Map Projections: cartographic information systems
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 713 S. graph. Darst. |
| ISBN: | 9783540367017 3540367012 |
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MARC
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| 100 | 1 | |a Grafarend, Erik W. |d 1939-2020 |e Verfasser |0 (DE-588)121959368 |4 aut | |
| 245 | 1 | 0 | |a Map Projections |b cartographic information systems |c Erik W. Grafarend ; Friedrich W. Krumm |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XVII, 713 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Cartography |x Mathematics | |
| 650 | 4 | |a Conformal mapping | |
| 650 | 4 | |a Map projection | |
| 650 | 4 | |a Surfaces, Representation of | |
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Record in the Search Index
| _version_ | 1805088400879910912 |
|---|---|
| adam_text |
Contents
Preface
1
Mapping from a left two-dimensional Riemann manifold to a right two-dimensional Riemann manifold
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
1-9
1-10
1-11 Areal
1-12
1-13
1-14
1-141
1-142
1-143
1-144
1-145
1-15
2
Mapping from a left two-dimensional Riemann manifold to a right two-dimensional Euclidean manifold
2-1 Eigenspace
2-2 Eigenspace
2-3
2-31
2-32
2-4
2-5
2-6
3
Coordinates (direct, transverse, oblique aspects)
3-1
3-2
XII
3-3
3-31
3-32
3-33
3-34
3-35
3-36
3-4
3-41
3-42
3-43
3-44
3-45
3-46
4
Classification of surfaces of Gaussian curvature zero in a two-dimensional Euclidean space
4-1
4-2
5
Mapping the sphere to a tangential plane: polar (normal) aspect
5-1
5-2
5-21
5-22
5-23
5-24
5-25
5-3
5-4
6
Mapping the sphere to a tangential plane: meta-azimuthal projections in the transverse aspect
6-1
(i-2 Special mapping equations
6-21
6-22
6-23
7
Mapping the sphere to a tangential plane: meta-azimuthal projections in the oblique aspect
7-1
7-2
7-21
7-22
7-23
Contents XIII
8 "Ellipsoid-of-revolution
Mapping the ellipsoid to a tangential plane (azimuthal projections in the normal aspect)
8-1
8-2
8-21
8-22
8-23
8-3
8-31
8-32
8-33
9
Mapping the ellipsoid to sphere and from sphere to plane (double projection, "authalic" projection)
9-1
9-11
9-12
9-13
9-14
9-15
9-16
9-17
9-2
9-3
10
Mapping the sphere to a cylinder: polar aspect
10-1
10-2
10-21
10-22
10-23
10-3
11
Mapping the sphere to a cylinder: meta-cylindrical projections in the transverse aspect
11-1
11-2
11-21
11-22
11-23
12
Mapping the sphere to a cylinder: meta-cylindrical projections in the oblique aspect
12-1
12-2
12-21
12-22
12-23
XIV Contents
13
Mapping the sphere to a cylinder: pseudo-cylindrical projections
13-1
13-2
13-21
13-22
13-23
13-24
14
Mapping the ellipsoid to a cylinder (polar aspect, generalization for rotational-symmetric surfaces)
14-1
14-2
14-21
14-22
14-23
14-24
14-3
14-31
14-32
14-33
14-34
15
Mapping the ellipsoid to a cylinder (transverse Mercator and Gauss-Krueger mappings)
15-1
15-2
15-3
15-4
15-5
15-6
15-61
15-62
16
Mapping the ellipsoid to a cylinder (oblique Mercator and rectified skew orthomorphic projections)
16-1
16-2
16-3
17
Mapping the sphere to a cone: polar aspect
17-1
17-2
17-21
17-22
17-23
Coiit ents
18
Mapping the sphere to a cone: pseudo-conic projections
18-1
18-2
18-21
18-22
19
Mapping the ellipsoid to a cone: polar aspect
19-1
19-2
19-21
19-22
19-23
20
Riemann,
20-1
20-2 Lagrange
20-21 Lagrange
20-22
20-3 Söldner
20-31
20-32
20-4
20-5
21
Analysis versus synthesis, Cartesian approach versus curvilinear approach
21-1
21-2
21-3
21-4
21-41
21-42
21-43
21-5
21-51
21-52
A Law and order
Relation preserving maps
A-l Law and order: Cartesian product, power sets
A-
В
Univariate, bivariate, and multivariate polynomials and their inversion formulae
B-l Inversion of a univariate homogeneous polynomial of degree n
B-2 Inversion of a bivariate homogeneous polynomial of degree n
B-3 Inversion of a multivariate homogeneous polynomial of degree n
XVI Contents
С
Elliptic kernel, elliptic modulus, elliptic functions, elliptic integrals
C-l Introductory example
C-2 Elliptic kernel, elliptic modulus, elliptic functions, elliptic integrals
D Korn-Lichtenstein and d'Alembert Euler equations
