Multiresolution on spherical curves

Alderson, Troy; Mahdavi-Amiri, Ali; Samavati, Faramarz

doi:10.1016/j.gmod.2016.05.002

Cited by 9 publications

(10 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While curve subdivision schemes can be reversed using optimization on a given subdivision matrix [18], [22], this method does not generalize well to surface subdivision schemes or non-Euclidean spaces. For this reason, Alderson et al [6], [23] explored modifying the Lane-Riesenfeld algorithm using local smoothing operators with local inverses (see [8]) in order to establish multiresolution for curves on the surface of a sphere in a general and efficient way. Our work generalizes this repeated invertible averaging method to surface subdivision, much as Stam, Zorin, and Schröder generalized the Lane-Riesenfeld algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…The number of averaging operations applied, m, is linked to the support of the scheme (and its bi-degree, when the subdivision reproduces polynomial surfaces at the limit -as in the case of B-Spline subdivision). Similarly to the works of [2] and [6], we divide our schemes into odd degree (primal) schemes and even degree (dual) schemes.…”

Section: Rias For Multiresolution Surfacesmentioning

confidence: 99%

“…Our averaging operators, inspired by those of [6], have the property that both the operator and its inverse are both local (i.e. operate on direct neighbours of a vertex only), in contrast to other averaging operators that do not guarantee locality of the inverse (if, indeed, they are invertible at all).…”

Section: B Remarks On Local Inversesmentioning

confidence: 99%

“…Our work extends the methodology of [6], which operates on spherical curves. In their method, which we refer to as repeated invertible averaging (RIA), Alderson et al replaced the Lane-Riesenfeld algorithm's averaging operator with invertible variants whose inverses involve only direct neighbours of a vertex.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree

Alderson

Mahdavi-Amiri

Samavati

2021

IEEE Trans. Visual. Comput. Graphics

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce two local surface averaging operators with local inverses and use them to devise a method for surface multiresolution (subdivision and reverse subdivision) of arbitrary degree. Similar to previous works by Stam, Zorin, and Schröder that achieved forward subdivision only, our averaging operators involve only direct neighbours of a vertex, and can be configured to generalize B-Spline multiresolution to arbitrary topology surfaces. Our subdivision surfaces are hence able to exhibit C d continuity at regular vertices (for arbitrary values of d) and appear to exhibit C 1 continuity at extraordinary vertices. Smooth reverse and nonuniform subdivisions are additionally supported.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Rias For Multiresolution Surfacesmentioning

confidence: 99%

Section: B Remarks On Local Inversesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree

Alderson

Mahdavi-Amiri

Samavati

2021

IEEE Trans. Visual. Comput. Graphics

Self Cite

View full text Add to dashboard Cite

show abstract

“…While traditional GIS still makes heavy use of projection for analysis and visualization of geographic and geospatial data, there have been many works on developing algorithms and techniques for performing spatial analysis directly on the sphere. Some recent examples include better representations of rational points [23], multiresolution representations of B-spline [24] and NURBS [25] curves, and methods for offsetting curves in both vector and raster form [26].…”

Section: Related Workmentioning

confidence: 99%

General Method for Extending Discrete Global Grid Systems to Three Dimensions

Ulmer

Hall

Samavati

2020

IJGI

Self Cite

View full text Add to dashboard Cite

Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.

show abstract