Visualizing a function on a sphere

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What is the best way to visualize a real function on a sphere as a mountain, using spherical coordinates?

I would like to plot ArcCos[Cos[longitude] * Cos[latitude]] on a sphere in a way that I can see the sphere and the function on it like a mountain above the sea.

So the sphere should have radius 10, show the poles and the equator, and I should be able to the see both the sphere and the function above it. What is the best way? Ideally, I would be able to rotate the result with my mouse ...

plotting

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edited 1 hour ago

Henrik Schumacher

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asked 2 hours ago

Clara

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up vote
1
down vote

favorite

What is the best way to visualize a real function on a sphere as a mountain, using spherical coordinates?

I would like to plot ArcCos[Cos[longitude] * Cos[latitude]] on a sphere in a way that I can see the sphere and the function on it like a mountain above the sea.

So the sphere should have radius 10, show the poles and the equator, and I should be able to the see both the sphere and the function above it. What is the best way? Ideally, I would be able to rotate the result with my mouse ...

plotting

share|improve this question

edited 1 hour ago

Henrik Schumacher

43.7k263129

asked 2 hours ago

Clara

61

New contributor

Clara 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 | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

What is the best way to visualize a real function on a sphere as a mountain, using spherical coordinates?

I would like to plot ArcCos[Cos[longitude] * Cos[latitude]] on a sphere in a way that I can see the sphere and the function on it like a mountain above the sea.

So the sphere should have radius 10, show the poles and the equator, and I should be able to the see both the sphere and the function above it. What is the best way? Ideally, I would be able to rotate the result with my mouse ...

plotting

share|improve this question

edited 1 hour ago

Henrik Schumacher

43.7k263129

asked 2 hours ago

Clara

61

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

What is the best way to visualize a real function on a sphere as a mountain, using spherical coordinates?

I would like to plot ArcCos[Cos[longitude] * Cos[latitude]] on a sphere in a way that I can see the sphere and the function on it like a mountain above the sea.

So the sphere should have radius 10, show the poles and the equator, and I should be able to the see both the sphere and the function above it. What is the best way? Ideally, I would be able to rotate the result with my mouse ...

plotting

plotting

share|improve this question

edited 1 hour ago

Henrik Schumacher

43.7k263129

asked 2 hours ago

Clara

61

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 1 hour ago

Henrik Schumacher

43.7k263129

asked 2 hours ago

Clara

61

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

share|improve this question

edited 1 hour ago

Henrik Schumacher

43.7k263129

edited 1 hour ago

Henrik Schumacher

43.7k263129

edited 1 hour ago

Henrik Schumacher

43.7k263129

43.7k263129

asked 2 hours ago

Clara

61

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Clara

61

asked 2 hours ago

Clara

61

61

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

New contributor

Clara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

Clara 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 | 

add a comment | 

2 Answers
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up vote
2
down vote

I suppose it could be like this. Change the "5" to change the scale of the sphere.

ParametricPlot3D[5 Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], 
Sin[[Theta]], (5 + 
 ArcCos[Cos[[Phi]] Cos[[Theta]]]) Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], Sin[[Theta]], [Phi], -Pi, 
Pi, [Theta], -Pi/2, Pi/2, PlotStyle -> Opacity[0.5], 

AxesLabel -> "x", "y", "z", ColorFunctionScaling -> False]

share|improve this answer

answered 1 hour ago

t-smart

1,003114

add a comment | 

up vote
1
down vote

Maybe this is waht you look for?

ParametricPlot3D[
 (10 + ArcCos[Cos[ϕ] Cos[θ]]) Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ],
 ϕ, -Pi, Pi, θ, -Pi/2, Pi/2,
 ColorFunction -> Function[x, y, z, ϕ, θ, ColorData["AlpineColors"][Sqrt[x^2 + y^2 + z^2] - 12]],
 AxesLabel -> "x", "y", "z",
 ColorFunctionScaling -> False
 ]

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

add a comment | 

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

I suppose it could be like this. Change the "5" to change the scale of the sphere.

ParametricPlot3D[5 Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], 
Sin[[Theta]], (5 + 
 ArcCos[Cos[[Phi]] Cos[[Theta]]]) Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], Sin[[Theta]], [Phi], -Pi, 
Pi, [Theta], -Pi/2, Pi/2, PlotStyle -> Opacity[0.5], 

AxesLabel -> "x", "y", "z", ColorFunctionScaling -> False]

share|improve this answer

answered 1 hour ago

t-smart

1,003114

add a comment | 

up vote
2
down vote

I suppose it could be like this. Change the "5" to change the scale of the sphere.

