Browsing by Author "Campen, Marcel"

Now showing 1 - 5 of 5
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    The 3D Motorcycle Complex for Structured Volume Decomposition
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Brückler, Hendrik; Gupta, Ojaswi; Mandad, Manish; Campen, Marcel; Chaine, Raphaëlle; Kim, Min H.
    The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi-structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three-dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher-dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T-spline construction.
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    Combinatorial Construction of Seamless Parameter Domains
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Zhou, Jiaran; Tu, Changhe; Zorin, Denis; Campen, Marcel; Panozzo, Daniele and Assarsson, Ulf
    The problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline-based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.
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    HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Ludwig, Ingmar; Tyson, Daniel; Campen, Marcel; Memari, Pooran; Solomon, Justin
    We describe HalfedgeCNN, a collection of modules to build neural networks that operate on triangle meshes. Taking inspiration from the (edge-based) MeshCNN, convolution, pooling, and unpooling layers are consistently defined on the basis of halfedges of the mesh, pairs of oppositely oriented virtual instances of each edge. This provides benefits over alternative definitions on the basis of vertices, edges, or faces. Additional interface layers enable support for feature data associated with such mesh entities in input and output as well. Due to being defined natively on mesh entities and their neighborhoods, lossy resampling or interpolation techniques (to enable the application of operators adopted from image domains) do not need to be employed. The operators have various degrees of freedom that can be exploited to adapt to application-specific needs.
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    Quad Layouts via Constrained T-Mesh Quantization
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Lyon, Max; Campen, Marcel; Kobbelt, Leif; Mitra, Niloy and Viola, Ivan
    We present a robust and fast method for the creation of conforming quad layouts on surfaces. Our algorithm is based on the quantization of a T-mesh, i.e. an assignment of integer lengths to the sides of a non-conforming rectangular partition of the surface. This representation has the benefit of being able to encode an infinite number of layout connectivity options in a finite manner, which guarantees that a valid layout can always be found. We carefully construct the T-mesh from a given seamless parametrization such that the algorithm can provide guarantees on the results' quality. In particular, the user can specify a bound on the angular deviation of layout edges from prescribed directions. We solve an integer linear program (ILP) to find a coarse quad layout adhering to that maximal deviation. Our algorithm is guaranteed to yield a conforming quad layout free of T-junctions together with bounded angle distortion. Our results show that the presented method is fast, reliable, and achieves high quality layouts.
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    VMV 2021: Frontmatter
    (The Eurographics Association, 2021) Andres, Bjoern; Campen, Marcel; Sedlmair, Michael; Andres, Bjoern and Campen, Marcel and Sedlmair, Michael