# GeoVisibleRegionBoundary

GeoVisibleRegionBoundary[{lat,lon,h}]

is a one-dimensional GeoGraphics primitive that represents the boundary of the region on the surface of the Earth visible from the point of coordinates lat,lon and height h above the reference ellipsoid.

represents the boundary of the region visible from the position pos.

GeoVisibleRegionBoundary[{pos1,pos2,}]

represents the collection of boundaries of the regions visible from the positions posi.

# Details

• GeoVisibleRegionBoundary assumes an ellipsoidal shape for the Earth and does not take into account the terrain elevation. Corrections for atmospheric refraction are not included.
• The angles lat,lon in GeoVisibleRegionBoundary[{lat,lon,h}] can be given as numeric objects in degrees, DMS strings, or as Quantity angles.
• The height h in GeoVisibleRegionBoundary[{lat,lon,h}] can be given as a numeric amount of meters or as a Quantity length.

# Examples

open allclose all

## Basic Examples(3)

The visible region from an altitude of 10 km over the reference ellipsoid:

The visible region from geostationary orbit:

The region currently viewable from the International Space Station:

## Scope(4)

Visible region boundary from a {lat,lon,h} position:

Smaller heights correspond to smaller visible regions:

For vanishing height, the visible region collapses to a point and default padding is used:

Specify the coordinates as Quantity objects:

Specify latitude and longitude as DMS strings:

Specify the viewing position as any type of geodetic position:

Move vertically 1 kilometer from New York, assuming the city is on the reference ellipsoid:

Boundaries of the visible regions from a collection of different locations at different elevations:

## Applications(1)

Show the region boundary currently viewable from the International Space Station together with its orbital track:

## Properties & Relations(3)

GeoVisibleRegionBoundary corresponds to the boundary of a GeoVisibleRegion primitive:

Position and height of Willis Tower:

Show the region visible from the top of the building, assuming flat local terrain:

Horizon distance from elevation d, assuming a spherical Earth of radius :

Evaluate the formula for the height of Willis Tower:

Compare a GeoDisk of that radius with the result of GeoVisibleRegionBoundary:

Zoom around the east border of the geo disk:

## Interactive Examples(1)

Take an ellipsoid of semiaxes {a,b} and a point at distance r from its center and geocentric latitude α. Then the boundary of the visible region is parametrized as follows:

The viewing point is denoted in red and the visible region boundary in blue. It is a plane curve, orthogonal to the vector colored in blue:

## Neat Examples(1)

Define a list of various notable (tall) North American structures:

Form a list of properties for each building:

Show the visible region, assuming flat local terrain:

Wolfram Research (2014), GeoVisibleRegionBoundary, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html (updated 2021).

#### Text

Wolfram Research (2014), GeoVisibleRegionBoundary, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html (updated 2021).

#### CMS

Wolfram Language. 2014. "GeoVisibleRegionBoundary." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html.

#### APA

Wolfram Language. (2014). GeoVisibleRegionBoundary. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html

#### BibTeX

@misc{reference.wolfram_2022_geovisibleregionboundary, author="Wolfram Research", title="{GeoVisibleRegionBoundary}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html}", note=[Accessed: 02-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2022_geovisibleregionboundary, organization={Wolfram Research}, title={GeoVisibleRegionBoundary}, year={2021}, url={https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.html}, note=[Accessed: 02-August-2024 ]}