Iterated snap rounding

A b s t r a c tA rule-based topology software system providing a highly flexible and fast procedure to enforce integrity in spatial relationships among datasets is presented. This improved topology rule system is built over the spatial extension Jaspa. Both projects are open source, freely available software developed by the corresponding author of this paper.Currently, there is no spatial DBMS that implements a rule-based topology engine (considering that the topology rules are designed and performed in the spatial backend). If the topology rules are applied in the frontend (as in many GIS desktop programs), ArcGIS is the most advanced solution. The system presented in this paper has several major advantages over the ArcGIS approach: it can be extended with new topology rules, it has a much wider set of rules, and it can mix feature attributes with topology rules as filters. In addition, the topology rule system can work with various DBMSs, including PostgreSQL, H2 or Oracle, and the logic is performed in the spatial backend.The proposed topology system allows users to check the complex spatial relationships among features (from one or several spatial layers) that require some complex cartographic datasets, such as the data specifications proposed by INSPIRE in Europe and the Land Administration Domain Model (LADM) for Cadastral data.

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“…The ST_Snap algorithm follows the well-known family of snap rounding algorithms like (Halperin and Packer, 2002). Fig.…”

Section: Cluster Tolerancementioning

confidence: 99%

Rule-based topology system for spatial databases to validate complex geographic datasets

Martínez-Llario

Coll

Nez-Andrs

et al. 2017

Computers & Geosciences

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“…Iterated Snap Rounding (ISR), introduced by Halperin and Packer [12], ensures that no rounded segment intersects a hot pixel. As a side effect this solves the problem of snap rounding instability.…”

Section: B))mentioning

confidence: 99%

Stable snap rounding

Hershberger

2011

Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry

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Snap rounding is a popular method for rounding the vertices of a planar arrangement of line segments to the integer grid. It has many advantages, including minimum perturbation of the segments, preservation of the arrangement topology, and ease of implementation. However, snap rounding has one significant weakness: it is not stable (i.e., not idempotent). That is, applying snap rounding to a snap-rounded arrangement of n segments may cause additional segment perturbation, and the number of iterations of snap rounding needed to reach stability may be as large as Θ(n 2 ). This paper introduces stable snap rounding, a variant of snap rounding that has all of snap rounding's advantages and is also idempotent. In particular, stable snap rounding does not change any arrangement whose vertices are already grid points (such as those produced by stable snap rounding or standard snap rounding).

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“…(As noted by Halperin and Packer [14], rounded arcs may still pass very near hot pixel centers; recent work by Packer [18] shows how to avoid this near-degeneracy while preserving the approximation guarantees of snap rounding. )…”

Section: Introductionmentioning

confidence: 99%

“…Goodrich et al [9] avoid the dependence on the input size I with an algorithm that runs in time O((n + h∈H |h|) log n); they claim optimality to within a logarithmic factor for their algorithm. However, as Halperin and co-authors have noted [5,13,14], the definition of h∈H |h| as the output size is misleading, because it can be as large as (n 3 ), even though the size of the snap rounded arrangement, (|H|), can never be larger than O(n 2 ). See Fig.…”

Section: Introductionmentioning

confidence: 99%

Improved Output-Sensitive Snap Rounding

Hershberger

2007

Discrete Comput Geom

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This paper presents new algorithms for snap rounding an arrangement A of line segments in the plane. Snap rounding defines a set of hot pixels, which are unit squares centered on the integer grid points closest to the vertices of A. Snap rounding simplifies A by replacing every input segment by a piecewise linear curve connecting the centers of the hot pixels the segment intersects. Let H be the set of all hot pixels, and for each h ∈ H let is(h) be the number of segments with an intersection or endpoint inside h. If A contains n input segments, the running time of the first new algorithm is O( h∈H is(h) log n). This improves previous input-and outputsensitive algorithms by a factor of (n) in the worst case. The second algorithm has an even better running time of O( h∈H ed(h) log n); here ed(h) is the description complexity of the crossing pattern in h, which may be substantially less than is(h) and is never greater.

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Iterated snap rounding

Cited by 28 publications

References 8 publications

Rule-based topology system for spatial databases to validate complex geographic datasets

Rule-based topology system for spatial databases to validate complex geographic datasets

Stable snap rounding

Improved Output-Sensitive Snap Rounding

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