Conformai
D-l Korn Liechtenstein equations
D-2 D'Alembert Euler (Caucliy Riemann) equations
E
Geodetic curvature and geodetic torsion, the Newton form of a geodesic in Maupertuis gauge
E-l Geodetic curvature, geodetic torsion, and normal curvature
E-2 The differential equations of third order of a geodesic circle
E-3 The Newton form of a geodesic in Maupertuis gauge (sphere, ellipsoid-of-revolution)
E-31 The
E-32 The Maupertuis gauge and the Newton portrait of a geodesic
E-33 A geodesic as a submanifold of' the sphere
E-.'M A geodesic as a submanifold of the ellispoid-of-revohition
E-35 Maupertuis gauged geodesies (normal coordinates, local tangent plane)
E-36 Maupertuis gauged geodesies (Lie series, Hamilton portrait)
F
Mixed cylindric map projections of the ellipsoid-of-revolution, Lambert/Sanson-Flamsteed projections
F-
F-2 Mixed equiareal cylindric mapping: biaxial ellipsoid onto plane
F-3 Deformation analysis of vertically/horizontally averaged equiareal cylindric mappings
G
Generalized
G-l The pseudo-cylindrical mapping of the biaxial ellipsoid onto the plane
G-2 The generalized
G-3 Examples
H
Generalized Hammer projection of the ellipsoid-of-revolution: azimuthal, transverse, resolved equiareal
H-l The transverse equiareal projection of the biaxial ellipsoid
11-11
H-l
H-13 The equiareal mapping in terms of ellipsoidal longitude, ellipsoidal latitude
H-2 The ellipsoidal Hammer projection
H-21 The equiareal mapping from a left biaxial ellipsoid to a right biaxial ellipsoid
H-22 The explicit form of the mapping equations generating an equiareal map
H-3 An integration formula
H-4 The transformation of the radial function r(A*.B") into
H-5 The inverse of a special univariate homogeneous polynomial
Contents
I Mercator projection and polycylindric projection
Optimal Mercator projection and optimal polycylindric projection of
1-1
1-2
J Gauss surface normal coordinates in geometry and gravity space
Three-dimensional geodesy, minimal distance mapping, geometric heights
J-l Protective heights in geometry space: from planar/spherical to ellipsoidal mapping
J-2 Gauss surface normal coordinates: case study ellipsoid-of-revolution
J-21 Review of surface normal coordinates for the elhpsoid-of-revolution
J-22 Buchberger algorithm of forming a constraint minimum distance mapping
J-3 Gauss surface normal coordinates: case study
J-31 Review of surface normal coordinates for the
J-32 Position, orientation, form parameters: case study Earth
J-33 Form parameters of a surface normal
Bibliography
Index |
| adam_txt |
Contents
Preface
1
Mapping from a left two-dimensional Riemann manifold to a right two-dimensional Riemann manifold
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
1-9
1-10
1-11 Areal
1-12
1-13
1-14
1-141
1-142
1-143
1-144
1-145
1-15
2
Mapping from a left two-dimensional Riemann manifold to a right two-dimensional Euclidean manifold
2-1 Eigenspace
2-2 Eigenspace
2-3
2-31
2-32
2-4
2-5
2-6
3
Coordinates (direct, transverse, oblique aspects)
3-1
3-2
XII
3-3
3-31
3-32
3-33
3-34
3-35
3-36
3-4
3-41
3-42
3-43
3-44
3-45
3-46
4
Classification of surfaces of Gaussian curvature zero in a two-dimensional Euclidean space
4-1
4-2
5
Mapping the sphere to a tangential plane: polar (normal) aspect
5-1
5-2
5-21
5-22
5-23
5-24
5-25
5-3
5-4
6
Mapping the sphere to a tangential plane: meta-azimuthal projections in the transverse aspect
6-1
(i-2 Special mapping equations
6-21
6-22
6-23
7
Mapping the sphere to a tangential plane: meta-azimuthal projections in the oblique aspect
7-1
7-2
7-21
7-22
7-23
Contents XIII
8 "Ellipsoid-of-revolution
Mapping the ellipsoid to a tangential plane (azimuthal projections in the normal aspect)
8-1
8-2
8-21
8-22
8-23
8-3
8-31
8-32
8-33
9
Mapping the ellipsoid to sphere and from sphere to plane (double projection, "authalic" projection)
9-1
9-11
9-12
9-13
9-14
9-15
9-16
9-17
9-2
9-3
10
Mapping the sphere to a cylinder: polar aspect
10-1
10-2
10-21
10-22
10-23
10-3
11
Mapping the sphere to a cylinder: meta-cylindrical projections in the transverse aspect
11-1
11-2
11-21
11-22
11-23
12
