Latitude longitude mapping with image of my house - image

I have top view image of my house and know lat longitude for left top pixel i.e 0,0 now how to get latitude longitude values of other pixels?
While googling i came across following:
function longToX(longitudeDegrees)
{
var longitude =degreesToRadians(longitudeDegrees);
return (radius * longitude);
}
function latToY(latitudeDegrees)
{
var latitude =degreesToRadians(latitudeDegrees);
var newy = radius/2.0 *
Math.log( (1.0 + Math.sin(latitude)) /
(1.0 - Math.sin(latitude)) );
return newy;
}
function xToLong(xx)
{
var longRadians = xx/radius;
var longDegrees = radiansToDegrees(longRadians);
/* The user could have panned around the world a lot of times.
Lat long goes from -180 to 180. So every time a user gets
to 181 we want to subtract 360 degrees. Every time a user
gets to -181 we want to add 360 degrees. */
var rotations = Math.floor((longDegrees + 180)/360)
var longitude = longDegrees - (rotations * 360)
return longitude;
}
function yToLat(yo)
{
var latitude = (Math.PI/2) -
(2 * Math.atan(
Math.exp(-1.0 * yo / radius)));
return radiansToDegrees(latitude);
}
radius = 6371 km radius of earth..
but however if i pass 0,0 i get 0,0 how to fix latitude longitude for 0,0 and derive from it other values

You need to know the distance between pixels. To convert distance to degrees, you can use the fact that one nautical minute (1/60 of a degree) latitude is 1,852 meters or about 6076 feet. The longitude is the same at the equator, but you need to multiply by the cosine of the latitude elsewhere.
One degree latitude = 1852 meters
One degree longitude = 1852 meters * cos(latitude)
(You might need to multiply the degrees latitude by pi/180 to convert them to radians for the cosine function.)

Related

How do I find things that are nearby to me? [duplicate]

