# Tagged Questions

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

67k views

### Algorithm for offsetting a latitude/longitude by some amount of meters

I'm looking for an algorithm which when given a latitude and longitude pair and a vector translation in meters in Cartesian coordinates (x,y) would give me a new coordinate. Sort of like a reverse ...
14k views

### Why is the 'straight line' path across continent so curved?

This is the result of mapping the straight line path from a point in US to Poland using Distance Measurement Tool. Also, planes from Asia to US would travel almost over North Pole. Why is the path ...
4k views

### How accurate is approximating the Earth as a sphere?

What level of error do I encounter when approximating the earth as a sphere? Specifically, when dealing with the location of points and, for example, the great circle distances between them. Are ...
19k views

### Why is law of cosines more preferable than haversine when calculating distance between two latitude-longitude points?

In fact, when Sinnott published the haversine formula, computational precision was limited. Nowadays, JavaScript (and most modern computers & languages) use IEEE 754 64-bit ...
4k views

### How to calculate the intersection of 2 Circles?

I'm trying to figure out how to mathematically derive the common points of two intersecting circles on earth's surface given a center Lat/Lon and a radius for each point. Ex. Given: Lat/Lon ...
29k views

### Calculating Lat/Lng X miles from point

I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude. This appears to be the opposite of this question (Distance between lat/long ...
4k views

### Calculate distortion outside a UTM zone

One of my colleagues is working with data that is spread across two UTM zone. The majority of the data is in one zone, with a few outliers in another zone. He would like to know what the area ...
6k views

### Lon/lat transformation

First I should clarify I don't have previous experience with the field, so I don't know the technical terminology. My question is as follows: I have two weather datasets: The first one has the ...
3k views

### What is the approximate error of the Pythagorean Theorem vs. Haversine Formula in measuring distances on a sphere at various scales?

Many people when first trying to calculate distances between two longitude / latitude pairs ask if Pythagorean theorem works as an appropriate distance function. Most often people answer "no, the ...
5k views

### Algorithm to find nearest point

I've a list of a few hundred cities with their latitude/longitude. Given another location (also in lat/long) I need to find the nearest city. As I don't use any GIS, by now the obvious algorithm is ...
1k views

### Calculating visible sky percentage?

Can anyone explain, as simply as possible, how to calculate the visible sky percentage? I have done a satellite survey and have worked out the height of buildings and the distance between them. ...
1k views

### Finding most remote spot in Eastern United States?

I have this hunch that I could travel no more than 50 miles from the most remote spot in the Eastern United States (east of the Mississippi River), in the direction of the nearest road, and find a ...
1k views

### Great-circle lines in Equirectangular projection

Just to check that I'm on the right track: Are all great-circles on the sphere and in equirectangular projection (i.e. latitude, longitude pairs) either: meridians (i.e. going pole to pole) of the ...
880 views

### How to visualize azimuthal data with uncertainties?

I am trying to make a figure showing azimuthal data with a different range of uncertainties at each point. This oldschool figure from a 1991 paper captures the "bowtie plot" idea that I'm aiming for: ...
208 views

### Point sampling along a pole-wrapping coastline with PostGIS

I am working on a task that requires me to get sample points every 1000 km along coastlines, and have run into a problem with Antarctica. From what I can tell, it seems to be an issue with the use of ...
237 views

### Mercator bias plot in Leaflet

I was inspired by this wikipedia image from the mercator projections page to hack around with leaflet. The idea was to interactively have your cursor move a continent and that it would be corrected ...
9k views

### How to convert Distance, Azimuth, Dip to XYZ?

I have an excel spreadsheet with header and survey drill data. Header data contains hole ID, and location coordinates, and the survey data contains related downhole survey with Distance, Azimuth and ...
3k views

### Calculating a spherical polygon centroid

I'd like a general way to calculate centroids for polygons on a sphere. So far, the best online reference appears to be: Tools for Graphics and Shapes by Jeff Jenness. The method described ...
1k views

### Given a line on the earth's surface, how do I plot a line perpendicular to it?

Given a line on the earth's surface, how do I plot a line perpendicular to it? Apologies if this is a very simple question. I thought this would be a straightforward task, but it is proving ...
2k views

### Nearest point on a line ( Spherical / Mercator projection )

I have a line (Ax,Ay - Bx,By) over a mercator projection (google maps) and a random point (Cx,Cy) nearest to that line, i would to know the closest point (transparent blue on the image) over that line ...
4k views

### How to find a point half way between two other points?

I'm working on implementing the OSM Mobile Binary format for map data, and because it uses a 16 bit delta for each point along a way, it cannot represent a way if there is a large distance between two ...
11k views

### Calculate midpoint from a series of latitude and longitude coordinates

I've got a series of longitude and latitude coordinates which represent a building outline e.g. -0.5485381346101759,53.2285150736142 -0.5482220594232723,53.22842450827133 ...
479 views

### Method to generate points in any projection

I am writing an application in ArcMap to generate a grid of points. These points have a very defined layout and I have worked out an algorithm that works great under a projected coordinate system. ...
873 views

### How does one calculate an angle in a geographic coordinate system?

Given three points on a line in a geographic coordinate system, how does one calculate the angle formed by these three points? Please, give a general solution but also include system specific ...
522 views

