The detection and classification of triangle intersections in virtual environments are key ingredients in many computer graphics and geometry processing applications, especially for 3D reconstruction, rendering, modeling, and mesh optimization. Current solutions often necessitate rewriting intersection algorithms when transitioning between numerical representation systems, such as floating-point and rational numbers, to maintain robustness and precision. This work-in-progress report introduces a tool designed to address the triangle-triangle intersection problem robustly and exhaustively. By breaking down the problem into lower-dimensional simplex intersections and utilizing robust geometric predicates, our approach aims to provide a flexible, efficient, and general solution. The tool, developed using C++ templates, will support multiple numerical representation systems, ensuring adaptability without compromising accuracy. Upon completion, it will be benchmarked against state-of-the-art methods and released as an open-source resource, offering a trustworthy foundation for future advancements in research and development.

In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.

In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.

We propose a novel technique to compose new 3D animated models, such as videogame characters, by combining pieces from existing ones. Our method works on production-ready rigged, skinned, and animated 3D models to reassemble new ones. We exploit mix-and-match operations on the skeletons to trigger the automatic creation of a new mesh, linked to the new skeleton by a set of skinning weights and complete with a set of animations. The resulting model preserves the quality of the input meshings (which can be quad-dominant and semi-regular), skinning weights (inducing believable deformation), and animations, featuring coherent movements of the new skeleton. Our method enables content creators to reuse valuable, carefully designed assets by assembling new ready-to-use characters while preserving most of the hand-crafted subtleties of models authored by digital artists. As shown in the accompanying video, it allows for drastically cutting the time needed to obtain the final result.

We propose a novel technique to compose new 3D animated models, such as videogame characters, by combining pieces from existing ones. Our method works on production-ready rigged, skinned, and animated 3D models to reassemble new ones. We exploit mix-and-match operations on the skeletons to trigger the automatic creation of a new mesh, linked to the new skeleton by a set of skinning weights and complete with a set of animations. The resulting model preserves the quality of the input meshings (which can be quad-dominant and semi-regular), skinning weights (inducing believable deformation), and animations, featuring coherent movements of the new skeleton. Our method enables content creators to reuse valuable, carefully designed assets by assembling new ready-to-use characters while preserving most of the hand-crafted subtleties of models authored by digital artists. As shown in the accompanying video, it allows for drastically cutting the time needed to obtain the final result.

Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it intersects; (2) filling the so generated hole with two polygons that have the wanted segment as shared edge; (3) triangulate each polygon separately. In this article we prove that these polygons are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear. The fact that any simple polygon contains at least three convex vertices guarantees the existence of a valid ear to cut, ensuring convergence. Not only this translates to an optimal deterministic linear time triangulation algorithm, but such algorithm is also trivial to implement. We formally prove the correctness of our approach, also validating it in practical applications and comparing it with prior art.

Many real-world hand-crafted objects are decorated with elements that are packed onto the object’s surface and deformed to cover it as much as possible. Examples are artisanal ceramics and metal jewelry. Inspired by these objects, we present a method to enrich surfaces with packed volumetric decorations. Our algorithm works by first determining the locations in which to add the decorative elements and then removing the non-physical overlap between them while preserving the decoration volume. For the placement, we support several strategies depending on the desired overall motif. To remove the overlap, we use an approach based on implicit deformable models creating the qualitative effect of plastic warping while avoiding expensive and hard-to-control physical simulations. Our decorative elements can be used to enhance virtual surfaces, as well as 3D-printed pieces, by assembling the decorations onto real surfaces to obtain tangible reproductions.

Due to their nice numerical properties, conforming hexahedral meshes are considered a prominent computational domain for simulation tasks. However, the automatic decomposition of a general 3D volume into a small number of hexahedral elements is very challenging. Methods that create an adaptive Cartesian grid and convert it into a conforming mesh offer superior robustness and are the only ones concretely used in the industry. Topological schemes that permit this conversion can be applied only if precise compatibility conditions among grid elements are observed. Some of these conditions are local, hence easy to formulate; others are not and are much harder to satisfy. State-of-the-art approaches fulfill these conditions by prescribing additional refinement based on special building rules for octrees. These methods operate in a restricted space of solutions and are prone to severely over-refine the input grids, creating a bottleneck in the simulation pipeline. In this article, we introduce a novel approach to transform a general adaptive grid into a new grid meeting hexmeshing criteria, without resorting to tree rules. Our key insight is that we can formulate all compatibility conditions as linear constraints in an integer programming problem by choosing the proper set of unknowns. Since we operate in a broader solution space, we are able to meet topological hexmeshing criteria at a much coarser scale than methods using octrees, also supporting generalized grids of any shape or topology. We demonstrate the superiority of our approach for both traditional grid-based hexmeshing and adaptive polycube-based hexmeshing. In all our experiments, our method never prescribed more refinement than the prior art and, in the average case, it introduced close to half the number of extra cells.

We introduce a novel geometry‐processing pipeline to guide the fabrication of complex shapes from a single block of material using 4‐axis CNC milling machines. This setup extends classical 3‐axis CNC machining with an extra degree of freedom to rotate the object around a fixed axis. The first step of our pipeline identifies the rotation axis that maximizes the overall fabrication accuracy. Then we identify two height‐field regions at the rotation axis's extremes used to secure the block on the rotation tool. We segment the remaining portion of the mesh into a set of height‐fields whose principal directions are orthogonal to the rotation axis. The segmentation balances the approximation quality, the boundary smoothness, and the total number of patches. Additionally, the segmentation process takes into account the object's geometric features, as well as saliency information. The output is a set of meshes ready to be processed by off‐the‐shelf software for the 3‐axis tool‐path generation. We present several results to demonstrate the quality and efficiency of our approach to a range of inputs.

