What are the ranges of $x$ and $y$ in the Mercator projection?
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What are the ranges of $x$ and $y$ in the Mercator projection ?
I searched about it but I couldn't find anything.
Any ideas?
Thanks in advance
geometry mathematical-physics 3d projective-geometry projection
edited Aug 29 at 9:33
Pablo
33612
asked Aug 29 at 9:19
M Rezaei
14
add a comment |Â
up vote
0
down vote
favorite
What are the ranges of $x$ and $y$ in the Mercator projection ?
I searched about it but I couldn't find anything.
Any ideas?
Thanks in advance
geometry mathematical-physics 3d projective-geometry projection
edited Aug 29 at 9:33
Pablo
33612
asked Aug 29 at 9:19
M Rezaei
14
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What are the ranges of $x$ and $y$ in the Mercator projection ?
I searched about it but I couldn't find anything.
Any ideas?
Thanks in advance
geometry mathematical-physics 3d projective-geometry projection
edited Aug 29 at 9:33
Pablo
33612
asked Aug 29 at 9:19
M Rezaei
14
What are the ranges of $x$ and $y$ in the Mercator projection ?
I searched about it but I couldn't find anything.
Any ideas?
Thanks in advance
geometry mathematical-physics 3d projective-geometry projection
edited Aug 29 at 9:33
Pablo
33612
asked Aug 29 at 9:19
M Rezaei
14
edited Aug 29 at 9:33
Pablo
33612
edited Aug 29 at 9:33
Pablo
33612
edited Aug 29 at 9:33
Pablo
33612
33612
asked Aug 29 at 9:19
M Rezaei
14
asked Aug 29 at 9:19
M Rezaei
14
asked Aug 29 at 9:19
M Rezaei
14
14
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
As a mathematician, I'd say $mathbb R$ for both $x$ and $y$.
The Wikipedia article has many formulas describing this projection. A Mercator map is periodic in the East/West direction, reflecting the fact that you can circle the earth as many times by going East or West. That's what's behind the range $mathbb R$ for $x$. The range $mathbb R$ for $y$ is caused by the fact that the
North and South poles are not represented by a Mercator map, even though they are actual places on the Earth.
As a practical matter, one prints a bounded rectangular portion of a Mercator map to put in an atlas or to put on a wall map. Such a truncated map will not include some neighborhood of the N and S poles, but (because of the E/W periodicity) show the full extent of the Equator, etc. Often one sees (on American or European-made) Mercator maps two copies of the International Date Line; one can imagine maps printed in (say New Zeeland) as having two copies of the Greenwich meridian and one of the IDL.
Most software packages deliver an $x,y$ pair in the ranges $-pi/2 le x le pi/2$ (or $-180le xle180$) and $-infty<y<infty$. It is not clear to me from your comments how this matches up with what you want.
answered Aug 29 at 11:00
kimchi lover
8,86531128
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
As a mathematician, I'd say $mathbb R$ for both $x$ and $y$.
The Wikipedia article has many formulas describing this projection. A Mercator map is periodic in the East/West direction, reflecting the fact that you can circle the earth as many times by going East or West. That's what's behind the range $mathbb R$ for $x$. The range $mathbb R$ for $y$ is caused by the fact that the
North and South poles are not represented by a Mercator map, even though they are actual places on the Earth.
As a practical matter, one prints a bounded rectangular portion of a Mercator map to put in an atlas or to put on a wall map. Such a truncated map will not include some neighborhood of the N and S poles, but (because of the E/W periodicity) show the full extent of the Equator, etc. Often one sees (on American or European-made) Mercator maps two copies of the International Date Line; one can imagine maps printed in (say New Zeeland) as having two copies of the Greenwich meridian and one of the IDL.
Most software packages deliver an $x,y$ pair in the ranges $-pi/2 le x le pi/2$ (or $-180le xle180$) and $-infty<y<infty$. It is not clear to me from your comments how this matches up with what you want.
answered Aug 29 at 11:00
kimchi lover
8,86531128
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
add a comment |Â
up vote
1
down vote
As a mathematician, I'd say $mathbb R$ for both $x$ and $y$.
The Wikipedia article has many formulas describing this projection. A Mercator map is periodic in the East/West direction, reflecting the fact that you can circle the earth as many times by going East or West. That's what's behind the range $mathbb R$ for $x$. The range $mathbb R$ for $y$ is caused by the fact that the
North and South poles are not represented by a Mercator map, even though they are actual places on the Earth.
