8,991 research outputs found
Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces
We introduce a coupled finite and boundary element formulation for acoustic
scattering analysis over thin shell structures. A triangular Loop subdivision
surface discretisation is used for both geometry and analysis fields. The
Kirchhoff-Love shell equation is discretised with the finite element method and
the Helmholtz equation for the acoustic field with the boundary element method.
The use of the boundary element formulation allows the elegant handling of
infinite domains and precludes the need for volumetric meshing. In the present
work the subdivision control meshes for the shell displacements and the
acoustic pressures have the same resolution. The corresponding smooth
subdivision basis functions have the continuity property required for the
Kirchhoff-Love formulation and are highly efficient for the acoustic field
computations. We validate the proposed isogeometric formulation through a
closed-form solution of acoustic scattering over a thin shell sphere.
Furthermore, we demonstrate the ability of the proposed approach to handle
complex geometries with arbitrary topology that provides an integrated
isogeometric design and analysis workflow for coupled structural-acoustic
analysis of shells
High-quality tree structures modelling using local convolution surface approximation
In this paper, we propose a local convolution surface approximation approach for quickly modelling tree structures with pleasing visual effect. Using our proposed local convolution surface approximation, we present a tree modelling scheme to create the structure of a tree with a single high-quality quad-only mesh. Through combining the strengths of the convolution surfaces, subdivision surfaces and GPU, our tree modelling approach achieves high efficiency and good mesh quality. With our method, we first extract the line skeletons of given tree models by contracting the meshes with the Laplace operator. Then we approximate the original tree mesh with a convolution surface based on the extracted skeletons. Next, we tessellate the tree trunks represented by convolution surfaces into quad-only subdivision surfaces with good edge flow along the skeletal directions. We implement the most time-consuming subdivision and convolution approximation on the GPU with CUDA, and demonstrate applications of our proposed approach in branch editing and tree composition
Compression for Smooth Shape Analysis
Most 3D shape analysis methods use triangular meshes to discretize both the
shape and functions on it as piecewise linear functions. With this
representation, shape analysis requires fine meshes to represent smooth shapes
and geometric operators like normals, curvatures, or Laplace-Beltrami
eigenfunctions at large computational and memory costs.
We avoid this bottleneck with a compression technique that represents a
smooth shape as subdivision surfaces and exploits the subdivision scheme to
parametrize smooth functions on that shape with a few control parameters. This
compression does not affect the accuracy of the Laplace-Beltrami operator and
its eigenfunctions and allow us to compute shape descriptors and shape
matchings at an accuracy comparable to triangular meshes but a fraction of the
computational cost.
Our framework can also compress surfaces represented by point clouds to do
shape analysis of 3D scanning data
A progressive refinement approach for the visualisation of implicit surfaces
Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting
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