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Eurographics 2023

We present a new method to compute continuous and bijective maps (surface homeomorphisms) between two or more genus-0 triangle meshes. In contrast to previous approaches, we decouple the resolution at which a map is represented from the resolution of the input meshes. We discretize maps via common triangulations that approximate the input meshes while remaining in bijective correspondence to them. Both the geometry and the connectivity of these triangulations are optimized with respect to a single objective function that simultaneously controls mapping distortion, triangulation quality, and approximation error. A discrete-continuous optimization algorithm performs both energy-based remeshing as well as global second-order optimization of vertex positions, parametrized via the sphere. With this, we combine the disciplines of compatible remeshing and surface map optimization in a unified formulation and make a contribution in both fields. While existing compatible remeshing algorithms often operate on a fixed pre-computed surface map, we can now globally update this correspondence during remeshing. On the other hand, bijective surface-to-surface map optimization previously required computing costly overlay meshes that are inherently tied to the input mesh resolution. We achieve significant complexity reduction by instead assessing distortion between the approximating triangulations. This new map representation is inherently more robust than previous overlay-based approaches, is less intricate to implement, and naturally supports mapping between more than two surfaces. Moreover, it enables adaptive multi-resolution schemes that, e.g., first align corresponding surface regions at coarse resolutions before refining the map where needed. We demonstrate significant speedups and increased flexibility over state-of-the art mapping algorithms at similar map quality, and also provide a reference implementation of the method.

SIGGRAPH 2022

Boolean operators are an essential tool in a wide range of geometry processing and CAD/CAM tasks. We present a novel method, EMBER, to compute Boolean operations on polygon meshes which is exact, reliable, and highly performant at the same time. Exactness is guaranteed by using a plane-based representation for the input meshes along with recently introduced homogeneous integer coordinates. Reliability and robustness emerge from a formulation of the algorithm via generalized winding numbers and mesh arrangements. High performance is achieved by avoiding the (pre-)construction of a global acceleration structure. Instead, our algorithm performs an adaptive recursive subdivision of the scene’s bounding box while generating and tracking all required data on the fly. By leveraging a number of early-out termination criteria, we can avoid the generation and inspection of regions that do not contribute to the output. With a careful implementation and a work-stealing multi-threading architecture, we are able to compute Boolean operations between meshes with millions of triangles at interactive rates. We run an extensive evaluation on the Thingi10K dataset to demonstrate that our method outperforms state-of-the-art algorithms, even inexact ones like QuickCSG, by orders of magnitude.

EUROGRAPHICS Workshop on Graphics and Cultural Heritage

Preservation of cultural heritage is important to prevent singular objects or sites of cultural importance to decay. One aspect of preservation is the creation of a digital twin. In case of a catastrophic event, this twin can be used to support repairs or reconstruction, in order to stay faithful to the original object or site. Certain activities in prolongation of such an objects lifetime may involve adding or replacing structural support elements to prevent a collapse. We propose an automatic method that is capable of transforming a point cloud into a geometric representation that is suitable for structural analysis. We robustly find cuboids and their connections in a point cloud to approximate the wooden beam structure contained inside. We export the necessary information to perform structural analysis, on the example of the timber attic of the UNESCO World Heritage Aachen Cathedral. We provide evaluation of the resulting cuboids’ quality and show how a user can interactively refine the cuboids in order to improve the approximated model, and consequently the simulation results.