127 research outputs found
Flexible G1 Interpolation of Quad Meshes
International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces
Radially symmetric thin plate splines interpolating a circular contour map
Profiles of radially symmetric thin plate spline surfaces minimizing the
Beppo Levi energy over a compact annulus have been
studied by Rabut via reproducing kernel methods. Motivated by our recent
construction of Beppo Levi polyspline surfaces, we focus here on minimizing the
radial energy over the full semi-axis . Using a -spline
approach, we find two types of minimizing profiles: one is the limit of Rabut's
solution as and (identified as a
`non-singular' -spline), the other has a second-derivative singularity and
matches an extra data value at . For both profiles and , we establish the -approximation order in
the radial energy space. We also include numerical examples and obtain a novel
representation of the minimizers in terms of dilates of a basis function.Comment: new figures and sub-sections; new Proposition 1 replacing old
Corollary 1; shorter proof of Theorem 4; one new referenc
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
The Construction of Nonseparable Wavelet Bi-Frames and Associated Approximation Schemes
Wavelet analysis and its fast algorithms are widely used in many fields of applied mathematics such as in signal and image processing. In the present thesis, we circumvent the restrictions of orthogonal and biorthogonal wavelet bases by constructing wavelet frames. They still allow for a stable decomposition, and so-called wavelet bi-frames provide a series expansion very similar to those of pairs of biorthogonal wavelet bases. Contrary to biorthogonal bases, primal and dual wavelets are no longer supposed to satisfy any geometrical conditions, and the frame setting allows for redundancy. This provides more flexibility in their construction. Finally, we construct families of optimal wavelet bi-frames in arbitrary dimensions with arbitrarily high smoothness. Then we verify that the n-term approximation can be described by Besov spaces and we apply the theoretical findings to image denoising
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