Marco Livesu

PolyCut: monotone graph-cuts for PolyCube base-complex construction

PolyCubes, or orthogonal polyhedra, are useful as parameterization base-complexes for various operations in computer graphics. However, computing quality PolyCube base-complexes for general shapes, providing a good trade-off between mapping distortion and singularity counts, remains a challenge. Our work improves on the state-of-the-art in PolyCube computation by adopting a graph-cut inspired approach. We observe that, given an arbitrary input mesh, the computation of a suitable PolyCube base-complex can be formulated as associating, or labeling, each input mesh triangle with one of six signed principal axis directions. Most of the criteria for a desirable PolyCube labeling can be satisfied using a multi-label graph-cut optimization with suitable local unary and pairwise terms. However, the highly constrained nature of PolyCubes, imposed by the need to align each chart with one of the principal axes, enforces additional global constraints that the labeling must satisfy. To enforce these constraints, we develop a constrained discrete optimization technique, PolyCut, which embeds a graph-cut multi-label optimization within a hill-climbing local search framework that looks for solutions that minimize the cut energy while satisfying the global constraints. We further optimize our generated PolyCube base-complexes through a combination of distortion-minimizing deformation, followed by a labeling update and a final PolyCube parameterization step. Our PolyCut formulation captures the desired properties of a PolyCube base-complex, balancing parameterization distortion against singularity count, and produces demonstrably better PolyCube base-complexes then previous work.

Extraction of the Quad Layout of a Triangle Mesh Guided by Its Curve Skeleton

Starting from the triangle mesh of a digital shape, that is, mainly an articulated object, we produce a coarse quad layout that can be used in character modeling and animation. Our quad layout follows the intrinsic object structure described by its curve skeleton; it contains few irregular vertices of low degree; it can be immediately refined into a semiregular quad mesh; it provides a structured domain for UV mapping and parametrization. Our method is fast, one-click, and does not require any parameter setting. The user can steer and refine the process through simple interactive tools during the construction of the quad layout.

Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull

Curve-skeletons are the most important descriptors for shapes, capable of capturing in a synthetic manner the most relevant features. They are useful for many different applications: from shape matching and retrieval, to medical imaging, to animation. This has led, over the years, to the development of several different techniques for extraction, each trying to comply with specific goals. We propose a novel technique which stems from the intuition of reproducing what a human being does to deduce the shape of an object holding it in his or her hand and rotating. To accomplish this, we use the formal definitions of epipolar geometry and visual hull. We show how it is possible to infer the curve-skeleton of a broad class of 3D shapes, along with an estimation of the radii of the maximal inscribed balls, by gathering information about the medial axes of their projections on the image planes of the stereographic vision. It is definitely worth to point out that our method works indifferently on (even unoriented) polygonal meshes, voxel models, and point clouds. Moreover, it is insensitive to noise, pose-invariant, resolution-invariant, and robust when applied to incomplete data sets.

Practical hex-mesh optimization via edge-cone rectification

The usability of hexahedral meshes depends on the degree to which the shape of their elements deviates from a perfect cube; a single concave, or inverted element makes a mesh unusable. While a range of methods exist for discretizing 3D objects with an initial topologically suitable hex mesh, their output meshes frequently contain poorly shaped and even inverted elements, requiring a further quality optimization step. We introduce a novel framework for optimizing hex-mesh quality capable of generating inversion-free high-quality meshes from such poor initial inputs. We recast hex quality improvement as an optimization of the shape of overlapping cones, or unions, of tetrahedra surrounding every directed edge in the hex mesh, and show the two to be equivalent. We then formulate cone shape optimization as a sequence of convex quadratic optimization problems, where hex convexity is encoded via simple linear inequality constraints. As this solution space may be empty, we therefore present an alternate formulation which allows the solver to proceed even when constraints cannot be satisfied exactly. We iteratively improve mesh element quality by solving at each step a set of local, per-cone, convex constrained optimization problems, followed by a global energy minimization step which reconciles these local solutions. This latter method provides no theoretical guarantees on the solution but produces inversion-free, high quality meshes in practice. We demonstrate the robustness of our framework by optimizing numerous poor quality input meshes generated using a variety of initial meshing methods and producing high-quality inversion-free meshes in each case. We further validate our algorithm by comparing it against previous work, and demonstrate a significant improvement in both worst and average element quality.

