39 research outputs found
Extracting curve-skeletons from digital shapes using occluding contours
Curve-skeletons are compact and semantically relevant shape descriptors, able to summarize 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 curve-skeleton, then we propose a novel method for skeleton extraction that rely 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 by a small set of its planar projections. The proposed method is fast, insensitive to noise, capable of working with different shape representations, resolution insensitive and easy to implement
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, in particular along the Process Planning pipeline, can now count
on dozens of methods that prepare the 3D model for fabrication, while analysing
and optimizing 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 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.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and
Innovation action; Grant agreement N. 68044
Understanding the Structure of 3D Shapes
Compact representations of three dimensional objects are very often used
in computer graphics to create effective ways to analyse, manipulate and
transmit 3D models. Their ability to abstract from the concrete shapes and
expose their structure is important in a number of applications, spanning
from computer animation, to medicine, to physical simulations. This thesis
will investigate new methods for the generation of compact shape representations.
In the first part, the problem of computing optimal PolyCube base
complexes will be considered. PolyCubes are orthogonal polyhedra used
in computer graphics to map both surfaces and volumes. Their ability to
resemble the original models and at the same time expose a very simple and
regular structure is important in a number of applications, such as texture
mapping, spline fitting and hex-meshing. The second part will focus on
medial descriptors. In particular, two new algorithms for the generation
of curve-skeletons will be presented. These methods are completely based
on the visual appearance of the input, therefore they are independent from
the type, number and quality of the primitives used to describe a shape,
determining, thus, an advancement to the state of the art in the field
Optimal Dual Schemes for Adaptive Grid Based Hexmeshing
Hexahedral meshes are an ubiquitous domain for the numerical resolution of
partial differential equations. Computing a pure hexahedral mesh from an
adaptively refined grid is a prominent approach to automatic hexmeshing, and
requires the ability to restore the all hex property around the hanging nodes
that arise at the interface between cells having different size. The most
advanced tools to accomplish this task are based on mesh dualization. These
approaches use topological schemes to regularize the valence of inner vertices
and edges, such that dualizing the grid yields a pure hexahedral mesh. In this
paper we study in detail the dual approach, and propose four main contributions
to it: (i) we enumerate all the possible transitions that dual methods must be
able to handle, showing that prior schemes do not natively cover all of them;
(ii) we show that schemes are internally asymmetric, therefore not only their
implementation is ambiguous, but different implementation choices lead to
hexahedral meshes with different singular structure; (iii) we explore the
combinatorial space of dual schemes, selecting the minimum set that covers all
the possible configurations and also yields the simplest singular structure in
the output hexmesh; (iv) we enlarge the class of adaptive grids that can be
transformed into pure hexahedral meshes, relaxing one of the tight requirements
imposed by previous approaches, and ultimately permitting to obtain much
coarser meshes for same geometric accuracy. Last but not least, for the first
time we make grid-based hexmeshing truly reproducible, releasing our code and
also revealing a conspicuous amount of technical details that were always
overlooked in previous literature, creating an entry barrier that was hard to
overcome for practitioners in the field
Parametric shape optimization for combined additive–subtractive manufacturing
The final publication is available at Springer via http://dx.doi.org/10.1007/s11837-019-03886-xIn industrial practice, additive manufacturing (AM) processes are often followed by post-processing operations such as heat treatment, subtractive machining, milling, etc., to achieve the desired surface quality and dimensional accuracy. Hence, a given part must be 3D-printed with extra material to enable this finishing phase. This combined additive/subtractive technique can be optimized to reduce manufacturing costs by saving printing time and reducing material and energy usage. In this work, a numerical methodology based on parametric shape optimization is proposed for optimizing the thickness of the extra material, allowing for minimal machining operations while ensuring the finishing requirements. Moreover, the proposed approach is complemented by a novel algorithm for generating inner structures to reduce the part distortion and its weight. The computational effort induced by classical constrained optimization methods is alleviated by replacing both the objective and constraint functions by their sparse grid surrogates. Numerical results showcase the effectiveness of the proposed approach.Peer ReviewedPostprint (published version