Map Projections

Grafarend, Erik W.; You, Rey-Jer; Syffus, Rainer

doi:10.1007/978-3-642-36494-5

Cited by 37 publications

(27 citation statements)

References 96 publications

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“…On the other hand, he is right when he says that the aspect depends on the class to which the observed projection belongs. In references on map projections, the aspect is sometimes defined according to the area represented in the central part of a map (Snyder 1987, Grafarend and Krumm 2006, Fenna 2007, Kessler 2018. According to this definition, the aspect can be polar, equatorial or oblique.…”

Section: Discussionmentioning

confidence: 99%

Polar and Equatorial Aspects of Map Projections?

Lapaine

Frančula

2019

Proc. Int. Cartogr. Assoc.

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<p><strong>Abstract.</strong> There is no standard or generally accepted terminology of aspect in the theory of map projections. The term is probably derived from the concept that a graticule is produced by perspective projection of the meridians and parallels on a sphere onto a developable surface. Developable surfaces are widely accepted, and it is almost impossible to find a publication that deals with map projections in general and without developable surfaces story. If found, it usually classifies projections as cylindrical, conical and azimuthal, and applies developable surfaces to define the projection aspect. This paper explains why applying developable surfaces in the interpretation of map projections is not recommended, nor defining the aspect of all projections by the position of a midpoint as polar, equatorial, or oblique. In fact, defining a projection aspect this way is invalid in general, and obscures the fact that the aspect depends on the class to which a particular map projection belongs.</p>

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Section: Discussionmentioning

confidence: 99%

Polar and Equatorial Aspects of Map Projections?

Lapaine

Frančula

2019

Proc. Int. Cartogr. Assoc.

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“…There are many projections available offering a variety of different results: Some preserve angles, while others preserve areas. For further discussion regarding several cartographic methods, we refer to (Grafarend and Krumm, 2006). (ii) Future additions to our framework will be the usage of primitives such as ellipsoids or parameterizable surfaces.…”

Section: Discussionmentioning

confidence: 99%

“…More recent works uses triangle strips that are adjusted to the surface of arbitrary objects in order to unfold them (Massarwi et al, 2007). A detailed body of methods for unwrapping spherical objects can be found in cartography (Grafarend and Krumm, 2006). Our method enables experts of cultural heritage to rapidly compute planar representations of cultural heritage objects for important tasks such as iconographic analysis.…”

Section: Related Workmentioning

confidence: 99%

Unwrapping Highly-Detailed 3d Meshes of Rotationally Symmetric Man-Made Objects

Rieck

Mara

Krömker

2013

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Rotationally symmetric objects commonly occur at archaeological finds. Instead of creating 2D images for documentation purposes by manual drawing or photographic methods, we propose a method based on digitally colored surface models that are acquired by 3D scanners, thereby including color information. We then transform these highly-detailed meshes using simple geometrical objects such as cones and spheres and unwrap the objects onto a plane. Our method can handle curved vessel profiles by dividing the surface into multiple segments and approximating each segment with a cone frustum that serves as an auxiliary surface. In order to minimize distortions, we introduce a simple quality measure based on distances of points to a fitted cone. We then extend our method to approximately spherical objects by fitting a sphere on the surface of the object and applying a map projection, namely the equirectangular projection known from cartography. Our implementation generates true-to-scale images from triangular meshes. Exemplary results demonstrate our methods on real objects, ranging from small and medium-sized objects such as clay cones from the Ancient Orient and figural friezes of Greek vessels to extremely large objects such as the remains of a cylindrical tower of Heidelberg Castle.

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“…The use of map-like projections has already proved effective for the achievement of raster images of frescoes painted on arches or spherical surfaces [18,19]. A thorough discussion of the development methods for spherical objects can be found in the cartographic literature [20]. In later works, arbitrary surfaces were interpolated with triangle strips prior to their development [21].…”

Section: Geometry Pseudo-developmentmentioning

confidence: 99%

A Methodology for Planar Representation of Frescoed Oval Domes: Formulation and Testing on Pisa Cathedral

Piemonte

Crepaldi

Zaragoza

et al. 2018

IJGI

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This paper presents an original methodology for planar development of a frescoed dome with an oval plan. Input data include a rigorous geometric survey, performed with a laser scanner, and a photogrammetry campaign, which associates a high-quality photographic texture to the 3D model. Therefore, the main topics include the development of geometry and, contextually, of the associated textures. In order to overcome the inability to directly develop the surface, an orthographic azimuthal projection is used. Starting from a prerequisite study of building methodology, the dome is divided into sectors and bands, each linked with the maximum acceptable deformations and the actual geometric discontinuities detectable by the analysis of Gaussian curvature. Upon definition of the development model, a custom automation script has been devised for geometry projection. This effectively generates a (u,v) map, associated to the model, which is used for model texturing and provides the planar development of the fresco.

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Map Projections

Cited by 37 publications

References 96 publications

Polar and Equatorial Aspects of Map Projections?

Polar and Equatorial Aspects of Map Projections?

Unwrapping Highly-Detailed 3d Meshes of Rotationally Symmetric Man-Made Objects

A Methodology for Planar Representation of Frescoed Oval Domes: Formulation and Testing on Pisa Cathedral

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