arXiv subjects

Daniel Zint

Publications and source records attributed to Daniel Zint.

3 recordsLinked to original sources

arXiv2026

Topology-First B-Rep Meshing

Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order surface and curve intersections to low-order primitives: the resulting geometric realization often fails to respect the exact topology encoded in the B-Rep, producing meshes with incorrect or missing adjacencies. Existing meshing pipelines address these inconsistencies through heuristic feature-merging and repair strategies that offer no topological guarantees and frequently fail on complex models. We propose a fundamentally different approach: the B-Rep topology is treated as an invariant of the meshing process. Our algorithm enforces the exact B-Rep topology while allowing a single user-defined tolerance to control the deviation of the mesh from the underlying parametric surfaces. Consequently, for any admissible tolerance, the output mesh is topologically correct; only its geometric fidelity degrades as the tolerance increases. This decoupling eliminates the need for post-hoc repairs and yields robust meshes even when the underlying geometry is inconsistent or highly approximated. We evaluate our method on thousands of real-world CAD models from the ABC and Fusion 360 repositories, including instances that fail with standard meshing tools. The results demonstrate that topological guarantees at the algorithmic level enable reliable mesh generation suitable for downstream applications.

cs.GR↗

arXiv2024

Topological Offsets

We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a manifold, watertight, and self-intersection-free offset surface strictly enclosing the input, while doing a best effort to move it to a prescribed distance from the input. Differently from existing approaches, we embed the input in a background mesh and insert a topological offset around the input with purely combinatorial operations. The topological offset is then inflated/deflated to match the user-prescribed distance while enforcing that no intersections or non-manifold configurations are introduced. We evaluate the effectiveness and robustness of our approach on the Thingi10k dataset, and show that topological offsets are beneficial in multiple graphics applications, including (1) converting non-manifold surfaces to manifold ones, (2) creating layered offsets, and (3) reliably computing finite offsets.

cs.CG↗

arXiv2019

Towards whole program generation of quadrature-free discontinuous Galerkin methods for the shallow water equations

The shallow water equations (SWE) are a commonly used model to study tsunamis, tides, and coastal ocean circulation. However, there exist various approaches to discretize and solve them efficiently. Which of them is best for a certain scenario is often not known and, in addition, depends heavily on the used HPC platform. From a simulation software perspective, this places a premium on the ability to adapt easily to different numerical methods and hardware architectures. One solution to this problem is to apply code generation techniques and to express methods and specific hardware-dependent implementations on different levels of abstraction. This allows for a separation of concerns and makes it possible, e.g., to exchange the discretization scheme without having to rewrite all low-level optimized routines manually. In this paper, we show how code for an advanced quadrature-free discontinuous Galerkin (DG) discretized shallow water equation solver can be generated. Here, we follow the multi-layered approach from the ExaStencils project that starts from the continuous problem formulation, moves to the discrete scheme, spells out the numerical algorithms, and, finally, maps to a representation that can be transformed to a distributed memory parallel implementation by our in-house Scala-based source-to-source compiler. Our contributions include: A new quadrature-free discontinuous Galerkin formulation, an extension of the class of supported computational grids, and an extension of our toolchain allowing to evaluate discrete integrals stemming from the DG discretization implemented in Python. As first results we present the whole toolchain and also demonstrate the convergence of our method for higher order DG discretizations.

cs.MS↗