Reconstructing polygons from scanner data

Biedl, Thérèse; Durocher, Stéphane; Snoeyink, Jack

doi:10.1016/j.tcs.2010.10.026

Cited by 22 publications

(12 citation statements)

References 18 publications

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“…[7,2] also preserve the input point set, but, as we show below can struggle in the presence of poorly sampled data. Interestingly, there are several NP-hardness results for surface reconstruction [5,8], which both explain the prevalence of heuristics, and point towards the use of data-driven priors. More fundamentally, classical approaches are not differentiable in nature and thus do not allow endto-end training or backpropagation of the mesh with respect to input positions.…”

Section: Related Workmentioning

confidence: 99%

PointTriNet: Learned Triangulation of 3D Point Sets

Sharp,

Ovsjanikov

2020

Preprint

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This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D learning pipelines. The method iteratively applies two neural networks to generate a triangulation: a classification network predicts whether a candidate triangle should appear in the triangulation, while a proposal network suggests additional candidates. Both networks are structured as PointNets over nearby points and triangles, using a novel triangle-relative input encoding. Since these learning problems operate on local geometric data, our method scales effectively to large input sets and unseen shape categories, and we can train the networks in an unsupervised manner from a collection of shapes represented as meshes or point clouds. We demonstrate the effectiveness of this approach for classical meshing tasks, robustness to outliers, and as a component in end-to-end learning systems.

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Section: Related Workmentioning

confidence: 99%

PointTriNet: Learned Triangulation of 3D Point Sets

Sharp,

Ovsjanikov

2020

Preprint

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“…3 Proof sketch: The polyline goes through interior-disjoint regions of type BB in i \ BB in i−1 and in order to visit three consecutive such regions, it needs a separate vertex inside the interior of each of the three regions. 4 Without loss of generality, S has at most (W + 1)(H + 1) vertices and the inner ladders have at most 4X + 4Y vertices in total. Since i ≥ √ ρ > maxCenterCost > (W + 1)(H + 1) + 4X + 4Y , i is greater than the number of vertices.…”

Section: But This Inequality Contradicts Lemma 13mentioning

confidence: 99%

Minimum Rectilinear Polygons for Given Angle Sequences

Evans

Fleszar

Kindermann

et al. 2016

Lecture Notes in Computer Science

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A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns plus 4. It is known that any such sequence can be realized by a rectilinear polygon. In this paper, we consider the problem of finding realizations that minimize the perimeter or the area of the polygon or the area of the bounding box of the polygon. We show that all three problems are NP-hard in general. Then we consider the special cases of x-monotone and xy-monotone rectilinear polygons. For these, we can optimize the three objectives efficiently.

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“…Biedl et al [3] considered various types of measurements in a simple polygon, and considered the complexity of the problem to decide whether or not there is a simple polygon that is consistent with the given data. Examples for the measurements considered are (1) a set of points on the boundary of the original simple polygon, such that every boundary edge contains at least one point, and (2) a set of visibility polygons, i.e., the regions of the polygon that are visible from certain points in the polygon (for the latter, cf.…”

Section: Reconstruction Not Involving Agentsmentioning

confidence: 99%