1,913 research outputs found
Robust Poisson Surface Reconstruction
Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator func-tion of the surfaceās interior. Compared to previous models, our recon-struction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hi-erarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, in-stead isogeometric finite-element techniques, to efficiently solve the min-imization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.
PARAMETRIZATION AND SHAPE RECONSTRUCTION TECHNIQUES FOR DOO-SABIN SUBDIVISION SURFACES
This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere -continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed surface is exactly the same as that of the data points. The new technique consists of two major steps. First, use an efficient surface reconstruction method to produce a polyhedral approximation to the given data points. Second, construct a Doo-Sabin subdivision surface that smoothly passes through all the data points in the given data set. A new technique is presented for the second step in this thesis. The new technique iteratively modifies the vertices of the polyhedral approximation 1CM until a new control meshM, whose Doo-Sabin subdivision surface interpolatesM, is reached. It is proved that, for any mesh M with any size and any topology, the iterative process is always convergent with Doo-Sabin subdivision scheme. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges and corners faithfully
Kirchhoff-Love shell representation and analysis using triangle configuration B-splines
This paper presents the application of triangle configuration B-splines
(TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the
context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation
requires global -continuous basis functions. The nonuniform rational
B-spline (NURBS)-based IGA has been extensively used for developing
Kirchhoff-Love shell elements. However, shells with complex geometries
inevitably need multiple patches and trimming techniques, where stitching
patches with high continuity is a challenge. On the other hand, due to their
unstructured nature, TCB-splines can accommodate general polygonal domains,
have local refinement, and are flexible to model complex geometries with
continuity, which naturally fit into the Kirchhoff-Love shell formulation with
complex geometries. Therefore, we propose to use TCB-splines as basis functions
for geometric representation and solution approximation. We apply our method to
both linear and nonlinear benchmark shell problems, where the accuracy and
robustness are validated. The applicability of the proposed approach to shell
analysis is further exemplified by performing geometrically nonlinear
Kirchhoff-Love shell simulations of a pipe junction and a front bumper
represented by a single patch of TCB-splines
Interpolation and scattered data fitting on manifolds using projected PowellāSabin splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(UĪ¾ , Ī¾)}Ī¾ā satisfying certain conditions of smooth dependence on Ī¾. If is a C2-manifold embedded into R3, then projections into tangent planes can be employed. The data fitting method is a two-stage method. We prove that the resulting function on the manifold is continuously differentiable, and establish error bounds for both methods for the case when the data are generated by a smooth function
Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes
Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and bio-medical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation.
We present two different approaches for using subdivision solids as the only representation for modeling, simulation and visualization. This has the advantage that no data must be converted between the CAD and CAE phases. The first approach is based on an adaptive and feature-preserving tetrahedral subdivision scheme. The second approach is based on Catmull-Clark subdivision solids
Multi-scale 3-D Surface Description: Open and Closed Surfaces
A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed automatically and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here
- ā¦