Browsing by Author "Mandad, Manish"

Now showing 1 - 3 of 3
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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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    Exact Constraint Satisfaction for Truly Seamless Parametrization
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Mandad, Manish; Campen, Marcel; Alliez, Pierre and Pellacini, Fabio
    In the field of global surface parametrization a recent focus has been on so-called seamless parametrization. This term refers to parametrization approaches which, while using an atlas of charts to enable the handling of surfaces of arbitrary topology, relate the parametrization across the cuts between charts via transition functions from special classes of transformations. This effectively makes the cuts invisible to applications which are invariant to these specific transformations in some sense. In actual implementations of these parametrization approaches, however, these restrictions are obeyed only approximately; errors stem from the tolerances of numerical solvers employed and, ultimately, from the limited accuracy of floating point arithmetic. In practice, robustness issues arise from these flaws in the seamlessness of a parametrization, no matter how small. We present a robust global algorithm that turns a given approximately seamless parametrization into an exactly seamless one - that still is representable by standard floating point numbers. It supports common practically relevant additional constraints regarding boundary and feature curve alignment or isocurve connectivity, and ensures that these are likewise fulfilled exactly. This allows subsequent algorithms to operate robustly on the resulting truly seamless parametrization. We believe that the core of our method will furthermore be of benefit in a broader range of applications involving linearly constrained numerical optimization.
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    Rational Bézier Guarding
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Khanteimouri, Payam; Mandad, Manish; Campen, Marcel; Campen, Marcel; Spagnuolo, Michela
    We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.