10,034 research outputs found
Intelligent sampling for the measurement of structured surfaces
Uniform sampling in metrology has known drawbacks such as coherent spectral aliasing and a lack of efficiency in terms of measuring time and data storage. The requirement for intelligent sampling strategies has been outlined over recent years, particularly where the measurement of structured surfaces is concerned. Most of the present research on intelligent sampling has focused on dimensional metrology using coordinate-measuring machines with little reported on the area of surface metrology. In the research reported here, potential intelligent sampling strategies for surface topography measurement of structured surfaces are investigated by using numerical simulation and experimental verification. The methods include the jittered uniform method, low-discrepancy pattern sampling and several adaptive methods which originate from computer graphics, coordinate metrology and previous research by the authors. By combining the use of advanced reconstruction methods and feature-based characterization techniques, the measurement performance of the sampling methods is studied using case studies. The advantages, stability and feasibility of these techniques for practical measurements are discussed
Subdivision surface fitting to a dense mesh using ridges and umbilics
Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach
ADAM: a general method for using various data types in asteroid reconstruction
We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple
and universal since it handles all disk-resolved data types (adaptive optics or
other images, interferometry, and range-Doppler radar data) in a uniform manner
via the 2D Fourier transform, enabling fast convergence in model optimization.
The resolved data can be combined with disk-integrated data (photometry). In
the reconstruction process, the difference between each data type is only a few
code lines defining the particular generalized projection from 3D onto a 2D
image plane. Occultation timings can be included as sparse silhouettes, and
thermal infrared data are efficiently handled with an approximate algorithm
that is sufficient in practice due to the dominance of the high-contrast
(boundary) pixels over the low-contrast (interior) ones. This is of particular
importance to the raw ALMA data that can be directly handled by ADAM without
having to construct the standard image. We study the reliability of the
inversion by using the independent shape supports of function series and
control-point surfaces. When other data are lacking, one can carry out fast
nonconvex lightcurve-only inversion, but any shape models resulting from it
should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&
An adaptive octree finite element method for PDEs posed on surfaces
The paper develops a finite element method for partial differential equations
posed on hypersurfaces in , . The method uses traces of
bulk finite element functions on a surface embedded in a volumetric domain. The
bulk finite element space is defined on an octree grid which is locally refined
or coarsened depending on error indicators and estimated values of the surface
curvatures. The cartesian structure of the bulk mesh leads to easy and
efficient adaptation process, while the trace finite element method makes
fitting the mesh to the surface unnecessary. The number of degrees of freedom
involved in computations is consistent with the two-dimension nature of surface
PDEs. No parametrization of the surface is required; it can be given implicitly
by a level set function. In practice, a variant of the marching cubes method is
used to recover the surface with the second order accuracy. We prove the
optimal order of accuracy for the trace finite element method in and
surface norms for a problem with smooth solution and quasi-uniform mesh
refinement. Experiments with less regular problems demonstrate optimal
convergence with respect to the number of degrees of freedom, if grid
adaptation is based on an appropriate error indicator. The paper shows results
of numerical experiments for a variety of geometries and problems, including
advection-diffusion equations on surfaces. Analysis and numerical results of
the paper suggest that combination of cartesian adaptive meshes and the
unfitted (trace) finite elements provide simple, efficient, and reliable tool
for numerical treatment of PDEs posed on surfaces
Towards multiple 3D bone surface identification and reconstruction using few 2D X-ray images for intraoperative applications
This article discusses a possible method to use a small number, e.g. 5, of conventional 2D X-ray images to reconstruct multiple 3D bone surfaces intraoperatively. Each boneâs edge contours in X-ray images are automatically identified. Sparse 3D landmark points of each bone are automatically reconstructed by pairing the 2D X-ray images. The reconstructed landmark point distribution on a surface is approximately optimal covering main characteristics of the surface. A statistical shape model, dense point distribution model (DPDM), is then used to fit the reconstructed optimal landmarks vertices to reconstruct a full surface of each bone separately. The reconstructed surfaces can then be visualised and manipulated by surgeons or used by surgical robotic systems
3D mesh refinement procedure using the bisection and rivara algorithms with mesh quality assessment
Mesh refinement procedures for the solution of three dimensional problems are described. The computational\ud
domain is represented by an assembly of tetrahedral elements and the mesh refinement is acheived by the bisection\ud
and Rivara methods using an explicit mesh density function coupled with an automatic 3D mesh generator.\ud
A couple of benchmark examples is used to compare the performance of both refinement methods in terms of mesh\ud
and size qualities, number of generated elements and CPU time consume
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