From 3D models to 3D prints: an overview of the processing pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step along the processing pipeline that prepares the 3D model for fabrication can now count on dozens of methods, that analyse and optimize geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during model preparation – a process globally refereed to as Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.

Extracting curve-skeletons from digital shapes using occluding contours

Curve-skeletons are compact and semantically relevant shape descriptors, able to summarise both topology and pose of a wide range of digital objects. Most of the state-of-the-art algorithms for their computation rely on the type of geometric primitives used and sampling frequency. In this paper, we introduce a formally sound and intuitive definition of a curve-skeleton, then we propose a novel method for skeleton extraction that relies on the visual appearance of the shapes. To achieve this result, we inspect the properties of occluding contours, showing how information about the symmetry axes of a 3D shape can be inferred from a small set of its planar projections. The proposed method is fast, insensitive to noise and resolution, capable of working with different shape representations, and easy to implement.

Polycube simplification for coarse layouts of surfaces and volumes

Representing digital objects with structured meshes that embed a coarse block decomposition is a relevant problem in applications like computer animation, physically‐based simulation and Computer Aided Design (CAD). One of the key ingredients to produce coarse block structures is to achieve a good alignment between the mesh singularities (i.e., the corners of each block). In this paper we improve on the polycube‐based meshing pipeline to produce both surface and volumetric coarse block‐structured meshes of general shapes. To this aim we add a new step in the pipeline. Our goal is to optimize the positions of the polycube corners to produce as coarse as possible base complexes. We rely on re‐mapping the positions of the corners on an integer grid and then using integer numerical programming to reach the optimal. To the best of our knowledge this is the first attempt to solve the singularity misalignment problem directly in polycube space. Previous methods for polycube generation did not specifically address this issue. Our corner optimization strategy is efficient and requires a negligible extra running time for the meshing pipeline. In the paper we show that our optimized polycubes produce coarser block structured surface and volumetric meshes if compared with previous approaches. They also induce higher quality hexahedral meshes and are better suited for spline fitting because they reduce the number of splines necessary to cover the domain, thus improving both the efficiency and the overall level of smoothness throughout the volume.

Skeleton-driven adaptive hexahedral meshing of tubular shapes

We propose a novel method for the automatic generation of structured hexahedral meshes of articulated 3D shapes. We recast the complex problem of generating the connectivity of a hexahedral mesh of a general shape into the simpler problem of generating the connectivity of a tubular structure derived from its curve‐skeleton. We also provide volumetric subdivision schemes to nicely adapt the topology of the mesh to the local thickness of tubes, while regularizing per‐element size. Our method is fast, one‐click, easy to reproduce, and it generates structured meshes that better align to the branching structure of the input shape if compared to previous methods for hexa mesh generation.

Gestural Interaction for Robot Motion Control

Recent advances in gesture recognition made the problem of controlling a humanoid robot in the most natural possible way an interesting challenge. Learning from Demonstration field takes strong advantage from this kind of interaction since users who have no robotics knowledge are allowed to teach new tasks to robots easier than ever before. In this work we present a cheap and easy way to implement humanoid robot along with a visual interaction interface allowing users to control it. The visual system is based on the Microsoft Kinect’s RGB-D camera. Users can deal with the robot just by standing in front of the depth camera and mimicking a particular task they want to be performed by the robot. Our framework is cheap, easy to reproduce, and does not strictly depend on the particular underlying sensor or gesture recognition system.

Practical Medial Axis Filtering for Occlusion-Aware Contours

We propose a filtering system for occlusion-aware contours. Given a point of view, we use the silhouette of a 3D shape from that point of view, its medial axis and a map of the occluded areas. Our filter is able to select the points of the medial axis which are projections of the curve-skeleton of the 3D shape, discarding all the points affected by occlusions. Our algorithm is easy to implement and works in real time. It can be plugged as is into existing methods for curve-skeleton extraction from 2D images; it can be used to robustly rank silhouettes according to how much they are representative of the 3D shape that generated them and can also be used for shape recognition from images or video sequences.