8,355 research outputs found
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
Steiner Variations on Random Surfaces
Ambartzumian et.al. suggested that the modified Steiner action functional had
desirable properties for a random surface action. However, Durhuus and Jonsson
pointed out that such an action led to an ill-defined grand-canonical partition
function and suggested that the addition of an area term might improve matters.
In this paper we investigate this and other related actions numerically for
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
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
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Smooth parametric surfaces and n-sided patches
The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed
Embedded Plateau Problem
We show that if C is a simple closed curve bounding an embedded disk in a
closed 3-manifold M, then there exists a disk D in M with boundary C such that
D minimizes the area among the embedded disks with boundary C. Moreover, D is
smooth, minimal and embedded everywhere except where the boundary C meets the
interior of D. The same result is also valid for homogenously regular manifolds
with sufficiently convex boundary
Point-Normal Subdivision Curves and Surfaces
This paper proposes to generalize linear subdivision schemes to nonlinear
subdivision schemes for curve and surface modeling by refining vertex positions
together with refinement of unit control normals at the vertices. For each
round of subdivision, new control normals are obtained by projections of
linearly subdivided normals onto unit circle or sphere while new vertex
positions are obtained by updating linearly subdivided vertices along the
directions of the newly subdivided normals. Particularly, the new position of
each linearly subdivided vertex is computed by weighted averages of end points
of circular or helical arcs that interpolate the positions and normals at the
old vertices at one ends and the newly subdivided normal at the other ends.
The main features of the proposed subdivision schemes are three folds:
(1) The point-normal (PN) subdivision schemes can reproduce circles, circular
cylinders and spheres using control points and control normals;
(2) PN subdivision schemes generalized from convergent linear subdivision
schemes converge and can have the same smoothness orders as the linear schemes;
(3) PN subdivision schemes generalizing linear subdivision schemes that
generate subdivision surfaces with flat extraordinary points can generate
visually subdivision surfaces with non-flat extraordinary points.
Experimental examples have been given to show the effectiveness of the
proposed techniques for curve and surface modeling.Comment: 30 pages, 17 figures, 22.5M
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