We introduce a novel algorithm to transform any generic set of triangles in 3D space into a well-formed simplicial complex. Intersecting elements in the input are correctly identified, subdivided, and connected to arrange a valid configuration, leading to a topologically sound partition of the space into piece-wise linear cells. Our approach does not require the exact coordinates of intersection points to calculate the resulting complex. We represent any intersection point as an unevaluated combination of input vertices. We then extend the recently introduced concept of indirect predicates [Attene 2020] to define all the necessary geometric tests that, by construction, are both exact and efficient since they fully exploit the floating-point hardware. This design makes our method robust and guaranteed correct, while being virtually as fast as non-robust floating-point based implementations. Compared with existing robust methods, our algorithm offers a number of advantages: it is much faster, has a better memory layout, scales well on extremely challenging models, and allows fully exploiting modern multi-core hardware with a parallel implementation. We thoroughly tested our method on thousands of meshes, concluding that it consistently outperforms prior art. We also demonstrate its usefulness in various applications, such as computing efficient mesh booleans, Minkowski sums, and volume meshes.

Volumetric meshes are useful assets in many different research and application fields, like physical simulations, FEM or IGA. In the last decade, the Computer Graphics community dedicated a lot of effort in studying and developing new algorithms for the creation, manipulation, and visualization of this family of meshes. In the meantime, Game Development became a relevant field of application for CG practitioners entangled with AR and VR techniques. In this work, we position ourselves at the confluence of these two broad research and development paths. We introduce a custom data structure aiming at using volumetric meshes in Unity. To this purpose, we combine gaming techniques and interactions with typical operations of volumetric meshes. Besides this, to make the researcher experience more realistic, we also introduce features to manipulate volumetric meshes for their projects in an immersive environment using VR techniques. We think this feature can be useful in developing tools for 3D Sculpting or Digital Fabrication.

Skeleton-based and cage-based deformation techniques represent the two most popular approaches to control real-time deformations of digital shapes and are, to a vast extent, complementary to one another. Despite their complementary roles, high-end modeling packages do not allow for seamless integration of such control structures, thus inducing a considerable burden on the user to maintain them synchronized. In this paper, we propose a framework that seamlessly combines rigging skeletons and deformation cages, granting artists with a real-time deformation system that operates using any smooth combination of the two approaches. By coupling the deformation spaces of cages and skeletons, we access a much larger space, containing poses that are impossible to obtain by acting solely on a skeleton or a cage. Our method is oblivious to the specific techniques used to perform skinning and cage-based deformation, securing it compatible with pre-existing tools. We demonstrate the usefulness of our hybrid approach on a variety of examples.

We propose QuadMixer, a novel interactive technique to compose quad mesh components preserving the majority of the original layouts. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. We first perform robust boolean operations on the corresponding triangle meshes. Then we use this result to identify and build new surface patches for small regions neighboring the intersection curves. These blending patches are carefully quadrangulated respecting boundary constraints and stitched back to the untouched parts of the original models. The resulting mesh preserves the designed edge flow that, by construction, is captured and incorporated to the new quads as much as possible. We present our technique in an interactive tool to show its usability and robustness.

In this poster, we present a visualization tool for the in-depth analysis of domestic electricity consumption. The web-interface allows users to visualize their electricity consumption, compare them with their own records or with the means of selected communities. CCS Concepts • Human-centered computing → Information visualization; • Hardware → Sensors and actuators;

Fast research and prototyping, nowadays, is shifting towards languages that allow interactive execution and quick changes. Python is very widely used for rapid prototyping. We introduce Py3DViewer, a new Python library that allows researchers to quickly prototype geometry processing algorithms by interactively editing and viewing meshes. Polygonal and polyhedral meshes are both supported. The library is designed to be used in conjunction with Jupyter environments, which allow interactive Python code execution and data visualization in a browser, thus opening up the possibility of viewing a mesh while editing the underlying geometry and topology. CCS Concepts • Computing methodologies → Mesh models; Volumetric models; Rendering;

We propose QuadMixer, a novel interactive technique to compose quad mesh components preserving the majority of the original layouts. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. We first perform robust boolean operations on the corresponding triangle meshes. Then we use this result to identify and build new surface patches for small regions neighboring the intersection curves. These blending patches are carefully quadrangulated respecting boundary constraints and stitched back to the untouched parts of the original models. The resulting mesh preserves the designed edge flow that, by construction, is captured and incorporated to the new quads as much as possible. We present our technique in an interactive tool to show its usability and robustness.

Hexahedral meshes generated from polycube mapping often exhibit a low number of singularities but also poor-quality elements located near the surface. It is thus necessary to improve the overall mesh quality, in terms of the minimum scaled Jacobian (MSJ) or average SJ (ASJ). Improving the quality may be obtained via global padding (or pillowing), which pushes the singularities inside by adding an extra layer of hexahedra on the entire domain boundary. Such a global padding operation suffers from a large increase of complexity, with unnecessary hexahedra added. In addition, the quality of elements near the boundary may decrease. We propose a novel optimization method which inserts sheets of hexahedra so as to perform selective padding, where it is most needed for improving the mesh quality. A sheet can pad part of the domain boundary, traverse the domain and form singularities. Our global formulation, based on solving a binary problem, enables us to control the balance between quality improvement, increase of complexity and number of singularities. We show in a series of experiments that our approach increases the MSJ value and preserves (or even improves) the ASJ, while adding fewer hexahedra than global padding.