Averaged ratio between complementary profiles for evaluating shape distortions of map projections and spherical hierarchical tessellations

Yan, Jin; Song, Xiao Yan; Gong, Guanghong

doi:10.1016/j.cageo.2015.11.009

Cited by 11 publications

(11 citation statements)

References 27 publications

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“…The combination of low angular distortion and area equivalence makes the projection better suited for panorama applications than the commonly used equirectangular format, which has both extreme area distortions and extreme angle distortions. The equal-area property avoids the storage of redundant information across multiple pixels, while the low angular distortion reduces the occurrence of sampling artifacts in rectilinear views [27]. Taken together, these properties allow for reduced image file sizes, which reduce both storage and data transfer requirements for websites displaying panoramas.…”

Section: Discussionmentioning

confidence: 99%

“…The other significant existing square equal-area projection is what will be referred to here as the Collignon quincuncial projection, which consists of an interrupted Collignon projection [5] for each octant of a spherical octahedron displayed in a quincuncial arrangement. It is called the equal-area zenithal orthotriangular projection in Huang et al [12], the octahedral equal area partition in Yan et al [27], and the triangular octahedral equal area projection in McGlynn et al [16]. It is briefly described as a possible variant of the Collignon projection, with neither a specific name nor a figure, in Snyder [22] and is described with neither a specific name, a figure, nor a reference to the Collignon projection in Maurer [15] (translated to English in Warntz [26]); it is also described for a single hemisphere in Roşca [20] and Holhoş and Roşca [11].…”

Section: Introductionmentioning

confidence: 99%

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A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

Petroff

2021

ACM Trans. Spatial Algorithms Syst.

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A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

Petroff

2021

ACM Trans. Spatial Algorithms Syst.

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“…Other general measures of distortion include Tissot's ellipses (Snyder, 1987;Bauer-Marschallinger et al, 2014) and derived measures (e.g. averaged ratio between complementary profiles, Yan et al, 2016). However, for the case of a conformal projection (no angular distortion, linear distortion k1, areal distortion k2 = k1 2 and Tissot's ellipses degenerated to circles of radius k1) it seems sensible to study only k1 and, in particular, its typical deviation from the optimum value 1, as we will see next.…”

Section: Distortion Measuresmentioning

confidence: 99%

Fibonacci lattices for the evaluation and optimization of map projections

Baselga

2018

Computers & Geosciences

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Latitude-longitude grids are frequently used in geosciences for global numerical modelling although they are remarkably inhomogeneous due to meridian convergence. In contrast, Fibonacci lattices are highly isotropic and homogeneous so that the area represented by each lattice point is virtually the same. In the present paper we show the higher performance of Fibonacci versus latitude-longitude lattices for evaluating distortion coefficients of map projections. In particular, we obtain first a typical distortion for the Lambert Conformal Conic projection with their currently defined parameters and geographic boundaries for Europe that has been adopted as standard by the INSPIRE directive. Further, we optimize the defining parameters of this projection, lower and upper standard parallel latitudes, so that the typical distortion for Europe is reduced a 10% when they are set to 36º and 61.5º, respectively. We also apply the optimization procedure to the determination of the best standard parallels for using this projection in Spain, whose values remained unspecified by the National decree that commanded its official adoption, and obtain optimum values of 37º and 42º and a resulting typical distortion of 828 ppm.

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“…Projection transformation is often used in vector geographic data processing and application [24,30]. Therefore, in view of the poor robustness of current vector geographic data zero-watermarking algorithms to projection transformation, a zero-watermarking algorithm based on vector geographic data feature invariants is proposed, which can resist any projection transformation.…”

Section: Introductionmentioning

confidence: 99%

A zero-watermarking algorithm for vector geographic data based on feature invariants

Wang

Zhang

et al. 2022

Earth Sci Inform

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Most researches on zero-watermarking algorithms for vector geographic data focus on improving the robustness against geometrical attacks, compression attacks and object attacks. However, there are few zero-watermarking algorithms against projection transformation. We proposed a zerowatermarking algorithm for vector geographic data based on feature invariants. After any projection transformation of vector geographic data, the number of vertices and relative storage order of objects does not change. Therefore, the number of vertices and relative storage order of objects can be considered as the feature invariants. Firstly, according to relative storage order of objects, the watermark bit is determined by comparing the number of vertices between any two objects. Secondly, the watermark index is calculated by the number of vertices of two objects. Then, a feature matrix is constructed combining the watermark bit and the watermark index. Finally, the XOR operation is performed between the feature matrix and the scrambled watermark image to generate the zerowatermark image. The experiments show that the watermark can be detected from the vector geographic data after any projection transformation. And this algorithm can effectively against geometrical attacks, object attacks and precision reduction attacks, showing superior performance compared with previous algorithms.

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Averaged ratio between complementary profiles for evaluating shape distortions of map projections and spherical hierarchical tessellations

Cited by 11 publications

References 27 publications

A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

Fibonacci lattices for the evaluation and optimization of map projections

A zero-watermarking algorithm for vector geographic data based on feature invariants

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