ParametricPlot3D[5 Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], 
Sin[[Theta]], (5 + 
 ArcCos[Cos[[Phi]] Cos[[Theta]]]) Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], Sin[[Theta]], [Phi], -Pi, 
Pi, [Theta], -Pi/2, Pi/2, PlotStyle -> Opacity[0.5], 

AxesLabel -> "x", "y", "z", ColorFunctionScaling -> False]

share|improve this answer

answered 1 hour ago

t-smart

1,003114

add a comment | 

up vote
2
down vote

up vote
2
down vote

I suppose it could be like this. Change the "5" to change the scale of the sphere.

ParametricPlot3D[5 Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], 
Sin[[Theta]], (5 + 
 ArcCos[Cos[[Phi]] Cos[[Theta]]]) Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], Sin[[Theta]], [Phi], -Pi, 
Pi, [Theta], -Pi/2, Pi/2, PlotStyle -> Opacity[0.5], 

AxesLabel -> "x", "y", "z", ColorFunctionScaling -> False]

share|improve this answer

answered 1 hour ago

t-smart

1,003114

I suppose it could be like this. Change the "5" to change the scale of the sphere.

ParametricPlot3D[5 Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], 
Sin[[Theta]], (5 + 
 ArcCos[Cos[[Phi]] Cos[[Theta]]]) Cos[[Phi]] Cos[[Theta]], 
Sin[[Phi]] Cos[[Theta]], Sin[[Theta]], [Phi], -Pi, 
Pi, [Theta], -Pi/2, Pi/2, PlotStyle -> Opacity[0.5], 

AxesLabel -> "x", "y", "z", ColorFunctionScaling -> False]

share|improve this answer

answered 1 hour ago

t-smart

1,003114

share|improve this answer

share|improve this answer

answered 1 hour ago

t-smart

1,003114

answered 1 hour ago

t-smart

1,003114

answered 1 hour ago

t-smart

1,003114

1,003114

add a comment | 

add a comment | 

up vote
1
down vote

Maybe this is waht you look for?

ParametricPlot3D[
 (10 + ArcCos[Cos[ϕ] Cos[θ]]) Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ],
 ϕ, -Pi, Pi, θ, -Pi/2, Pi/2,
 ColorFunction -> Function[x, y, z, ϕ, θ, ColorData["AlpineColors"][Sqrt[x^2 + y^2 + z^2] - 12]],
 AxesLabel -> "x", "y", "z",
 ColorFunctionScaling -> False
 ]

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

add a comment | 

up vote
1
down vote

Maybe this is waht you look for?

ParametricPlot3D[
 (10 + ArcCos[Cos[ϕ] Cos[θ]]) Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ],
 ϕ, -Pi, Pi, θ, -Pi/2, Pi/2,
 ColorFunction -> Function[x, y, z, ϕ, θ, ColorData["AlpineColors"][Sqrt[x^2 + y^2 + z^2] - 12]],
 AxesLabel -> "x", "y", "z",
 ColorFunctionScaling -> False
 ]

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

add a comment | 

up vote
1
down vote

up vote
1
down vote

Maybe this is waht you look for?

ParametricPlot3D[
 (10 + ArcCos[Cos[ϕ] Cos[θ]]) Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ],
 ϕ, -Pi, Pi, θ, -Pi/2, Pi/2,
 ColorFunction -> Function[x, y, z, ϕ, θ, ColorData["AlpineColors"][Sqrt[x^2 + y^2 + z^2] - 12]],
 AxesLabel -> "x", "y", "z",
 ColorFunctionScaling -> False
 ]

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

Maybe this is waht you look for?

ParametricPlot3D[
 (10 + ArcCos[Cos[ϕ] Cos[θ]]) Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ],
 ϕ, -Pi, Pi, θ, -Pi/2, Pi/2,
 ColorFunction -> Function[x, y, z, ϕ, θ, ColorData["AlpineColors"][Sqrt[x^2 + y^2 + z^2] - 12]],
 AxesLabel -> "x", "y", "z",
 ColorFunctionScaling -> False
 ]

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

share|improve this answer

share|improve this answer

answered 1 hour ago

Henrik Schumacher

43.7k263129

answered 1 hour ago

Henrik Schumacher

43.7k263129

answered 1 hour ago

Henrik Schumacher

43.7k263129

43.7k263129

add a comment | 

add a comment | 

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