Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized, time-coupled deformation trajectories. Starting from inverse tracing—collapsing the deployed structure with a lightweight rod model while recording node paths under a shared parameter—we obtain feasible node paths and formulate a polyline approximation problem that selects globally synchronized time steps and minimizes a robust tail-aggregated deviation measure under monotonicity constraints. We solve the resulting non-smooth optimization problem via global optimization to obtain compact, synchronized displacement sequences for all paths simultaneously. We evaluate the method using geometry-centric metrics (deviation versus step count, scaling with trajectory count) and demonstrate its utility by driving finite element deployment simulations that avoid intermediate buckling and capture deployment-induced prestress.

We propose a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion processes which generalizes existing PDE-based approaches. Our forward pass formulates image corruption via a physically motivated PDE that couples directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless numbers (Peclet, Fourier). We implement this PDE numerically through a GPU-accelerated custom Lattice Boltzmann solver for fast evaluation. To induce realistic turbulence, we generate stochastic velocity fields that introduce coherent motion and capture multi-scale mixing. In the generative process, a neural network learns to reverse the advection-diffusion operator thus constituting a novel generative model. We discuss how previous methods emerge as specific cases of our operator, demonstrating that our framework generalizes prior PDE-based corruption techniques. We illustrate how advection improves the diversity and quality of the generated images while keeping the overall color palette unaffected. This work bridges fluid dynamics, dimensionless PDE theory, and deep generative modeling, offering a fresh perspective on physically informed image corruption processes for diffusion-based synthesis.

In computer graphics and vision, recovering easily modifiable scene appearance from image data is crucial for applications such as content creation. We introduce a novel method that integrates 3D Gaussian Splatting with an implicit surface representation, enabling intuitive editing of recovered scenes through mesh manipulation. Starting with a set of input images and camera poses, our approach reconstructs the scene surface using a neural signed distance field. This neural surface acts as a geometric prior guiding the training of Gaussian Splatting components, ensuring their alignment with the scene geometry. To facilitate editing, we encode the visual and geometric information into a lightweight triangle soup proxy. Edits applied to the mesh extracted from the neural surface propagate seamlessly through this intermediate structure to update the recovered appearance. Unlike previous methods relying on the triangle soup proxy representation, our approach supports a wider range of modifications and fully leverages the mesh topology, enabling a more flexible and intuitive editing process. The complete source code for this project can be accessed at github.com/WJakubowska/NeuralSurfacePriors.

Abstract Neural signed‐distance fields (SDFs) are a versatile backbone for neural geometry representation, but enforcing CAD‐style developability usually requires Gaussian‐curvature penalties with full Hessian evaluation and second‐order differentiation, which are costly in memory and time. We introduce an off‐diagonal Weingarten loss that regularizes only the mixed shape operator term that represents the gap between principal curvatures and flattens the surface. We present two variants: a finite‐difference version using six SDF evaluations plus one gradient, and an auto‐diff version using a single Hessian‐vector product. Both converge to the exact mixed term and preserve the intended geometric properties without assembling the full Hessian. On the ABC benchmarks the losses match or exceed Hessian‐based baselines while cutting GPU memory and training time by roughly a factor of two. The method is drop‐in and framework‐agnostic, enabling scalable curvature‐aware SDF learning for engineering‐grade shape reconstruction. Our code is available at https://flatcad.github.io/ .

Implicit neural representations (INRs) have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary as the zero-level set of the learned continuous function and learns a mapping from a low-dimensional latent space to the space of all possible shapes represented by its signed distance function. However, most INRs struggle to retain high-frequency details, which are crucial for accurate geometric depiction, and they are computationally expensive. To address these limitations, we present a novel approach that both reduces computational expenses and enhances the capture of fine details. Our method integrates periodic activation functions, positional encodings, and normals into the neural network architecture. This integration significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

We address the problem of indoor layout synthesis, which is a topic of continuing research interest in computer graphics. The newest works made significant progress using data-driven generative methods; however, these approaches rely on suitable datasets. In practice, desirable layout properties may not exist in a dataset, for instance, specific expert knowledge can be missing in the data. We propose a method that combines expert knowledge, for example, knowledge about ergonomics, with a data-driven generator based on the popular Transformer architecture. The knowledge is given as differentiable scalar functions, which can be used both as weights or as additional terms in the loss function. Using this knowledge, the synthesized layouts can be biased to exhibit desirable properties, even if these properties are not present in the dataset. Our approach can also alleviate problems of lack of data and imperfections in the data. Our work aims to improve generative machine learning for modeling and provide novel tools for designers and amateurs for the problem of interior layout creation.