### How do different GIS systems determine a Polygon's interior?

I'm interested in understanding how real-world GIS systems and their data encode Polygons. Specifically, how do they resolve the ambiguity of a Polygon's interior on a sphere? Background: in 2D, ...
125 views

### Compute visibility graph on sphere

I have a PostGIS table with some polygons (stored using the geography data type). They represent regions on a spherical earth. For each pair of vertices chosen from among all the polygons, I want to ...
354 views

### How do I represent the whole Earth as a Polygon?

This is related to determining the interior of a Polygon. My difficulty is that if I specify a Polygon covering the Earth going from East to West, it will still have a boundary along the ...
2k views

### Find tangent point on circle furthest east or west

There are few ways of articulating my question. It starts with a known circle on a sphere, i.e. a point-radius, and one that does not cover a pole. I would like to calculate the point furthest west ...
2k views

### Find Perpendicular Distance and Minimum Perpendicular Vector between a Point and a Line using GeoTools and JTS

I have a line formed by 2 lat/lon pairs, and the lat/lon of a point. I would like to find out the perpendicular distance between the line and the point on the Earth surface (can assume Earth as great ...
214 views

### Project location on a (great circle) path

I've been searching this SE site for quite a few hours now, and I'm still struggling to find a solution to my question. My goal is that given a way in OSM and my location (lat/lon coordinates), I want ...
573 views

### how to find the point in a country furthest from a boundary

i'm trying to find the point in south africa furthest from the sea or a landward boundary. my method thus far: i obtained a first guess at the centre of the inscribed circle and the three segments ...
2k views

### How to calculate area of 1 x 1 degree cells in a raster

I have a simple array (not geo-referenced in any way) in Matlab (which is not a language I know a huge amount about...so I can export it to other languages if needed) which has the dimensions 180 x ...
4k views

### Converting Longitude and Latitude Coordinates to Square Miles?

I have a set of Long and Lat co-ordinates making up a five point polygon which I have converted in excel using the following formula: ...
963 views

### Quick way to determine if facing a given lat/lon pair with a heading

I'm looking for a fast way, preferably without trigonometric operations (just multiply, divide, add, sqrt and subtract) to determine if a point is visible. E.g. say I am facing 0 degrees N, I am at ...
184 views

### Distortion of equally sized world tiles

My question is related to this: http://stackoverflow.com/questions/7927863/location-data-format-for-adehabitat-package I have a relational database with 'world tiles'. Each tile has a side length of ...
222 views

### What is a delta in lat/lon called?

What is the delta between two lat/lon pairs called? Delta degrees? Arcs? Is it some quantity of distance but what is its unit of measurement? And related: Can we use pythagoras to calculate this ...
1k views

### Identify the latitudinal and longitudinal point directly beneath an object in space

Given the azimuth and altitude / latitude and longitude from the observer to the satellite, how can I accurately find the latitude and longitude of the point of intersection directly under the ...
347 views

### Does the Chamberlin trimetric projection map (some) great circles to straight lines?

I know that, in general, the Chamberlin trimetric projection maps most great circles on the sphere to some sort of non-straight curve on the flat map. But what about the 3 special great circles ...
1k views

### How to do stereographic projection conversion (w.r.t. changing point of projection)?

Given a stereographic point P1 projected from point P, and given another point Q, I would like to know how to transform P1's coordinates to that of a stereographic point Q1 projected from point Q. ...
351 views

### Intermediate points on a small circle

I need to interpolate lat/lon points along a small circle, with a given centre and radius. I've successfully used these formulas for great circles. What is the equivalent for small circles?
2k views

### How do I find the intersections of 2 circles on earths surface?

I have the circles' center in lat & long, as well as the radius in meters. How do I find the circles intersections? Edit: EXAMPLE: Circle 1: Center on Earth's surface (43.564627,-116.220524) ...
6k views

### Lat/Lon/Alt to spherical or cartesian coordinates

On my previous question, it was advised I convert lat/lon/altitude to spherical or Cartesian coordinates. I'm not working near the poles and it would be safe to assume a spherical earth. What would be ...
79 views

### What information is needed to determine the section of the earth's surface visible in a photograph?

What information (either provided by a user or taken from sensor readings) would be required to determine the geographic area encompassed by a photograph? It seems like the area visible from a ...
433 views

### Dividing a geographic region

I have a certain geographic region defined by the bottom left and top right coordinates. How can I divide this region into areas of 20x20km. I mean in practial the shape of the earth is not flat it's ...
85 views

### Is there any online viewer which displays the polygons assuming great circle lines for the edges?

My question is similar to this one: Are there any online WKT editors? The links given in answers have been very useful to me. However, it seems that when the tools in question display maps, they ...
1k views

### Line intersection with circle on a sphere (globe or earth)

How can I find the intersection point of a line and a circle on a sphere (on earth) Please, if any one knows a good solution help. Thanks in response :)
1k views

### Bearing/Course/Heading in WGS84 ellipsoid model

There is a common formula for computing the initial bearing for a course from lat1, lon1 to lat2, lon2. (And yes, I'm aware that the course will change when traveling). atan2( sin(lon2-lon1) * ...
2k views

### ST_Distance versus ST_Distance_Spheroid?

As my client software uses lat/lon coordinates when communicating with my (spherical mercator) postgis database i decided to ST_Transform every geometry to WGS-84. However i noticed that ST_Distance ...