5,965 research outputs found
BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning
The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples
Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions
This paper extends the Method of Particular Solutions (MPS) to the
computation of eigenfrequencies and eigenmodes of plates. Specific
approximation schemes are developed, with plane waves (MPS-PW) or
Fourier-Bessel functions (MPS-FB). This framework also requires a suitable
formulation of the boundary conditions. Numerical tests, on two plates with
various boundary conditions, demonstrate that the proposed approach provides
competitive results with standard numerical schemes such as the Finite Element
Method, at reduced complexity, and with large flexibility in the implementation
choices
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