arXiv subjects

J. Andreas Bærentzen

Publications and source records attributed to J. Andreas Bærentzen.

12 recordsLinked to original sources

arXiv2026

Point-Based 3D Reconstruction from Sparse Views under Known Illumination

Sparse view 3D reconstruction is commonly addressed with neural implicit surfaces or dense point-based representations such as Gaussian splatting. Surface-aware splatting methods improve extracted geometry through oriented primitives and regularization, while RadiosityGS incorporates differentiable light transport through a radiosity inspired finite-element surfel formulation. We propose a differentiable point rendering method based on opacity-bearing beta surfels. An opacity explicit adjoint light transport formulation provides gradients for surfel geometry and appearance parameters, allowing physically based light transport to constrain reconstruction. Across five synthetic objects reconstructed from ten posed views, our method achieves the lowest mean symmetric Chamfer distance among the evaluated baselines and reduces mean Chamfer distance by 28.5% relative to the strongest point-based baseline while using only 267 surfels on average, approximately ~161 fewer primitives. Directional Chamfer results further show improved accuracy and competitive completion relative to related point-based methods. These results show that, in the controlled direct illumination setting, compact beta surfels combined with transport-based optimization can recover surfaces without relying on the tens to hundreds of thousands of primitives used by the evaluated baselines.

cs.CV↗

arXiv2026

HRsR: Hierarchical Rotation System Reconstruction

Surface reconstruction from point clouds remains challenging when both geometric fidelity and topology control are required. Rotation System Reconstruction (RsR) reconstructs triangle meshes from point clouds while explicitly controlling topology through the Euler characteristic, but its sequential edge insertion limits scalability. We present Hierarchical Rotation System Reconstruction (HRsR), which accelerates RsR through a hierarchical pipeline of edge collapses and vertex splits. HRsR first simplifies the input using a $k$-nearest neighbor graph, performs reconstruction on the reduced structure, and then restores geometric detail while preserving topology. To maintain geometric consistency, we incorporate intersection handling and quality-driven vertex split selection. Experiments demonstrate up to a $6\times$ speedup and more than $8\times$ reduction in memory usage over RsR, while achieving comparable reconstruction results.

cs.CG↗

arXiv2026

Learning to Build Shapes by Extrusion

We introduce Text Encoded Extrusions (TEE), a text-based representation that expresses mesh construction as sequences of face extrusions rather than polygon lists, and a method for generating 3D meshes from TEE using a large language model (LLM). By learning extrusion sequences that assemble a mesh, similar to the way artists create meshes, our approach naturally supports arbitrary output face counts and produces manifold meshes by design, in contrast to recent mesh generative transformer based models. The learnt extrusion sequences can also be applied to existing meshes - enabling editing in addition to generation. To train our model, we decompose a library of quadrilateral meshes with non-self-intersecting face loops into constituent loops, which can be viewed as their building blocks, and finetune an LLM on the steps for reassembling the quadrilateral meshes by performing a sequence of extrusions. We demonstrate that our representation enables reconstruction, novel shape synthesis, and the addition of new features to existing meshes.

cs.GR↗

arXiv2024

Surface Reconstruction Using Rotation Systems

Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a spanning tree and a rotation system. Since the tree is trivially a planar graph, its rotation system determines a genus zero surface with a single face which we proceed to incrementally refine by inserting edges to split faces and thus merging them. In order to raise the genus, special handles are added by inserting edges between different faces and thus merging them. We apply our method to a wide range of input point clouds in order to investigate its effectiveness, and we compare our method to several other surface reconstruction methods. We find that our method offers better control over outlier classification, i.e. which points to include in the reconstructed surface, and also more control over the topology of the reconstructed surface.

cs.CG↗

arXiv2023

Phasor Noise for Dehomogenisation in 2D Multiscale Topology Optimisation

This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem or pre-trained models. By utilising a continuous and periodic representation of the translation at each intermediate step, appropriate length-scale and thicknesses can be obtained. Numerical tests verifies the performance of the proposed methodology compared to state-of-the-art alternatives, and the dehomogenised designs achieve structural performance within a few percentages of the optimised homogenised solution. The nature of the phasor-based dehomogenisation is inherently mesh-independent and highly parallelisable, allowing for further efficient implementations and future extensions to 3D problems on unstructured meshes.