Mapping the sphere to a cylinder: meta-cylindrical projections in the oblique aspect
12-1
12-2
12-21
12-22
12-23
XIV Contents
13
Mapping the sphere to a cylinder: pseudo-cylindrical projections
13-1
13-2
13-21
13-22
13-23
13-24
14
Mapping the ellipsoid to a cylinder (polar aspect, generalization for rotational-symmetric surfaces)
14-1
14-2
14-21
14-22
14-23
14-24
14-3
14-31
14-32
14-33
14-34
15
Mapping the ellipsoid to a cylinder (transverse Mercator and Gauss-Krueger mappings)
15-1
15-2
15-3
15-4
15-5
15-6
15-61
15-62
16
Mapping the ellipsoid to a cylinder (oblique Mercator and rectified skew orthomorphic projections)
16-1
16-2
16-3
17
Mapping the sphere to a cone: polar aspect
17-1
17-2
17-21
17-22
17-23
Coiit ents
18
Mapping the sphere to a cone: pseudo-conic projections
18-1
18-2
18-21
18-22
19
Mapping the ellipsoid to a cone: polar aspect
19-1
19-2
19-21
19-22
19-23
20
Riemann,
20-1
20-2 Lagrange
20-21 Lagrange
20-22
20-3 Söldner
20-31
20-32
20-4
20-5
21
Analysis versus synthesis, Cartesian approach versus curvilinear approach
21-1
21-2
21-3
21-4
21-41
21-42
21-43
21-5
21-51
21-52
A Law and order
Relation preserving maps
A-l Law and order: Cartesian product, power sets
A-
В
Univariate, bivariate, and multivariate polynomials and their inversion formulae
B-l Inversion of a univariate homogeneous polynomial of degree n
B-2 Inversion of a bivariate homogeneous polynomial of degree n
B-3 Inversion of a multivariate homogeneous polynomial of degree n
XVI Contents
С
Elliptic kernel, elliptic modulus, elliptic functions, elliptic integrals
C-l Introductory example
C-2 Elliptic kernel, elliptic modulus, elliptic functions, elliptic integrals
D Korn-Lichtenstein and d'Alembert Euler equations
Conformai
D-l Korn Liechtenstein equations
D-2 D'Alembert Euler (Caucliy Riemann) equations
E
Geodetic curvature and geodetic torsion, the Newton form of a geodesic in Maupertuis gauge
E-l Geodetic curvature, geodetic torsion, and normal curvature
E-2 The differential equations of third order of a geodesic circle
E-3 The Newton form of a geodesic in Maupertuis gauge (sphere, ellipsoid-of-revolution)
E-31 The
E-32 The Maupertuis gauge and the Newton portrait of a geodesic
E-33 A geodesic as a submanifold of' the sphere
E-.'M A geodesic as a submanifold of the ellispoid-of-revohition
E-35 Maupertuis gauged geodesies (normal coordinates, local tangent plane)
E-36 Maupertuis gauged geodesies (Lie series, Hamilton portrait)
F
Mixed cylindric map projections of the ellipsoid-of-revolution, Lambert/Sanson-Flamsteed projections
F-
F-2 Mixed equiareal cylindric mapping: biaxial ellipsoid onto plane
F-3 Deformation analysis of vertically/horizontally averaged equiareal cylindric mappings
G
Generalized
G-l The pseudo-cylindrical mapping of the biaxial ellipsoid onto the plane
G-2 The generalized
G-3 Examples
H
Generalized Hammer projection of the ellipsoid-of-revolution: azimuthal, transverse, resolved equiareal
H-l The transverse equiareal projection of the biaxial ellipsoid
11-11
H-l
H-13 The equiareal mapping in terms of ellipsoidal longitude, ellipsoidal latitude
H-2 The ellipsoidal Hammer projection
H-21 The equiareal mapping from a left biaxial ellipsoid to a right biaxial ellipsoid
H-22 The explicit form of the mapping equations generating an equiareal map
H-3 An integration formula
H-4 The transformation of the radial function r(A*.B") into
H-5 The inverse of a special univariate homogeneous polynomial
Contents
I Mercator projection and polycylindric projection
Optimal Mercator projection and optimal polycylindric projection of
1-1
1-2
J Gauss surface normal coordinates in geometry and gravity space
Three-dimensional geodesy, minimal distance mapping, geometric heights
J-l Protective heights in geometry space: from planar/spherical to ellipsoidal mapping
J-2 Gauss surface normal coordinates: case study ellipsoid-of-revolution
J-21 Review of surface normal coordinates for the elhpsoid-of-revolution
J-22 Buchberger algorithm of forming a constraint minimum distance mapping
J-3 Gauss surface normal coordinates: case study
J-31 Review of surface normal coordinates for the
