43-Issue 5

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https://diglib.eg.org/handle/10.2312/3607011

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Browsing 43-Issue 5 by Subject "CCS Concepts: Computing methodologies → Mesh geometry models"

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    Distance-Based Smoothing of Curves on Surface Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2024) Pawellek, Markus; Rössl, Christian; Lawonn, Kai; Hu, Ruizhen; Lefebvre, Sylvain
    The smoothing of surface curves is an essential tool in mesh processing, important to applications that require segmenting and cutting surfaces such as surgical planning. Surface curves are typically designed by professionals to match certain surface features. For this reason, the smoothed curves should be close to the original and easily adjustable by the user in interactive tools. Previous methods achieve this desired behavior, e.g., by utilizing energy-minimizing splines or generalizations of Bézier splines, which require a significant number of control points and may not provide interactive frame rates or numerical stability. This paper presents a new algorithm for robust smoothing of discrete surface curves on triangular surface meshes. By using a scalar penalty potential as the fourth coordinate, the given surface mesh is embedded into the 4D Euclidean space. Our method is based on finding geodesics in this lifted surface, which are then projected back onto the original 3D surface. The benefits of this approach include guaranteed convergence and good approximation of the initial curve. We propose a family of penalty potentials with one single parameter for adjusting the trade-off between smoothness and similarity. The implementation of our method is straightforward as we rely on existing methods for computing geodesics and penalty fields. We evaluate our implementation and confirm its robustness and efficiency.
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    KerGen: A Kernel Computation Algorithm for 3D Polygon Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2024) Asiler, Merve; Sahillioglu, Yusuf; Hu, Ruizhen; Lefebvre, Sylvain
    We compute the kernel of a shape embedded in 3D as a polygon mesh, which is defined as the set of all points that have a clear line of sight to every point of the mesh. The KerGen algorithm, short for Kernel Generation, employs efficient plane-plane and line-plane intersections, alongside point classifications based on their positions relative to planes. This approach allows for the incremental addition of kernel vertices and edges to the resulting set in a simple and systematic way. The output is a polygon mesh that represents the surface of the kernel. Extensive comparisons with the existing methods, CGAL and Polyhedron Kernel, demonstrate the remarkable timing performance of our novel additive kernel computation method. Yet another advantage of our additive process is the availability of the partial kernel at any stage, making it useful for specific geometry processing applications such as star decomposition and castable shape reconstruction.