SUMMARYA new fully automatic hex-dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy ÿeld that mimics a body-centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex-dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex-dominant mesh by merging some of the tetrahedrons.

SUMMARYThis paper presents a new computational method for anisotropic tetrahedral meshing. The method can control element anisotropy based on a speciÿed 3 × 3 tensor ÿeld deÿned over a volumetric domain. Our method creates a tetrahedral mesh in two steps: (1) placing nodes at the centres of tightly packed ellipsoidal cells, called bubbles, in the domain, and (2) connecting the nodes by a modiÿed advancing front followed by local transformation. The method creates a high-quality anisotropic mesh that conforms well to a speciÿed tensor ÿeld.

This paper presents a new mesh conversion template, called HEXHOOP, that fully automates a conversion from a hex-dominant mesh to an all-hex mesh. A HEXHOOP template subdivides a hex/prism/pyramid element to a set of smaller hex elements while maintaining the topological conformity with neighboring elements. A HEXHOOP template is constructed by assembling subtemplates, cores and caps. A dicing template for a hex and a prism is constructed by choosing the appropriate combination of a core and caps. A template that dices a pyramid without losing conformity to the adjacent element is derived from a HEXHOOP template. Some experimental results show that the HEXHOOP templates successfully convert a hex-dominant mesh to an all-hex mesh.

We propose a data-driven 3D shape design method that can learn a generative model from a corpus of existing designs, and use this model to produce a wide range of new designs. The approach learns an encoding of the samples in the training corpus using an unsupervised variational autoencoder-decoder architecture, without the need for an explicit parametric representation of the original designs. To facilitate the generation of smooth final surfaces, we develop a 3D shape representation based on a distance transformation of the original 3D data, rather than using the commonly utilized binary voxel representation. Once established, the generator maps the latent space representations to the high-dimensional distance transformation fields, which are then automatically surfaced to produce 3D representations amenable to physics simulations or other objective function evaluation modules. We demonstrate our approach for the computational design of gliders that are optimized to attain prescribed performance scores. Our results show that when combined with genetic optimization, the proposed approach can generate a rich set of candidate concept designs that achieve prescribed functional goals, even when the original dataset has only a few or no solutions that achieve these goals.

High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an upsampling of 3D point clouds without the need for hard-coded rules. Our approach uses a deep network with Chamfer distance as the loss function, capable of learning the latent features in point clouds belonging to different object categories. We evaluate our algorithm across different amplification factors, with upsampling learned and performed on objects belonging to the same category as well as different categories. We also explore the desirable characteristics of input point clouds as a function of the distribution of the point samples. Finally, we demonstrate the performance of our algorithm in single-category training versus multi-category training scenarios. The final proposed model is compared against a baseline, optimization-based upsampling method. Results indicate that our algorithm is capable of generating more accurate upsamplings with less Chamfer loss.