set of Bezier curves with an extended version of the score distillation sampling (SDS) loss, which allows us to use a raster-level diffusion model as a prior for optimizing a parametric vectorized sketch generator. Furthermore, we explore attention maps embedded in the diffusion model for effective stroke initialization to speed up the generation process. The generated sketches demonstrate multiple levels of abstraction while maintaining recognizability, underlying structure, and essential visual details of the subject drawn. Our experiments show that DiffSketcher achieves greater quality than prior work.

Recent text detection frameworks require several handcrafted components such as anchor generation, non-maximum suppression (NMS), or multiple processing stages (e.g. label generation) to detect arbitrarily shaped text images. In contrast, we propose an end-to-end trainable architecture based on Detection using Transformers (DETR), that outperforms previous state-of-the-art methods in arbitrary-shaped text detection. At its core, our proposed method leverages a bounding box loss function that accurately measures the arbitrary detected text regions' changes in scale and aspect ratio. This is possible due to a hybrid shape representation made from Bezier curves, that are further split into piece-wise polygons. The proposed loss function is then a combination of a generalized-split-intersection-over-union loss defined over the piece-wise polygons and regularized by a Smooth-ln regression over the Bezier curve's control points. We evaluate our proposed model using Total-Text and CTW-1500 datasets for curved text, and MSRA-TD500 and ICDAR15 datasets for multi-oriented text, and show that the proposed method outperforms the previous state-of-the-art methods in arbitrary-shape text detection tasks.

Artificial Intelligence Generated Content (AIGC) has shown remarkable progress in generating realistic images. However, in this paper, we take a step "backward" and address AIGC for the most rudimentary visual modality of human sketches. Our objective is on the creative nature of sketches, and that creative sketching should take the form of an interactive process. We further enable text to drive the sketch ideation process, allowing creativity to be freely defined, while simultaneously tackling the challenge of "I can't sketch". We present a method to generate controlled sketches using a text-conditioned diffusion model trained on pixel representations of images. Our proposed approach, referred to as SketchDreamer, integrates a differentiable rasteriser of Bezier curves that optimises an initial input to distil abstract semantic knowledge from a pretrained diffusion model. We utilise Score Distillation Sampling to learn a sketch that aligns with a given caption, which importantly enable both text and sketch to interact with the ideation process. Our objective is to empower non-professional users to create sketches and, through a series of optimisation processes, transform a narrative into a storyboard by expanding the text prompt while making minor adjustments to the sketch input. Through this work, we hope to aspire the way we create visual content, democratise the creative process, and inspire further research in enhancing human creativity in AIGC. The code is available at https://github.com/WinKawaks/SketchDreamer.

Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild condition. The generated space-filling curves for some known substitutions are elucidated. Some of those substitutions further induce relatively dense fractal-like sets in the plane, whenever some additional assumptions are met.

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with gradients remains a challenge. In this paper, we propose a segmentation-guided vectorization framework to convert raster images into concise vector graphics with radial gradient fills. With the guidance of an embedded gradient-aware segmentation subroutine, our approach progressively appends gradient-filled B\'ezier paths to the output, where primitive parameters are initiated with our newly designed initialization technique and are optimized to minimize our novel loss function. We build our method on a differentiable renderer with traditional segmentation algorithms to develop it as a model-free tool for raster-to-vector conversion. It is tested on various inputs to demonstrate its feasibility, independent of datasets, to synthesize vector graphics with improved visual quality and layer-wise topology compared to prior work.

Recently the author presented a new approach to solving the coefficient problems for various classes of holomorphic functions f(z) = sumlimits_0^infty c_n z^n, not necessarily univalent. This approach is based on lifting the given polynomial coefficient functionals J(f) = J(c_{m_1}, dots, c_{m_s}), 2 < c_{m_1} < dots < c_{m_s} < infty, onto the Bers fiber space over universal Teichmuller space and applying the analytic and geometric features of Teichm\"{u}ller spaces, especially the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces. In this paper, we extend this approach to more general classes of functions. In particular, this provides a strengthening of de Branges' theorem solving the Bieberbach conjecture.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric properties of these developable surfaces, we study the geometry of gluing two surfaces.

