We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allows to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions ...

An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creati...

A new method has been developed for overcoming some of the major obstacles of object recognition. It represents both 2D images and 3D models from a database by view-point invariant descriptors in the same invariant space. As there is a large number of possible matches between the image and model invariants, there is a crucial need to perform this match efficiently. We answer this need by using ...

We present an adaptive dynamic load balancing scheme for 3D texture based sort-last parallel volume rendering on a PC cluster equipped with GPUs. Our scheme exploits not only task parallelism but also data parallelism during rendering by combining the hierarchical data structures (octree and parallel BSP tree) in order to skip empty regions and distribute proper workloads to rendering nodes. Ou...

This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We ...

A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an defined by level set function. Our implementation employs quadtree/octree grids with adaptive refinement, cell-centered discretization and pointwise smoothing. Boundary locations are determined at subgrid resolution performing line searches. For grid b...

We provide a simple method that extracts an isosurface that is manifold and intersection-free from a function over an arbitrary octree. Our method samples the function dual to minimal edges, faces, and cells, and we show how to position those samples to reconstruct sharp and thin features of the surface. Moreover, we describe an error metric designed to guide octree expansion such that flat reg...

Jelloul Elmesbahi, Omar Bouattane, and Zouhair Benabbou t; Sk[f(Z’, 2 ) + W(.’) at;] = F ( d , z’) Sk[f(Z’, z ’ ) + w(z ’ ) at:] < F ( 2 , z k ) sk[f(xk, 2) + w ( x k ) at:] Abstract-Quadtree and octree decomposition of multicolored images is often used to solve problems of image processing. This paper describes a O(1) time algorithm for the decomposition of the images into quadtree and octree ...

"the present paper describes an interactive technique for measuring the symmetry degree of an arbitrary three-dimensional object. The drawback of the automatic symmetry detection algorithm formerly proposed is that figural distortion or local mass disappearance causes detection of unacceptable principal axes. To overcome this, an interactive symmetry detection system is proposed where part of a...