Related papers: The Shape Parameter in the Shifted Surface Spline
We classify all possible local linear procedures over triangular meshes resulting in polynomial $C^1$-spline functions with affinely uniform shape for the basic functions at the edges, and fitting the 9 value- and gradient data at the…
We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic…
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand,…
The instability and periodic deformation of bilayer membranes during freezing processes are studied as a function of the difference of the shape energy between the high and the low temperature membrane states. It is shown that there exists…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
It is shown, that the requirement of invariance under spatial rotations reveales an intrinsic fractional extended translation-rotation-like property for particles described with the fractional Schroedinger equation, which we call fractional…
We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $\R^d$, the cost is of an integral type, and the control variable is the domain of the state…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined…
We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
Establishing character shape correspondence is a critical and fundamental task in computer vision and graphics, with diverse applications including re-topology, attribute transfer, and shape interpolation. Current dominant functional map…
Flatness of a plate is a parameter has been put under consideration for long time. Factors influencing the accuracy of this parameter have been recognized and examined carefully but placed scatterringly. Beside that those reports have not…
It has previously been shown that response transformations can be very effective in improving dimension reduction outcomes for a continuous response. The choice of transformation used can make a big difference in the visualization of the…
The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. However, the "stability of physical theories principle" seems to be the one that provides, through the tools of algebraic deformation theory,…
Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously…
We define a new basis of cubic splines such that the coordinates of a natural cubic spline are sparse. We use it to analyse and to extend the classical Schoenberg and Reinsch result and to estimate a noisy cubic spline. We also discuss the…