Solving inverse configuration space problems by adaptive sampling

Nelaturi, Saigopal; Shapiro, Vadim

doi:10.1016/j.cad.2012.10.020

Cited by 9 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It follows that, in general, the idea of a direct approximation of d G seems unsuitable for applications. For the general problem of sampling SO(3), we refer the interested reader to the paper [23].…”

Section: Comments On the Use Of D F Matchmentioning

confidence: 99%

Combining Persistent Homology and Invariance Groups for Shape Comparison

Frosini

Jabłoński

2016

Discrete Comput Geom

View full text Add to dashboard Cite

In many applications concerning the comparison of data expressed by R m -valued functions defined on a topological space X, the invariance with respect to a given group G of self-homeomorphisms of X is required. While persistent homology is quite efficient in the topological and qualitative comparison of this kind of data when the invariance group G is the group Homeo(X) of all selfhomeomorphisms of X, this theory is not tailored to manage the case in which G is a proper subgroup of Homeo(X), and its invariance appears too general for several tasks. This paper proposes a way to adapt persistent homology in order to get invariance just with respect to a given group of self-homeomorphisms of X. The main idea consists in a dual approach, based on considering the set of all Ginvariant non-expanding operators defined on the space of the admissible filtering functions on X. Some theoretical results concerning this approach are proven and two experiments are presented. An experiment illustrates the application of the proposed technique to compare 1D-signals, when the invariance is expressed by the group of affinities, the group of orientation-preserving affinities, the group of isometries, the group of translations and the identity group. Another experiment shows how our technique can be used for image comparison.

show abstract

Section: Comments On the Use Of D F Matchmentioning

confidence: 99%

Combining Persistent Homology and Invariance Groups for Shape Comparison

Frosini

Jabłoński

2016

Discrete Comput Geom

View full text Add to dashboard Cite

show abstract

“…The collision-free space CS free is defined as the set of all free configurations in CS. The computation of the complete CS free by the adaptive sampling has been studied in [45,46]. However, computing the complete CS free cannot fulfill the efficiency requirement.…”

Section: Relationship Between the Motion Of An Object And Its Scenarimentioning

confidence: 99%

An interactive motion planning framework that can learn from experience

Poirson

Bennis

2015

Computer-Aided Design

View full text Add to dashboard Cite

“…In this paper, we sample the 3D rotation group SO(3) to obtain the set of candidate build orientations. However, there are many gradient-free or stochastic optimization methods [26] such as simulated annealing [27] that can be used to sample SO(3) more efficiently [28] or converge to global optimum.…”

Section: Build Orientation Optimizationmentioning

confidence: 99%

Optimizing Build Orientation for Support Removal using Multi-Axis Machining

Mirzendehdel,

Behandish,

Nelaturi

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Parts fabricated by additive manufacturing (AM) are often fabricated first as a near-net shape, a combination of intended nominal geometry and sacrificial support structures, which need to be removed in a subsequent post-processing stage using subtractive manufacturing (SM). In this paper, we present a framework for optimizing the build orientation with respect to removability of support structures. In particular, given a general multi-axis machining setup and sampled build orientations, we define a Pareto-optimality criterion based on the total support volume and the "secluded" support volume defined as the support volume that is not accessible by a given set of machining tools. Since total support volume mainly depends on the build orientation and the secluded volume is dictated by the machining setup, in many cases the two objectives are competing and their trade-off needs to be taken into account. The accessibility analysis relies on the inaccessibility measure field (IMF), which is a continuous field in the Euclidean space that quantifies the inaccessibility of each point given a collection of tools and fixturing devices. The value of IMF at each point indicates the minimum possible volumetric collision between objects in relative motion including the part, fixtures, and the tools, over all possible tool orientations and sharp points on the tool. We also propose an automated support removal planning algorithm based on IMF, where a sequence of actions are provided in terms of the fixturing devices, cutting tools, and tool orientation at each step. In our approach, each step is chosen based on the maximal removable volume to iteratively remove accessible supports. The effectiveness of the proposed approach is demonstrated through benchmark examples in 2D and realistic examples in 3D.

show abstract

Solving inverse configuration space problems by adaptive sampling

Cited by 9 publications

References 20 publications

Combining Persistent Homology and Invariance Groups for Shape Comparison

Combining Persistent Homology and Invariance Groups for Shape Comparison

An interactive motion planning framework that can learn from experience

Optimizing Build Orientation for Support Removal using Multi-Axis Machining

Contact Info

Product

Resources

About