A b s t r a c t In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.

In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by const...

This paper proposes a hybrid approach for modeling torsion of blood vessels that undergo deformation and joining. The proposed model takes 3D mesh of the blood vessel as input. It first fits a generalized cylinder to extract the blood vessel's medial axis. Then, it uses rotation minimizing frame as a reference to model and measure the torsion of blood vessel after deformation. In general, the p...

We present a method for matching curves which accommodates large and small deformation. The method preserves geometric similarities in the case of small deformation, and loosens these geometric constraints when large deformations occur. The approach is based on the computation of a set of geodesic paths connecting the curves. These two curves are defined as a source area and a destination area ...

In this paper we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows to represent a deformation field in a coordinate-free way as a linear operator acting on real-valued functions defined on the shape. Such a representation both provides a way to relate deformation fields to other cla...

A number of planar deformation mechanisms, such as microtwinning, a[112] dislocation ribbon, and superlattice intrinsic and superlattice extrinsic stacking fault formation, can operate during the intermediate temperature deformation of nickle-based superalloys. The fundamental, rate-limiting processes controlling these deformation mechanisms are not fully understood. It has been recently postul...

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components. However, these techniques suffer from fundamental limitations especially for meshes with noise or large-scale deformations, and may not always be able to ide...

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton-based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a...