Does the new firestore database from firebase natively support location based geo queries? i.e. Find posts within 10 miles, or find the 50 nearest posts?
I see that there are some existing projects for the real-time firebase database, projects such as geofire- could those be adapted to firestore as well?
UPDATE: Firestore does not support actual GeoPoint queries at present so while the below query executes successfully, it only filters by latitude, not by longitude and thus will return many results that are not nearby. The best solution would be to use geohashes. To learn how to do something similar yourself, have a look at this video.
This can be done by creating a bounding box less than greater than query. As for the efficiency, I can't speak to it.
Note, the accuracy of the lat/long offset for ~1 mile should be reviewed, but here is a quick way to do this:
SWIFT 3.0 Version
func getDocumentNearBy(latitude: Double, longitude: Double, distance: Double) {
// ~1 mile of lat and lon in degrees
let lat = 0.0144927536231884
let lon = 0.0181818181818182
let lowerLat = latitude - (lat * distance)
let lowerLon = longitude - (lon * distance)
let greaterLat = latitude + (lat * distance)
let greaterLon = longitude + (lon * distance)
let lesserGeopoint = GeoPoint(latitude: lowerLat, longitude: lowerLon)
let greaterGeopoint = GeoPoint(latitude: greaterLat, longitude: greaterLon)
let docRef = Firestore.firestore().collection("locations")
let query = docRef.whereField("location", isGreaterThan: lesserGeopoint).whereField("location", isLessThan: greaterGeopoint)
query.getDocuments { snapshot, error in
if let error = error {
print("Error getting documents: \(error)")
} else {
for document in snapshot!.documents {
print("\(document.documentID) => \(document.data())")
}
}
}
}
func run() {
// Get all locations within 10 miles of Google Headquarters
getDocumentNearBy(latitude: 37.422000, longitude: -122.084057, distance: 10)
}
UPDATE: Firestore does not support actual GeoPoint queries at present so while the below query executes successfully, it only filters by latitude, not by longitude and thus will return many results that are not nearby. The best solution would be to use geohashes. To learn how to do something similar yourself, have a look at this video.
(First let me apologize for all the code in this post, I just wanted anyone reading this answer to have an easy time reproducing the functionality.)
To address the same concern the OP had, at first I adapted the GeoFire library to work with Firestore (you can learn a lot about geo-stuff by looking at that library). Then I realized I didn't really mind if locations were returned in an exact circle. I just wanted some way to get 'nearby' locations.
I can't believe how long it took me to realize this, but you can just perform a double inequality query on a GeoPoint field using a SW corner and NE corner to get locations within a bounding box around a center point.
So I made a JavaScript function like the one below (this is basically a JS version of Ryan Lee's answer).
/**
* Get locations within a bounding box defined by a center point and distance from from the center point to the side of the box;
*
* #param {Object} area an object that represents the bounding box
* around a point in which locations should be retrieved
* #param {Object} area.center an object containing the latitude and
* longitude of the center point of the bounding box
* #param {number} area.center.latitude the latitude of the center point
* #param {number} area.center.longitude the longitude of the center point
* #param {number} area.radius (in kilometers) the radius of a circle
* that is inscribed in the bounding box;
* This could also be described as half of the bounding box's side length.
* #return {Promise} a Promise that fulfills with an array of all the
* retrieved locations
*/
function getLocations(area) {
// calculate the SW and NE corners of the bounding box to query for
const box = utils.boundingBoxCoordinates(area.center, area.radius);
// construct the GeoPoints
const lesserGeopoint = new GeoPoint(box.swCorner.latitude, box.swCorner.longitude);
const greaterGeopoint = new GeoPoint(box.neCorner.latitude, box.neCorner.longitude);
// construct the Firestore query
let query = firebase.firestore().collection('myCollection').where('location', '>', lesserGeopoint).where('location', '<', greaterGeopoint);
// return a Promise that fulfills with the locations
return query.get()
.then((snapshot) => {
const allLocs = []; // used to hold all the loc data
snapshot.forEach((loc) => {
// get the data
const data = loc.data();
// calculate a distance from the center
data.distanceFromCenter = utils.distance(area.center, data.location);
// add to the array
allLocs.push(data);
});
return allLocs;
})
.catch((err) => {
return new Error('Error while retrieving events');
});
}
The function above also adds a .distanceFromCenter property to each piece of location data that's returned so that you could get the circle-like behavior by just checking if that distance is within the range you want.
I use two util functions in the function above so here's the code for those as well. (All of the util functions below are actually adapted from the GeoFire library.)
distance():
/**
