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Offsetting spherical curves in vector and raster form

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Abstract

In this paper, we present techniques for offsetting spherical curves represented in vector or raster form. Such techniques allow us to efficiently determine and visualize the region within a given distance of a spherical curve. Our methods additionally support multiresolution representations of the underlying data, allowing the initial coarse offsets to be provided quickly, which may then be iteratively refined to the correct result. An example application of offsetting is also specifically explored in the form of improving the performance of inside/outside tests in the vector case.

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Notes

  1. At \(d = 0\), O(v) is equivalent to C(u). In such a case, the set of small circle centers Q becomes the point set P interspersed with the zero vector \(\mathbf {0}\) (representing the centers of the great circle arcs).

  2. Reconstructing arcs close to \(\mathbf {x}\) can be skipped in most practical scenarios through an appropriate choice of \(\mathbf {x}\). For instance, if C(u) is limited to a single hemisphere, then \(\mathbf {x}\) can be chosen as the antipode of the centroid of C(u), which is known to lie outside of C(u) and its simplifications.

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Funding

This research was funded by Alberta Innovates—Technology Futures (AITF) and by an NSERC CRD with our collaborator, the PYXIS innovation.

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Authors and Affiliations

  1. University of Calgary, Calgary, Canada

    Troy Alderson & Faramarz Samavati

  2. Simon Fraser University, Burnaby, Canada

    Ali Mahdavi-Amiri

Authors
  1. Troy Alderson
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  2. Ali Mahdavi-Amiri
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  3. Faramarz Samavati
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Correspondence to Troy Alderson.

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Alderson, T., Mahdavi-Amiri, A. & Samavati, F. Offsetting spherical curves in vector and raster form. Vis Comput 34, 973–984 (2018). https://doi.org/10.1007/s00371-018-1525-7

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