5.0% 2.6% 1.2% 0.6% 0.4% 0.2% 9.6% 6.8% 4.8% 3.7% 2.7% 1.5% 54.5% 26.9% 8.1% 1.9% 0.5% 0.1% 8.7% 2.1% 0.6% 0.2% 0.1% >1m >2m >4m >8m >16m >32m 0% 10% 20% 30% 40% 50% TetGen CGAL TetWild Ours CGAL #T = 1 362 980 444s TetGen #T = 8 221 130 1705s TetWild #T = 459 626 1588s Ours #T = 278 997 291s Input #F = 392 040 Fig. 1. A mouse skull model (from micro-CT) tetrahedralized by fTetWild (right) compared with other popular tetrahedral meshing algorithms. The plot shows the percentage of models requiring more than a certain time for the different approaches over 4540 inputs (the subset of Thingi10k where all 4 algorithms succeed). Our algorithm successfully meshes 99.4% of the input models in less than 2 minutes, and processes all models within 32 minutes. The comparison has been done using the experimental setup of TetWild ] and selecting a similar target resolution for all methods. The CGAL surface approximation parameter has been selected to be comparable to the envelope size used for TetWild and for our method.We propose a new tetrahedral meshing technique, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds upon the TetWild algorithm, inheriting its unconditional robustness, but dramatically reducing its computation cost and guaranteeing the generation of a valid tetrahedral mesh with floating point coordinates. This is achieved by introducing a new problem formulation, which is well suited for a pure floating point implementation and naturally leads to a parallel implementation. Our algorithm produces results qualitatively and quantitatively similar to TetWild, but at a fraction of the computational cost, with a running time comparable to Delaunay-based tetrahedralization algorithms. ACM Reference format:

We propose a robust and eicient ield-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding ields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The ield design phase of our method relies on a compact quaternionic representation of volumetric octa-ields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses ield-guided mesh simplification to convert the optimized ields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the beneits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results

We introduce a robust and automatic algorithm to simplify the structure and reduce the singularities of a hexahedral mesh. Our algorithm interleaves simplification operations to collapse sheets and chords of the base complex of the input mesh with a geometric optimization, which improves the elements quality. All our operations are guaranteed not to introduce elements with negative Jacobians, ensuring that our algorithm always produces valid hex-meshes, and not to increase the Hausdorff distance from the original shape more than a user-defined threshold, ensuring a faithful approximation of the input geometry. Our algorithm can improve meshes produced with any existing hexahedral meshing algorithm --- we demonstrate its effectiveness by processing a dataset of 194 hex-meshes created with octree-based, polycube-based, and field-aligned methods.

Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under applicationspecific external loads; the second takes the optimized configuration (i.e. locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method. His research is focused on computational design and digital fabrication, with an emphasis on topology optimization.Dr. Weiming Wang is a Marie Curie postdoc fellow at the

The CRISPR/Cas9 system has been widely used for targeted genome editing in numerous plant species. In Arabidopsis, constitutive promoters usually result in a low efficiency of heritable mutation in the T1 generation. In this work, CRISPR/Cas9 gene editing efficiencies using different promoters to drive Cas9 expression were evaluated. Expression of Cas9 under the constitutive CaMV 35S promoter resulted in a 2.3% mutation rate in T1 plants and failed to produce homozygous mutations in the T1 and T2 generations. In contrast, expression of Cas9 under two cell division-specific promoters, YAO and CDC45, produced mutation rates of 80.9% to 100% in the T1 generation with nonchimeric mutations in the T1 (4.4–10%) and T2 (32.5–46.1%) generations. The pCDC45 promoter was used to modify a previously reported multiplex CRISPR/Cas9 system, replacing the original constitutive ubiquitin promoter. The multi-pCDC45-Cas9 system produced higher mutation efficiencies than the multi-pUBQ-Cas9 system in the T1 generation (60.17% vs. 43.71%) as well as higher efficiency of heritable mutations (11.30% vs. 4.31%). Sextuple T2 homozygous mutants were identified from a construct targeting seven individual loci. Our results demonstrate the advantage of using cell division promoters for CRISPR/Cas9 gene editing applications in Arabidopsis, especially in multiplex applications.

Figure 1: (a) An input hex-mesh : The image on the left shows its base-complex that partitions the hexahedral mesh into different large components, illustrated with different colors on the right. Due to the misalignments between singularities, many (typically small) components arise. For instance, a strip of small components near the sharp feature is highlighted. (b) Our alignment algorithm reduces the complexity of the base-complex but leads to a hex-mesh with a large distortion. (c) Both the singularity placement and the element quality of the resulting hex-mesh are improved by our structure-aware optimization algorithm. AbstractRecently, generating a high quality all-hex mesh of a given volume has gained much attention. However, little, if any, effort has been put into the optimization of the hex-mesh structure, which is equally important to the local element quality of a hex-mesh that may influence the performance and accuracy of subsequent computations. In this paper, we present a first and complete pipeline to optimize the global structure of a hex-mesh. Specifically, we first extract the base-complex of a hex-mesh and study the misalignments among its singularities by adapting the previously introduced hexahedral sheets to the base-complex. Second, we identify the valid removal base-complex sheets from the base-complex that contain misaligned singularities. We then propose an effective algorithm to remove these valid removal sheets in order. Finally, we present a structure-aware optimization strategy to improve the geometric quality of the resulting hex-mesh after fixing the misalignments. Our experimental results demonstrate that our pipeline can significantly reduce the number of components of a variety of hex-meshes generated by state-of-the-art methods, while maintaining high geometric quality.

We introduce the first fully automatic pipeline to convert arbitrary 3D shapes into knit models. Our pipeline is based on a global parametrization remeshing pipeline to produce an isotropic quad-dominant mesh aligned with a 2-RoSy field. The knitting directions over the surface are determined using a set of custom topological operations and a two-step global optimization that minimizes the number of irregularities. The resulting mesh is converted into a valid stitch mesh that represents the knit model. The yarn curves are generated from the stitch mesh and the final yarn geometry is computed using a yarn-level relaxation process. Thus, we produce topologically valid models that can be used with a yarn-level simulation. We validate our algorithm by automatically generating knit models from complex 3D shapes and processing over a hundred models with various shapes without any user input or parameter tuning. We also demonstrate applications of our approach for custom knit model generation using fabrication via 3D printing.

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