J-32 Position, orientation, form parameters: case study Earth
J-33 Form parameters of a surface normal
Bibliography
Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Grafarend, Erik W. 1939-2020 Krumm, Friedrich W. 1953- |
| author_GND | (DE-588)121959368 (DE-588)111918502 |
| author_facet | Grafarend, Erik W. 1939-2020 Krumm, Friedrich W. 1953- |
| author_role | aut aut |
| author_sort | Grafarend, Erik W. 1939-2020 |
| author_variant | e w g ew ewg f w k fw fwk |
| building | Verbundindex |
| bvnumber | BV021718363 |
| callnumber-first | G - Geography, Anthropology, Recreation |
| callnumber-label | GA110 |
| callnumber-raw | GA110 |
| callnumber-search | GA110 |
| callnumber-sort | GA 3110 |
| callnumber-subject | GA - Mathematical Geography and Cartography |
| classification_rvk | RB 10208 ZI 9710 RB 10104 |
| classification_tum | BAU 970f |
| ctrlnum | (OCoLC)73108858 (DE-599)BVBBV021718363 |
| dewey-full | 526/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 526 - Mathematical geography |
| dewey-raw | 526/.8 |
| dewey-search | 526/.8 |
| dewey-sort | 3526 18 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik Geologie / Paläontologie Bauingenieurwesen Vermessungswesen Geographie |
| discipline_str_mv | Physik Geologie / Paläontologie Bauingenieurwesen Vermessungswesen Geographie |
| format | Book |
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| id | DE-604.BV021718363 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:22:36Z |
| indexdate | 2024-07-20T09:07:25Z |
| institution | BVB |
| isbn | 9783540367017 3540367012 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014932067 |
| oclc_num | 73108858 |
| open_access_boolean | |
| owner | DE-384 DE-29 DE-355 DE-BY-UBR DE-706 DE-1028 DE-83 DE-11 DE-703 |
| owner_facet | DE-384 DE-29 DE-355 DE-BY-UBR DE-706 DE-1028 DE-83 DE-11 DE-703 |
| physical | XVII, 713 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| spelling | Grafarend, Erik W. 1939-2020 Verfasser (DE-588)121959368 aut Map Projections cartographic information systems Erik W. Grafarend ; Friedrich W. Krumm Berlin [u.a.] Springer 2006 XVII, 713 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Cartography Mathematics Conformal mapping Map projection Surfaces, Representation of Kartennetzentwurf (DE-588)4163370-2 gnd rswk-swf Kartennetzentwurf (DE-588)4163370-2 s DE-604 Krumm, Friedrich W. 1953- Verfasser (DE-588)111918502 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2841928&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014932067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grafarend, Erik W. 1939-2020 Krumm, Friedrich W. 1953- Map Projections cartographic information systems Mathematik Cartography Mathematics Conformal mapping Map projection Surfaces, Representation of Kartennetzentwurf (DE-588)4163370-2 gnd |
| subject_GND | (DE-588)4163370-2 |
| title | Map Projections cartographic information systems |
| title_auth | Map Projections cartographic information systems |
| title_exact_search | Map Projections cartographic information systems |
| title_exact_search_txtP | Map Projections cartographic information systems |
| title_full | Map Projections cartographic information systems Erik W. Grafarend ; Friedrich W. Krumm |
| title_fullStr | Map Projections cartographic information systems Erik W. Grafarend ; Friedrich W. Krumm |
| title_full_unstemmed | Map Projections cartographic information systems Erik W. Grafarend ; Friedrich W. Krumm |
| title_short | Map Projections |
| title_sort | map projections cartographic information systems |
| title_sub | cartographic information systems |
| topic | Mathematik Cartography Mathematics Conformal mapping Map projection Surfaces, Representation of Kartennetzentwurf (DE-588)4163370-2 gnd |
| topic_facet | Mathematik Cartography Mathematics Conformal mapping Map projection Surfaces, Representation of Kartennetzentwurf |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2841928&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014932067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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