cs.CE↗

arXiv2023

Efficient Inverse-designed Structural Infill for Complex Engineering Structures

Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for additive manufacturing, infill is often neglected as a component of the optimized structure. In this paper, both concerns are addressed using a de-homogenization topology optimization procedure on complex engineering structures discretized by 3D unstructured hexahedrals. Using a rectangular-hole microstructure (reminiscent to the stiffness optimal orthogonal rank-3 multi-scale) as a base material for the multi-scale optimization, a coarse-scale optimized geometry can be obtained using homogenization-based topology optimization. Due to the microstructure periodicity, this coarse-scale geometry can be up-sampled to a fine physical geometry with optimized infill, with minor loss in structural performance and at a fraction of the cost of a fine-scale solution. The upsampling on 3D unstructured grids is achieved through stream surface tracing which aligns with the optimized local orientation. The periodicity of the physical geometry can be tuned, such that the material serves as a structural component and also as an efficient infill for additive manufacturing designs. The method is demonstrated through three examples. It achieves comparable structural performance to state-of-the-art methods but stands out for its significant computational time reduction, much faster than the base-line method. By allowing multiple active layers, the mapped solution becomes more mechanically stable, leading to an increased critical buckling load factor without additional computational expense. The proposed approach achieves promising results, benchmarking against large-scale SIMP models demonstrates computational efficiency improvements of up to 250 times.

cs.GR↗

arXiv2023

Multilevel Skeletonization Using Local Separators

In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to quickly obtain a skeleton. We do this in a highly modular fashion, ensuring complete flexibility in adapting the algorithm for specific types of input or for otherwise targeting specific applications. Separator based skeletonization was first proposed by Bærentzen and Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost of running times which become prohibitive for large inputs. Our new approach retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes. We test our skeletonization algorithm for efficiency and quality in practice, comparing it to local separator skeletonization on the University of Groningen Skeletonization Benchmark [Telea'16].

cs.CG↗

arXiv2022

On the use of Artificial Neural Networks in Topology Optimisation

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation have been proposed with varying success. Other works focused on speed-up through replacing expensive optimisers and state solvers, or reducing the design-space have been attempted, but have not yet received the same attention. The portfolio of articles presenting different applications has as such become extensive, but few real breakthroughs have yet been celebrated. An overall trend in the literature is the strong faith in the "magic" of artificial intelligence and thus misunderstandings about the capabilities of such methods. The aim of this article is therefore to present a critical review of the current state of research in this field. To this end, an overview of the different model-applications is presented, and efforts are made to identify reasons for the overall lack of convincing success. A thorough analysis identifies and differentiates between problematic and promising aspects of existing models. The resulting findings are used to detail recommendations believed to encourage avenues of potential scientific progress for further research within the field.

cs.CE↗

arXiv2021

De-homogenization using Convolutional Neural Networks

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt. domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within $7-25\%$ of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization.

cs.LG↗

arXiv2021

Shape from Projections via Differentiable Forward Projector for Computed Tomography

In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simulate data acquisition, but not for reconstruction, for which a 3D mesh means the inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward model for 3D meshes that bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending recent work in differentiable rendering. We use the proposed forward model to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that the proposed method outperforms traditional voxel-based methods on noisy simulated data. We also apply the proposed method on electron tomography images of nanoparticles to demonstrate the applicability of the method on real data.

eess.IV↗

arXiv2019

De-homogenization of optimal multi-scale 3D topologies

This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal multi-scale designs on a very fine mesh (de-homogenization). By performing homogenization-based topology optimization, optimal multi-scale designs are obtained on a relatively coarse mesh resulting in a low computational cost. As microstructure parameterization we use orthogonal rank-3 microstructures, which are known to be optimal for a single loading case. Furthermore, a method to get explicit control of the minimum feature size and complexity of the final shapes will be discussed. Numerical examples show excellent performance of these fine-scale designs resulting in objective values similar to the homogenization-based designs. Comparisons with well-established density-based topology optimization methods show a reduction in computational cost of 3 orders of magnitude, paving the way for giga-scale designs on a standard PC.

cs.CE↗

arXiv2018

Bézier curves that are close to elastica

We study the problem of identifying those cubic Bézier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special Bézier curves as a proxy. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a Bézier curve has lambda-residual below 0.4, which effectively implies that the curve is within 1 percent of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input Bézier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.

math.NA↗