In this paper, we propose a set of free-form shape deformation techniques. The basic approach can be described as follows. Given a surface represented by a mesh and a control point, for every mesh vertex let us consider the difference between the control point and the vertex. The vertex is shifted by a displacement equal to the difference times a scale factor where the scale factor is given by ...

Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., B-splines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinations of the initial control points. We present a new non-linear subdivision scheme for the refine...

There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on S2, examine their equidistribution properties, separation, covering, and mesh ratio constants and present a new point set, equal area icosahedral points, with low mesh ratio. We analyze numerically the leading order asymptoti...

We consider the task of stereo-reconstruction under the following fairly broad assumptions. A single and continuously shaped object is captured by two uncalibrated cameras. It is assumed, that almost all surface points are binocular visible. We propose a statistical model which represents the surface as a triangular (hexagonal) mesh of pairs of corresponding points. We introduce an iterative sc...

A 3D biomechanical finite element model of the face is presented. Muscles are represented by piecewise uniaxial tension cable elements linking the insertion points. Such insertion points are specific entities differing from nodes of the finite element mesh, which makes possible to change either the mesh or the muscle implementation totally independently of each other. Lip/teeth and upper lip/lo...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...

We describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for general two-dimensional geometries. We generalize the existing sequential point placement strategies for guaranteed quality mesh refinement: instead of a specific position for a new point, we derive two types of two-dimensional regions which we call selection disks. Both types...

The original fast sweeping method, which is an efficient iterative method for stationary Hamilton-Jacobi equations, relies on natural ordering provided by a rectangular mesh. We propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily to any unstructured mesh. To that end we introduce multiple reference points and order all the nodes according to...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional deri...

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and ma...