4,488 research outputs found
Scan registration for autonomous mining vehicles using 3D-NDT
Scan registration is an essential subtask when building maps based on range finder data from mobile robots. The problem is to deduce how the robot has moved between consecutive scans, based on the shape of overlapping portions of the scans. This paper presents a new algorithm for registration of 3D data. The algorithm is a generalization and improvement of the normal distributions transform (NDT) for 2D data developed by Biber and Strasser, which allows for accurate registration using a memory-efficient representation of the scan surface. A detailed quantitative and qualitative comparison of the new algorithm with the 3D version of the popular ICP (iterative closest point) algorithm is presented. Results with actual mine data, some of which were collected with a new prototype 3D laser scanner, show that the presented algorithm is faster and slightly more reliable than the standard ICP algorithm for 3D registration, while using a more memory efficient scan surface representation
High-Order AFEM for the Laplace-Beltrami Operator: Convergence Rates
We present a new AFEM for the Laplace-Beltrami operator with arbitrary
polynomial degree on parametric surfaces, which are globally and
piecewise in a suitable Besov class embedded in with . The idea is to have the surface sufficiently well resolved in
relative to the current resolution of the PDE in . This gives
rise to a conditional contraction property of the PDE module. We present a
suitable approximation class and discuss its relation to Besov regularity of
the surface, solution, and forcing. We prove optimal convergence rates for AFEM
which are dictated by the worst decay rate of the surface error in
and PDE error in .Comment: 51 pages, the published version contains an additional glossar
Ray casting implicit fractal surfaces with reduced affine arithmetic
A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store
Robustness of Boolean operations on subdivision-surface models
This work was presented in two parts at Dagstuhl seminar 08021.
The two presentations described work in
progress, including a ``backward bound\u27\u27 for a combined backward/forward
error analysis for the problem mentioned in the title.
We seek rigorous proofs that representations of computed sets, produced by
algorithms to compute Boolean operations, are well formed, and that the
algorithms are correct. Such proofs should eventually take account of the use of
finite-precision arithmetic, although the proofs presented here do not.
The representations studied are based on subdivision surfaces. Such
representations are being used more and more frequently in place of trimmed
NURBS representations, and the robustness analysis for these new representations
is simpler than for trimmed NURBS.
The particular subdivision-surface representation used is based on the Loop
subdivision scheme. The analysis is broken into three parts. First, it is
established that the input operands are well-formed two-dimensional manifolds
without boundary. This can be done with existing methods.
Secondly, we introduce the so-called ``limit mesh\u27\u27, and view the
limit meshes corresponding to the input sets as defining an approximate problem
in the sense of a backward error analysis. The presentations mentioned above
described a proof of the corresponding error bound. The third part of the
analysis corresponds to the ``forward bound\u27\u27: this remains to be done
Subdivision Shell Elements with Anisotropic Growth
A thin shell finite element approach based on Loop's subdivision surfaces is
proposed, capable of dealing with large deformations and anisotropic growth. To
this end, the Kirchhoff-Love theory of thin shells is derived and extended to
allow for arbitrary in-plane growth. The simplicity and computational
efficiency of the subdivision thin shell elements is outstanding, which is
demonstrated on a few standard loading benchmarks. With this powerful tool at
hand, we demonstrate the broad range of possible applications by numerical
solution of several growth scenarios, ranging from the uniform growth of a
sphere, to boundary instabilities induced by large anisotropic growth. Finally,
it is shown that the problem of a slowly and uniformly growing sheet confined
in a fixed hollow sphere is equivalent to the inverse process where a sheet of
fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless,
quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl
Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves
Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive
epsilon, we want to compute an epsilon-isotopic polygonal approximation to the
restriction of the curve S=f^{-1}(0)={p in R^2: f(p)=0} to B_0. We focus on
subdivision algorithms because of their adaptive complexity and ease of
implementation. Plantinga and Vegter gave a numerical subdivision algorithm
that is exact when the curve S is bounded and non-singular. They used a
computational model that relied only on function evaluation and interval
arithmetic. We generalize their algorithm to any bounded (but possibly
non-simply connected) region that does not contain singularities of S. With
this generalization as a subroutine, we provide a method to detect isolated
algebraic singularities and their branching degree. This appears to be the
first complete purely numerical method to compute isotopic approximations of
algebraic curves with isolated singularities
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