In this article, we introduce and study singular foliations of b^k-type. These singular foliations formalize the properties of vector fields that are tangent to order k along a submanifold W subset M. Our first result is a classification of these foliations, relating them to geometric structures defined in a formal neighborhood of the submanifold, such as jets of distributions that are involutive up to order k-1. When W is a hypersurface, singular foliations of b^k-type are Lie algebroids. In this particular case, they are generalizations of the b^k-tangent bundles introduced by Scott. Indeed, they are always locally isomorphic to b^k-tangent bundles, but globally such an isomorphism is obstructed by a holonomy invariant. Our second main result is a Riemann-Hilbert-style classification of singular foliations of b^k-type in terms of holonomy representations. In this paper, we study singular foliations of b^k-type from several different perspectives. In particular: (1) We study the problem of extending a k-th-order foliation to a (k+1)-th order foliation and prove that this is obstructed by a characteristic class. (2) When W is a hypersurface, we give a detailed study of algebroid differential forms and extend Scott's calculation of the cohomology. (3) We study algebroid symplectic forms in terms of the geometric structures induced on W. In particular, we find that there is a close relationship between the above obstruction class for extensions and the symplectic variation of the symplectic foliation induced on W.

Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data, planar rotations of the input will result in correspondingly rotated outputs. It is therefore desirable that deep learning models be rotationally equivariant. In addition, contours are typically represented as an ordered sequence of edge points, where the choice of starting point is arbitrary. It is therefore also desirable for deep learning methods to be equivariant under cyclic shifts. We present RotaTouille, a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution. We further introduce and characterize equivariant non-linearities, coarsening layers, and global pooling layers to obtain invariant representations for downstream tasks. Finally, we demonstrate the effectiveness of RotaTouille through experiments in shape classification, reconstruction, and contour regression.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

We present a novel approach to adjust global image properties such as colour, saturation, and luminance using human-interpretable image enhancement curves, inspired by the Photoshop curves tool. Our method, dubbed neural CURve Layers (CURL), is designed as a multi-colour space neural retouching block trained jointly in three different colour spaces (HSV, CIELab, RGB) guided by a novel multi-colour space loss. The curves are fully differentiable and are trained end-to-end for different computer vision problems including photo enhancement (RGB-to-RGB) and as part of the image signal processing pipeline for image formation (RAW-to-RGB). To demonstrate the effectiveness of CURL we combine this global image transformation block with a pixel-level (local) image multi-scale encoder-decoder backbone network. In an extensive experimental evaluation we show that CURL produces state-of-the-art image quality versus recently proposed deep learning approaches in both objective and perceptual metrics, setting new state-of-the-art performance on multiple public datasets. Our code is publicly available at: https://github.com/sjmoran/CURL.

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multi-view 3D reconstruction.

Line segment detection is essential for high-level tasks in computer vision and robotics. Currently, most stateof-the-art (SOTA) methods are dedicated to detecting straight line segments in undistorted pinhole images, thus distortions on fisheye or spherical images may largely degenerate their performance. Targeting at the unified line segment detection (ULSD) for both distorted and undistorted images, we propose to represent line segments with the Bezier curve model. Then the line segment detection is tackled by the Bezier curve regression with an end-to-end network, which is model-free and without any undistortion preprocessing. Experimental results on the pinhole, fisheye, and spherical image datasets validate the superiority of the proposed ULSD to the SOTA methods both in accuracy and efficiency (40.6fps for pinhole images). The source code is available at https://github.com/lh9171338/Unified-LineSegment-Detection.

A comparative analysis of the special shapes (patterns, profiles) of the eclipses applied for the phenomenological modeling of the light curves of eclipsing binary stars is conducted. Families of functions are considered, generalizing local approximations (Andronov, 2010, 2012) and the functions theoretically unlimited in a width, based on a Gaussian (Mikulasek, 2015). For an analysis, the light curve of the star V0882 Car = 2MASS J11080308 - 6145589 of the classic Algol - subtype (\beta Persei) is used. By analyzing dozens of modified functions with additional parameters, it was chosen the 14 best ones according to the criterion of the least sum of squares of deviations. The best are the functions with an additional parameter, describing profiles, which are limited in phase.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling sequences that are executed by a solid modeling kernel in postprocess to recover a B-rep. In this paper we present a new approach that enables learning from and synthesizing B-reps without the need for supervision through CAD modeling sequence data. Our method SolidGen, is an autoregressive neural network that models the B-rep directly by predicting the vertices, edges, and faces using Transformer-based and pointer neural networks. Key to achieving this is our Indexed Boundary Representation that references B-rep vertices, edges and faces in a well-defined hierarchy to capture the geometric and topological relations suitable for use with machine learning. SolidGen can be easily conditioned on contexts e.g., class labels, images, and voxels thanks to its probabilistic modeling of the B-rep distribution. We demonstrate qualitatively, quantitatively, and through perceptual evaluation by human subjects that SolidGen can produce high quality, realistic CAD models.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for G^1 smoothness are given, which, up to a certain degenerate case, are also necessary. Further, we investigate curvature integrability and present examples