2179068
Guaranteed quality triangulation of molecular skin surfaces
We present an efficient algorithm to mesh the macromolecules surface model represented by the skin surface defined by Edelsbrunner. Our algorithm overcomes several challenges residing in current surface meshing methods. First, we guarantee the mesh quality with a provable lower bound of 21/spl deg/ on its minimum angle. Second, we ensure the triangulation is homeomorphic to the original surface. Third, we improve the efficiency of constructing the restricted Delaunay triangulation (RDT) of smooth surfaces. We achieve this by constructing the RDT using the advancing front method without computing the Delaunay tetrahedrization of the sample points on the surfaces. The difficulty of handling the front collision problem is tackled by employing the Morse theory. In particular, we construct the Morse-Smale complex to simplify the topological changes of the front. Our implementation results suggest that the algorithm decrease the time of generating high quality homeomorphic skin mesh from hours to a few minutes.
33621218
Superimposing Voronoi Complexes for Shape Deformation
Edelsbrunner et al. defined a framework of shape deformations with shapes bounded by skin manifold. We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes. Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time. This makes generating, visualizing, and customizing shape deformations feasible.
37186338
Shape space from deformation
The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of this paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions.
16843658
Shape space from deformation
The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined, reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of the paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions.
5883116
Subdividing Alpha Complex
Given two simplicial complexes C 1 and C 2 embedded in Euclidean space d , C 1 subdivides C 2 if (i) C1 and C 2 have the same underlying space, and (ii) every simplex in C 1 is contained in a simplex in C 2 . In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex. Following this, we also show a simple method to approximate a given polygonal object with a set of balls via computing the subdividing alpha complex of the boundary of the object. The approximation is robust and is able to achieve a union of balls whose Hausdorff distance to the object is less than a given positive real number e.
6203082
Area and Perimeter Derivatives of a Union of Disks
We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.
14350917
A non-linear dimensionality-reduction technique for fast similarity search in large databases
To enable efficient similarity search in large databases, many indexing techniques use a linear transformation scheme to reduce dimensions and allow fast approximation. In this reduction approach the approximation is unbounded, so that the approximation volume extends across the dataspace. This causes over-estimation of retrieval sets and impairs performance.This paper presents a non-linear transformation scheme that extracts two important parameters specifying the data. We prove that these parameters correspond to a bounded volume around the search sphere, irrespective of dimensionality. We use a special workspace-mapping mechanism to derive tight bounds for the parameters and to prove further results, as well as highlighting insights into the problems and our proposed solutions. We formulate a measure that lower-bounds the Euclidean distance, and discuss the implementation of the technique upon a popular index structure. Extensive experiments confirm the superiority of this technique over recent state-of-the-art schemes.
46280169
Edge-gracefulness of the composition of paths with null graphs
Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,..., q} be a bijection. The induced mapping f+ : V → Zp of f is defined by f+(u) ≡ Σuυ∈Ef(uυ) (modp) for u ∈ V. If f+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm > Nn, where there are mn vertices and (m - 1)n2 edges. We show that P3 > Nn is edge-graceful if n is odd.