Elastic geodesic grids (EGG) are lightweight structures that can be deployed to approximate designer-provided free-form surfaces. Initially, the grids are perfectly flat, during deployment, a curved shape emerges, as grid elements bend and twist. Their layout is based on networks of geodesic curves and is found geometrically. Encoded in the planar grids is the intrinsic shape of the design surface. Such structures may serve purposes like free-form sub-structures, panels, sun and rain protectors, pavilions, etc. However, so far the EGG have only been investigated using a generic set of design surfaces and small-scale desktop models. Some limitations become apparent when considering more sophisticated design surfaces, like from free-form architecture. Due to characteristics like high local curvature or non-geodesic boundaries, they may be captured only poorly by a single EGG. We show how decomposing such surfaces into smaller patches serves as an effective strategy to tackle these problems. We furthermore show that elastic geodesic grids are in fact well suited for this approach. Finally, we present a showcase model of some meters in size and discuss practical aspects concerning fabrication, size, and easy deployment.

Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid bends and approximates the given 3d surface. Our method is based purely on the notions from differential geometry of curves and surfaces and avoids any physical simulations. In particular, we introduce a well-defined elastic grid energy functional that allows identifying networks of curves that minimize the bending energy and at the same time nestle to the provided input surface well. Further, we generalize the concept of such grids to cases where the surface boundary does not need to be convex, which allows for the creation of sophisticated and visually pleasing shapes. The algorithm finally ensures that the 2d grid is perfectly planar, making the resulting gridshells inexpensive, easy to fabricate, transport, assemble, and finally also to deploy. Additionally, since the whole structure is pre-strained, it also comes with load-bearing capabilities. We evaluate our method using physical simulation and we also provide a full fabrication pipeline for desktop-size models and present multiple examples of surfaces with elliptic and hyperbolic curvature regions. Our method is meant as a tool for quick prototyping for designers, architects, and engineers since it is very fast and results can be obtained in a matter of seconds.

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.

Abstract In this paper we propose a novel method for the automatic computation and digital fabrication of artistic string images. String art is a technique used by artists for the creation of abstracted images which are composed of straight lines of strings tensioned between pins distributed on a frame. Together the strings fuse to a perceptible image. Traditionally, artists craft such images manually in a highly sophisticated and tedious design process. To achieve this goal fully automatically we propose a computational setup driven by a discrete optimization algorithm which takes an ordinary picture as input and converts it into a connected graph of strings that tries to reassemble the input image best possibly. Furthermore, we propose a hardware setup for automatic digital fabrication of these images using an industrial robot that spans the strings. Finally, we demonstrate the applicability of our approach by generating and fabricating a set of real string art images.

Abstract We propose a novel method for interactive design of well‐fitting body‐supporting surfaces that is driven by the pressure distribution on the body's surface. Our main contribution is an interactive modeling system that utilizes captured body poses and computes an importance field that is proportional to the pressure distribution on the body for a given pose. This distribution indicates where the body should be supported in order to easily hold a particular pose, which is one of the measures of comfortable sitting. Using our approximation, we propose the entire workflow for interactive design of C 2 smooth surfaces which serve as seats, or generally, as body supporting furniture for comfortable sitting. Finally, we also provide a design tool for R hinoceros /G rasshopper that allows for interactive creation of single designs or entire multi‐person sitting scenarios. We also test the tool with design students and present several results. Our method aims at interactive design in order to help designers to create appropriate surfaces digitally without additional empirical design passes.

We present a novel framework for visualizing routes on mobile devices. Our framework is suitable for helping users explore their environment. First, given a starting point and a maximum route length, the system retrieves nearby points of interest (POIs). Second, we automatically compute an attractive walking path through the environment trying to pass by as many highly ranked POIs as possible. Third, we automatically compute a route visualization that shows the current user position, POI locations via pins, and detail lenses for more information about the POIs. The visualization is an animation of an orthographic map view that follows the current user position. We propose an optimization based on a binary integer program (BIP) that models multiple requirements for an effective placement of detail lenses. We show that our path computation method outperforms recently proposed methods and we evaluate the overall impact of our framework in two user studies.

Abstract Traditionally, building floor plans are designed by architects with their usability, functionality and architectural aesthetics in mind; however, the structural properties of the distribution of load‐bearing walls and columns are usually not taken into account at this stage. In this paper, we propose a novel approach for the design of architectural floor plans by integrating structural layout analysis directly into the planning process. In order to achieve this, we introduce a planning tool which interactively enforces checks for structural stability of the current design, and which on demand proposes how to stabilize it if necessary. Technically, our solution contains an interactive architectural modelling framework as well as a constrained optimization module where both are based on respective architectural rules. Using our tool, an architect can predict already in a very early planning stage whose designs are structurally sound such that later changes due to stability reasons can be prevented. We compare manually computed solutions with optimal results of our proposed automated design process in order to show how much our proposed system can help architects to improve the process of laying out structural models optimally.

