Skip to main content

geographics - Geography in 3D perspective


I would like to build a GeoGraphics map showing a z-elevated perspective (e.g. the view from a plane). Specifically, I'm looking to use multiple GeoMarker's (with custom graphics) in the pseudo-3D perspective.


For example, consider this plot of the Eiffel Tower:


enter image description here



I would like to reproduce it in a 3D perspective like this:


enter image description here


Both examples come from google maps, I’m not sure if this is possible in 11.3, but would love to know.



Answer



You could use an orthographic with a custom centering:


GeoGraphics[
Entity["Building", "EiffelTower::5h9w8"],
GeoProjection -> {"Orthographic", "Centering" -> GeoPosition[{-30.858`, 2.295`}]},
GeoZoomLevel -> 18,
GeoRange -> {{48.852`, 48.872`}, {2.2895`, 2.2995`}}

]


Note that this does incorporate the curvature of the earth and will be noticeable over larger areas.


If you're after something flat, you could always inset the tiles in 3D and pick custom View* values. Note I pad the range to allow the map to be seen at an angle:


im = GeoImage[
Entity["Building", "EiffelTower::5h9w8"],
"StreetMapNoLabels",
GeoZoomLevel -> 17,
GeoRange -> {{48.852`, 48.872`}, {2.285`, 2.305`}}

];

{x, y} = ImageDimensions[im];

Graphics3D[
{Texture[im], EdgeForm[], Polygon[{{0, 0, 0}, {x, 0, 0}, {x, y, 0}, {0, y, 0}},
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]},
Background -> Black,
Boxed -> False,
Lighting -> "Neutral",

ViewAngle -> 0.03233723833101999`,
ViewCenter -> {{0.5`, 0.5`, 0.5`}, {1.4456583184354543`, 0.7806170277104297`}},
ViewPoint -> {1.076788325190908`, -3.1635309749673284`, 0.5316001064285271`},
ViewVertical -> {0.00011882147473772082`, -0.00015290540260965785`, 0.9999999812506973`}
]

enter image description here




Here's a way to 'lift' a GeoGraphics object into 3D. My solution is probably not robust but works for simple cases:


GeoGraphics3D[args__] := Block[{g2d, g3d, ε = .0001},

g2d = GeoGraphics[args][[1, 1]] /. {___, Opacity[0], ___} -> {};
g3d = g2d /. {
expr : _[VertexTextureCoordinates, _] :> expr,
Inset[g_, {x_, y_}, opos_, Offset[o_]] :> Inset[g, RotationTransform[\[CurlyEpsilon], {0, -1, 0}]@{x, y, 0}, opos, .5 o],
{x_Real, y_} :> RotationTransform[\[CurlyEpsilon], {0, -1, 0}][{x, y, 0}]
};

Graphics3D[
g3d,
Boxed -> False,

ImageSize -> Large,
Lighting -> {{"Ambient", White}}
]
]

Example:


eif = Entity["Building", "EiffelTower::5h9w8"];

Show[
GeoGraphics3D[

{GeoMarker[eif], Text[Style["Eiffel Tower", ColorData[112, 1], 14], eif, {0, 1}]},
GeoRange -> Quantity[1000, "Meters"],
GeoZoomLevel -> 17
],
ViewAngle -> 2°,
ViewPoint -> {1.75`, -2.85`, 0.55`}
]

enter image description here


Comments

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...