As a practical matter, one prints a bounded rectangular portion of a Mercator map to put in an atlas or to put on a wall map. Such a truncated map will not include some neighborhood of the N and S poles, but (because of the E/W periodicity) show the full extent of the Equator, etc. Often one sees (on American or European-made) Mercator maps two copies of the International Date Line; one can imagine maps printed in (say New Zeeland) as having two copies of the Greenwich meridian and one of the IDL.
Most software packages deliver an $x,y$ pair in the ranges $-pi/2 le x le pi/2$ (or $-180le xle180$) and $-infty<y<infty$. It is not clear to me from your comments how this matches up with what you want.
answered Aug 29 at 11:00
kimchi lover
8,86531128
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
add a comment |Â
up vote
1
down vote
up vote
1
down vote
As a mathematician, I'd say $mathbb R$ for both $x$ and $y$.
The Wikipedia article has many formulas describing this projection. A Mercator map is periodic in the East/West direction, reflecting the fact that you can circle the earth as many times by going East or West. That's what's behind the range $mathbb R$ for $x$. The range $mathbb R$ for $y$ is caused by the fact that the
North and South poles are not represented by a Mercator map, even though they are actual places on the Earth.
As a practical matter, one prints a bounded rectangular portion of a Mercator map to put in an atlas or to put on a wall map. Such a truncated map will not include some neighborhood of the N and S poles, but (because of the E/W periodicity) show the full extent of the Equator, etc. Often one sees (on American or European-made) Mercator maps two copies of the International Date Line; one can imagine maps printed in (say New Zeeland) as having two copies of the Greenwich meridian and one of the IDL.
Most software packages deliver an $x,y$ pair in the ranges $-pi/2 le x le pi/2$ (or $-180le xle180$) and $-infty<y<infty$. It is not clear to me from your comments how this matches up with what you want.
answered Aug 29 at 11:00
kimchi lover
8,86531128
As a mathematician, I'd say $mathbb R$ for both $x$ and $y$.
The Wikipedia article has many formulas describing this projection. A Mercator map is periodic in the East/West direction, reflecting the fact that you can circle the earth as many times by going East or West. That's what's behind the range $mathbb R$ for $x$. The range $mathbb R$ for $y$ is caused by the fact that the
North and South poles are not represented by a Mercator map, even though they are actual places on the Earth.
As a practical matter, one prints a bounded rectangular portion of a Mercator map to put in an atlas or to put on a wall map. Such a truncated map will not include some neighborhood of the N and S poles, but (because of the E/W periodicity) show the full extent of the Equator, etc. Often one sees (on American or European-made) Mercator maps two copies of the International Date Line; one can imagine maps printed in (say New Zeeland) as having two copies of the Greenwich meridian and one of the IDL.
Most software packages deliver an $x,y$ pair in the ranges $-pi/2 le x le pi/2$ (or $-180le xle180$) and $-infty<y<infty$. It is not clear to me from your comments how this matches up with what you want.
answered Aug 29 at 11:00
kimchi lover
8,86531128
edited Aug 31 at 6:47
answered Aug 29 at 11:00
kimchi lover
8,86531128
answered Aug 29 at 11:00
kimchi lover
8,86531128
answered Aug 29 at 11:00
kimchi lover
8,86531128
8,86531128
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
add a comment |Â
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Of course nobody in their right mind makes world maps in Mercator projection (nor have they ever done; the supposed prevalence of Mercator world maps is a myth that started as a marketing campaign for Gall-Peters maps).
– Henning Makholm
Aug 29 at 11:25
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Could be, but "nobody in their right mind" is a dense subset of humanity.
– kimchi lover
Aug 29 at 11:44
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Thank you but i don't want it for world map, I want it for my problem after that i want ti use a histogram so I need range of it.
– M Rezaei
Aug 30 at 2:06
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
Sorry: this wasn't clear to me from your problem statement.
– kimchi lover
Aug 30 at 22:28
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
I want to extract mercator projection for some points on the sphere then I want to show these with a 6 * 6 histogram that each bin shows number of points that mapped on that region
– M Rezaei
Aug 31 at 2:18
add a comment |Â
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