Browsing by Author "Lyon, Max"

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    Learning Direction Fields for Quad Mesh Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Dielen, Alexander; Lim, Isaak; Lyon, Max; Kobbelt, Leif; Digne, Julie and Crane, Keenan
    State of the art quadrangulation methods are able to reliably and robustly convert triangle meshes into quad meshes. Most of these methods rely on a dense direction field that is used to align a parametrization from which a quad mesh can be extracted. In this context, the aforementioned direction field is of particular importance, as it plays a key role in determining the structure of the generated quad mesh. If there are no user-provided directions available, the direction field is usually interpolated from a subset of principal curvature directions. To this end, a number of heuristics that aim to identify significant surface regions have been proposed. Unfortunately, the resulting fields often fail to capture the structure found in meshes created by human experts. This is due to the fact that experienced designers can leverage their domain knowledge in order to optimize a mesh for a specific application. In the context of physics simulation, for example, a designer might prefer an alignment and local refinement that facilitates a more accurate numerical simulation. Similarly, a character artist may prefer an alignment that makes the resulting mesh easier to animate. Crucially, this higher level domain knowledge cannot be easily extracted from local curvature information alone. Motivated by this issue, we propose a data-driven approach to the computation of direction fields that allows us to mimic the structure found in existing meshes, which could originate from human experts or other sources. More specifically, we make use of a neural network that aggregates global and local shape information in order to compute a direction field that can be used to guide a parametrization-based quad meshing method. Our approach is a first step towards addressing this challenging problem with a fully automatic learning-based method. We show that compared to classical techniques our data-driven approach combined with a robust model-driven method, is able to produce results that more closely exhibit the ground truth structure of a synthetic dataset (i.e. a manually designed quad mesh template fitted to a variety of human body types in a set of different poses).
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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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    Simpler Quad Layouts using Relaxed Singularities
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Lyon, Max; Campen, Marcel; Kobbelt, Leif; Digne, Julie and Crane, Keenan
    A common approach to automatic quad layout generation on surfaces is to, in a first stage, decide on the positioning of irregular layout vertices, followed by finding sensible layout edges connecting these vertices and partitioning the surface into quadrilateral patches in a second stage. While this two-step approach reduces the problem's complexity, this separation also limits the result quality. In the worst case, the set of layout vertices fixed in the first stage without consideration of the second may not even permit a valid quad layout. We propose an algorithm for the creation of quad layouts in which the initial layout vertices can be adjusted in the second stage. Whenever beneficial for layout quality or even validity, these vertices may be moved within a prescribed radius or even be removed. Our algorithm is based on a robust quantization strategy, turning a continuous T-mesh structure into a discrete layout. We show the effectiveness of our algorithm on a variety of inputs.