Stereographic projection of WGS84 ellipsoid Unicorn Meta Zoo #1: Why another podcast? ...
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Stereographic projection of WGS84 ellipsoid
Unicorn Meta Zoo #1: Why another podcast?
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According to this source, an optimal projection for small, roughly square areas is the stereographic projection. The wikipedia page of the stereographic projection shows how to convert from spherical coordinates to polar or xy coordinates. However, I would like to convert WGS84 data (latitude and longitude) to xy coordinates and WGS84 uses an ellipsoidal model of Earth instead of a sphere.
My questions are:
1) What are the formulae for a stereographic projection on an ellipsoid centred at lat0,lon0 (point tangent to the plane) projected from the antipode of lat0,lon0?
2) Is this projection still conformal?
3) What is the inverse transformation?
I have read section 3.3.1.1 of the Geomatics Guidance Note 7, part 2 "Coordinate Conversions & Transformations including Formulas" (March 2019) and while I believe it may contain the answers to questions (1) and (3), I'm not sure what does it mean by "For the ellipsoid the parameters defining the conformal sphere at the tangent point as origin are first derived". Does it first compute the parameters for a sphere tangent to lat0,lon0? Then uses the antipode of lat0,lon0 in that sphere instead of the ellipsoid? If so, why does it do it that way? To preserve conformality? If this is true then would there be any advantage in projecting stereographically from the antipode on the ellipsoid instead of projecting from the antipode in the conformal sphere?
coordinate-system convert wgs84 ellipsoid stereographic
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RicardoRicardo
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According to this source, an optimal projection for small, roughly square areas is the stereographic projection. The wikipedia page of the stereographic projection shows how to convert from spherical coordinates to polar or xy coordinates. However, I would like to convert WGS84 data (latitude and longitude) to xy coordinates and WGS84 uses an ellipsoidal model of Earth instead of a sphere.
My questions are:
1) What are the formulae for a stereographic projection on an ellipsoid centred at lat0,lon0 (point tangent to the plane) projected from the antipode of lat0,lon0?
2) Is this projection still conformal?
3) What is the inverse transformation?
I have read section 3.3.1.1 of the Geomatics Guidance Note 7, part 2 "Coordinate Conversions & Transformations including Formulas" (March 2019) and while I believe it may contain the answers to questions (1) and (3), I'm not sure what does it mean by "For the ellipsoid the parameters defining the conformal sphere at the tangent point as origin are first derived". Does it first compute the parameters for a sphere tangent to lat0,lon0? Then uses the antipode of lat0,lon0 in that sphere instead of the ellipsoid? If so, why does it do it that way? To preserve conformality? If this is true then would there be any advantage in projecting stereographically from the antipode on the ellipsoid instead of projecting from the antipode in the conformal sphere?
coordinate-system convert wgs84 ellipsoid stereographic
asked 21 mins ago
RicardoRicardo
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
According to this source, an optimal projection for small, roughly square areas is the stereographic projection. The wikipedia page of the stereographic projection shows how to convert from spherical coordinates to polar or xy coordinates. However, I would like to convert WGS84 data (latitude and longitude) to xy coordinates and WGS84 uses an ellipsoidal model of Earth instead of a sphere.
My questions are:
1) What are the formulae for a stereographic projection on an ellipsoid centred at lat0,lon0 (point tangent to the plane) projected from the antipode of lat0,lon0?
2) Is this projection still conformal?
3) What is the inverse transformation?
I have read section 3.3.1.1 of the Geomatics Guidance Note 7, part 2 "Coordinate Conversions & Transformations including Formulas" (March 2019) and while I believe it may contain the answers to questions (1) and (3), I'm not sure what does it mean by "For the ellipsoid the parameters defining the conformal sphere at the tangent point as origin are first derived". Does it first compute the parameters for a sphere tangent to lat0,lon0? Then uses the antipode of lat0,lon0 in that sphere instead of the ellipsoid? If so, why does it do it that way? To preserve conformality? If this is true then would there be any advantage in projecting stereographically from the antipode on the ellipsoid instead of projecting from the antipode in the conformal sphere?
coordinate-system convert wgs84 ellipsoid stereographic
asked 21 mins ago
RicardoRicardo
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
According to this source, an optimal projection for small, roughly square areas is the stereographic projection. The wikipedia page of the stereographic projection shows how to convert from spherical coordinates to polar or xy coordinates. However, I would like to convert WGS84 data (latitude and longitude) to xy coordinates and WGS84 uses an ellipsoidal model of Earth instead of a sphere.
My questions are:
1) What are the formulae for a stereographic projection on an ellipsoid centred at lat0,lon0 (point tangent to the plane) projected from the antipode of lat0,lon0?
2) Is this projection still conformal?
3) What is the inverse transformation?
I have read section 3.3.1.1 of the Geomatics Guidance Note 7, part 2 "Coordinate Conversions & Transformations including Formulas" (March 2019) and while I believe it may contain the answers to questions (1) and (3), I'm not sure what does it mean by "For the ellipsoid the parameters defining the conformal sphere at the tangent point as origin are first derived". Does it first compute the parameters for a sphere tangent to lat0,lon0? Then uses the antipode of lat0,lon0 in that sphere instead of the ellipsoid? If so, why does it do it that way? To preserve conformality? If this is true then would there be any advantage in projecting stereographically from the antipode on the ellipsoid instead of projecting from the antipode in the conformal sphere?
coordinate-system convert wgs84 ellipsoid stereographic
coordinate-system convert wgs84 ellipsoid stereographic
asked 21 mins ago
RicardoRicardo
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 21 mins ago
RicardoRicardo
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 21 mins ago
RicardoRicardo
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 21 mins ago
RicardoRicardo
1
asked 21 mins ago
RicardoRicardo
1
1
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ricardo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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