In this work, we present a technique to map any genus zero solid object onto a hexahedral decomposition of a solid cube. This problem appears in many applications ranging from finite element methods to visual tracking. From this, one can then hopefully utilize the proposed technique for shape analysis, registration, as well as other related computer graphics tasks. More importantly, given that we seek to establish a one-to-one correspondence of an input volume to that of a solid cube, our algorithm can naturally generate a quality hexahedral mesh as an output. In addition, we constrain the mapping itself to be volume preserving allowing for the possibility of further mesh simplification. We demonstrate our method both qualitatively and quantitatively on various 3D solid models
In addition to these related works, Martin and Cohen @cite_29 recently presented a methodology for hexahedral meshing that is able to handle higher order genus species through B-splines and T-splines. In contrast to these proposed approaches, our algorithm only requires the object to be of genus zero topology. By genus zero we mean that the solid has no holes (i.e., the surface is contractible). However, if the object is not of genus zero, it may be processed by separating the object into several genus zero parts.
@cite_29
2137312224 1975803044 2086550580 2055009036
Abstract This paper describes a novel method to construct solid rational T-splines for complex genus-zero geometry from boundary surface triangulations. We first build a parametric mapping between the triangulation and the boundary of the parametric domain, a unit cube. After that we adaptively subdivide the cube using an octree subdivision, project the boundary nodes onto the input triangle mesh, and at the same time relocate the interior nodes via mesh smoothing. This process continues until the surface approximation error is less than a pre-defined threshold. T-mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved. Templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap-free T-mesh. The obtained solid T-spline is C 2 -continuous except for the local region around each extraordinary node and partial extraordinary node. The boundary surface of the solid T-spline is C 2 -continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube. Finally, a Bezier extraction technique is used to facilitate T-spline based isogeometric analysis. The obtained Bezier mesh is analysis-suitable with no negative Jacobians. Several examples are presented in this paper to show the robustness of the algorithm. Abstract We present a new method to construct a trivariate T-spline representation of complex genus-zero solids for the application of isogeometric analysis. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation. We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero level-set of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laser-scanned data, image-based 3D reconstruction, and mesh repair. To achieve a tight integration of design and analysis, conformal solid T-spline construction with the input boundary spline representation preserved is desirable. However, to the best of our knowledge, this is still an open problem. In this paper, we provide its first solution. The input boundary T-spline surface has genus-zero topology and only contains eight extraordinary nodes, with an isoparametric line connecting each pair. One cube is adopted as the parametric domain for the solid T-spline. Starting from the cube with all the nodes on the input surface as T-junctions, we adaptively subdivide the domain based on the octree structure until each face or edge contains at most one face T-junction or one edge T-junction. Next, we insert two boundary layers between the input T-spline surface and the boundary of the subdivision result. Finally, knot intervals are calculated from the T-mesh and the solid T-spline is constructed. The obtained T-spline is conformal to the input T-spline surface with exactly the same boundary representation and continuity. For the interior region, the continuity is C 2 everywhere except for the local region surrounding irregular nodes. Several examples are presented to demonstrate the performance of the algorithm.