We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space S. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R. We extend this shape space to arbitrary triangulations in 3D using a...

and Applied Analysis 3 of the space λA is defined by λA {f : f g ◦ A; g ∈ λ′}. Let X be a seminormed space. A set Y ⊂ X is called fundamental set if the span of Y is dense in X. An application of HahnBanach theorem on fundamental set is as follows: if Y is the subset of a seminormed space X and f Y 0 implies f 0 for f ∈ X′, then Y is a fundamental set see 11 . By the idea mentioned above, let u...

Unification, a fundamental process for logic programming systems, relies on the ability to efficiently look up values of variables in a substitution. Triangular substitutions, which allow associations to variables that are themselves bound by another association, are an attractive choice for purely functional implementations of logic programming systems because of their fast extension time and ...

Techniques are presented for moving between adjacent triangles of equal size in a hierarchical representation for spherical data that is projected onto the faces of an icosahedron. The faces of the icosahedron are represented by a triangular quadtree. The operations are analogous to those used for a quadtree representation of data on the two-dimensional plane where the underlying space is tesse...

Schrödinger's equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, R9, naturally equipped with Jacobi's kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger's equation with respect to the translational symmetry enables us to reduce the configuration space to that of a...

Abstract. The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computati...

In this study, we investigate and present a new index structure, Triangular Decomposition Tree (TDtree), which can efficiently store and query temporal data in modern database applications. TD-tree is based on spatial representation of interval data and a recursive triangular decomposition of this space. A bounded number of intervals are stored in each leaf of the tree, which hence may be unbal...

In conventional percutaneous disc surgery, introducing instruments into disc space starts by inserting a guide needle into the triangular working zone. However, landing the guide needle tip on the annular window is a challenging step in endoscopic discectomy. Surgeons tend to repeat the needling procedure to reach an optimal position on the annular target. Obturator guiding technique is a modif...

We compute in small temperature expansion the two-loop renormalization constants and the three-loop coefficient of the β-function, that is the first non-universal term, for the σ-model with O(N) invariance on the triangular lattice at N = −1. The partition function of the corresponding Grassmann theory is, for negative temperature, the generating function of unrooted forests on such a lattice, ...