In this paper we present a novel method for non-linear shape optimization of 3d objects given by their surface representation. Our method takes advantage of the fact that various shape properties of interest give rise to underdetermined design spaces implying the existence of many good solutions. Our algorithm exploits this by performing iterative projections of the problem to local subspaces where it can be solved much more efficiently using standard numerical routines. We demonstrate how this approach can be utilized for various shape optimization tasks using different shape parameterizations. In particular, we show how to efficiently optimize natural frequencies, mass properties, as well as the structural yield strength of a solid body. Our method is flexible, easy to implement, and very fast.

Abstract We present a novel procedural framework for interactively modeling building façades. Common procedural approaches, such as shape grammars, assume that building façades are organized in a tree structure, while in practice this is often not the case. Consequently, the complexity of their layout description becomes unmanageable for interactive editing. In contrast, we obtain a façade by composing multiple overlapping layers, where each layer contains a single rectilinear grid of façade elements described by two simple generator patterns. This way, the design process becomes more intuitive and the editing effort for complex layouts is significantly reduced. To achieve this, we present a method for the automated merging of different layers in the form of a mixed discrete and continuous optimization problem. Finally, we provide several modeling examples and a comparison to shape grammars in order to highlight the advantages of our method when designing realistic building façades.

Given the 2-manifold surface of a 3d object, we propose a novel method for the computation of an offset surface with varying thickness such that the solid volume between the surface and its offset satisfies a set of prescribed constraints and at the same time minimizes a given objective functional. Since the constraints as well as the objective functional can easily be adjusted to specific application requirements, our method provides a flexible and powerful tool for shape optimization. We use manifold harmonics to derive a reduced-order formulation of the optimization problem, which guarantees a smooth offset surface and speeds up the computation independently from the input mesh resolution without affecting the quality of the result. The constrained optimization problem can be solved in a numerically robust manner with commodity solvers. Furthermore, the method allows simultaneously optimizing an inner and an outer offset in order to increase the degrees of freedom. We demonstrate our method in a number of examples where we control the physical mass properties of rigid objects for the purpose of 3d printing.

Abstract We present a novel framework for the automatic generation of tourist brochures that include routing instructions and additional information presented in the form of so‐called detail lenses. The first contribution of this paper is the automatic creation of layouts for the brochures. Our approach is based on the minimization of an energy function that combines multiple goals: positioning of the lenses as close as possible to the corresponding region shown in an overview map, keeping the number of lenses low, and an efficient numbering of the lenses. The second contribution is a route‐aware simplification of the graph of streets used for traveling between the points of interest (POIs). This is done by reducing the graph consisting of all shortest paths through the minimization of an energy function. The output is a subset of street segments that enable traveling between all the POIs without considerable detours, while at the same time guaranteeing a clutter‐free visualization.

We present a method to complete missing structures in facade layouts. Starting from an abstraction of the partially observed layout as a set of shapes, we can propose one or multiple possible completed layouts. Structure completion with large missing parts is an ill-posed problem. Therefore, we combine two sources of information to derive our solution: the observed shapes and a database of complete layouts. The problem is also very difficult, because shape positions and attributes have to be estimated jointly. Our proposed solution is to break the problem into two components: a statistical model to evaluate layouts and a planning algorithm to generate candidate layouts. This ensures that the completed result is consistent with the observation and the layouts in the database.

Abstract This paper provides a comprehensive overview of urban reconstruction. While there exists a considerable body of literature, this topic is still under active research. The work reviewed in this survey stems from the following three research communities: computer graphics, computer vision and photogrammetry and remote sensing. Our goal is to provide a survey that will help researchers to better position their own work in the context of existing solutions, and to help newcomers and practitioners in computer graphics to quickly gain an overview of this vast field. Further, we would like to bring the mentioned research communities to even more interdisciplinary work, since the reconstruction problem itself is by far not solved.

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an- HaLRTC the former is more efficient to obtain a low accuracy solution and the latter is preferred if a high-accuracy solution is desired.

Abstract We propose a novel interactive framework for modeling building façades from images. Our method is based on the notion of coherence‐based editing which allows exploiting partial symmetries across the façade at any level of detail. The proposed workflow mixes manual interaction with automatic splitting and grouping operations based on unsupervised cluster analysis. In contrast to previous work, our approach leads to detailed 3d geometric models with up to several thousand regions per façade. We compare our modeling scheme to others and evaluate our approach in a user study with an experienced user and several novice users.

In this paper we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process, or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by laying out the theoretical foundations and then by building a working algorithm. First, we propose a definition for the tensor trace norm, that generalizes the established definition of the matrix trace norm. Second, similar to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we employ a relaxation technique to separate the dependant relationships and use the block coordinate descent (BCD) method to achieve a globally optimal solution. Our experiments show potential applications of our algorithm and the quantitative evaluation indicates that our method is more accurate and robust than heuristic approaches.