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
 Sweep method is one of the most robust techniques to generate hexahedral meshes in extrusion volumes. One of the main issues to be dealt by any sweep algorithm is the projection of a source surface mesh onto the target surface. This paper presents a new algorithm to map a given mesh over the source surface onto the target surface. This projection is carried out by means of a least-squares approximation of an affine mapping defined between the parametric spaces of the surfaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped up according to the target surface parameterization. Therefore, the developed algorithm does not require to solve any root finding problem to ensure that the projected nodes are on the target surface. Afterwards, this projection algorithm is extended to three dimensional cases and it is used to generate the inner layers of elements in the physical space. This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided. Finite element (FE) analysis is a valuable tool in musculoskelet al research. The demands associated with mesh development, however, often prove daunting. In an effort to facilitate anatomic FE model development we have developed an open-source software toolkit (IA-FEMesh). IA-FEMesh employs a multiblock meshing scheme aimed at hexahedral mesh generation. An emphasis has been placed on making the tools interactive, in an effort to create a user friendly environment. The goal is to provide an efficient and reliable method for model development, visualization, and mesh quality evaluation. While these tools have been developed, initially, in the context of skelet al structures they can be applied to countless applications.  Despite thesuccess of quad-based 2D surface parameterization methods, effectiveparameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CUBECOVERis a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field. The input of CUBECOVER is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. CUBECOVER has similarities to the QUADCOVER algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space. Harmonic volumetric mapping aims to establish a smooth bijective correspondence between two solid shapes with the same topology. In this paper, we develop an automatic meshless method for creating such a mapping between two given objects. With the shell surface mapping as the boundary condition, we first solve a linear system constructed by a boundary method called the method of fundamental solution, and then represent the mapping using a set of points with different weights in the vicinity of the shell of the given model. Our algorithm is a true meshless method (without the need of any specific meshing structure within the solid interior) and the behavior of the interior region is directly determined by the boundary, which can improve the computational efficiency and robustness significantly. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in information transfer, shape registration, deformation sequence analysis, tetrahedral remeshing, and solid texture synthesis.  This paper describes an algorithm to extract adaptive and quality quadrilateral hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad hex mesh, which is decomposed into finer quads hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.   