* Calculates the distance, in kilometers, between two locations, via the
* Haversine formula. Note that this is approximate due to the fact that
* the Earth's radius varies between 6356.752 km and 6378.137 km.
*
* #param {Object} location1 The first location given as .latitude and .longitude
* #param {Object} location2 The second location given as .latitude and .longitude
* #return {number} The distance, in kilometers, between the inputted locations.
*/
distance(location1, location2) {
const radius = 6371; // Earth's radius in kilometers
const latDelta = degreesToRadians(location2.latitude - location1.latitude);
const lonDelta = degreesToRadians(location2.longitude - location1.longitude);
const a = (Math.sin(latDelta / 2) * Math.sin(latDelta / 2)) +
(Math.cos(degreesToRadians(location1.latitude)) * Math.cos(degreesToRadians(location2.latitude)) *
Math.sin(lonDelta / 2) * Math.sin(lonDelta / 2));
const c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
return radius * c;
}
boundingBoxCoordinates(): (There are more utils used in here as well that I've pasted below.)
/**
* Calculates the SW and NE corners of a bounding box around a center point for a given radius;
*
* #param {Object} center The center given as .latitude and .longitude
* #param {number} radius The radius of the box (in kilometers)
* #return {Object} The SW and NE corners given as .swCorner and .neCorner
*/
boundingBoxCoordinates(center, radius) {
const KM_PER_DEGREE_LATITUDE = 110.574;
const latDegrees = radius / KM_PER_DEGREE_LATITUDE;
const latitudeNorth = Math.min(90, center.latitude + latDegrees);
const latitudeSouth = Math.max(-90, center.latitude - latDegrees);
// calculate longitude based on current latitude
const longDegsNorth = metersToLongitudeDegrees(radius, latitudeNorth);
const longDegsSouth = metersToLongitudeDegrees(radius, latitudeSouth);
const longDegs = Math.max(longDegsNorth, longDegsSouth);
return {
swCorner: { // bottom-left (SW corner)
latitude: latitudeSouth,
longitude: wrapLongitude(center.longitude - longDegs),
},
neCorner: { // top-right (NE corner)
latitude: latitudeNorth,
longitude: wrapLongitude(center.longitude + longDegs),
},
};
}
metersToLongitudeDegrees():
/**
* Calculates the number of degrees a given distance is at a given latitude.
*
* #param {number} distance The distance to convert.
* #param {number} latitude The latitude at which to calculate.
* #return {number} The number of degrees the distance corresponds to.
*/
function metersToLongitudeDegrees(distance, latitude) {
const EARTH_EQ_RADIUS = 6378137.0;
// this is a super, fancy magic number that the GeoFire lib can explain (maybe)
const E2 = 0.00669447819799;
const EPSILON = 1e-12;
const radians = degreesToRadians(latitude);
const num = Math.cos(radians) * EARTH_EQ_RADIUS * Math.PI / 180;
const denom = 1 / Math.sqrt(1 - E2 * Math.sin(radians) * Math.sin(radians));
const deltaDeg = num * denom;
if (deltaDeg < EPSILON) {
return distance > 0 ? 360 : 0;
}
// else
return Math.min(360, distance / deltaDeg);
}
wrapLongitude():
/**
* Wraps the longitude to [-180,180].
*
* #param {number} longitude The longitude to wrap.
* #return {number} longitude The resulting longitude.
*/
function wrapLongitude(longitude) {
if (longitude <= 180 && longitude >= -180) {
return longitude;
}
const adjusted = longitude + 180;
if (adjusted > 0) {
return (adjusted % 360) - 180;
}
// else
return 180 - (-adjusted % 360);
}
A new project has been introduced since #monkeybonkey first ask this question. The project is called GEOFirestore.
With this library you can perform queries like query documents within a circle:
const geoQuery = geoFirestore.query({
center: new firebase.firestore.GeoPoint(10.38, 2.41),
radius: 10.5
});
You can install GeoFirestore via npm. You will have to install Firebase separately (because it is a peer dependency to GeoFirestore):
$ npm install geofirestore firebase --save
As of today, there is no way to do such a query. There are other questions in SO related to it:
Is there a way to use GeoFire with Firestore?
How to query closest GeoPoints in a collection in Firebase Cloud Firestore?
Is there a way to use GeoFire with Firestore?
In my current Android project I may use https://github.com/drfonfon/android-geohash to add a geohash field while Firebase team is developing native support.
Using Firebase Realtime Database like suggested in other questions means that you can't filter your results set by location and other fields simultaneously, the main reason I want to switch to Firestore in the first place.
As of late 2020 there is now also documentation of how to do geoqueries with Firestore.
These solutions for iOS, Android, and Web, build on top of a slimmed down version of the Firebase-created GeoFire libraries, and then show how to:
Generate geohash values and store them in Firestore
Determine geohash ranges of the bounding box for a certain point and radius
Perform queries across these geohash ranges
This a bit more low-level than most of the other libraries presented here, so it may be a better fit for some use-cases and a worse fit for others.
Hijacking this thread to hopefully help anyone still looking. Firestore still does not support geo-based queries, and using the GeoFirestore library isnt ideal either as it will only let you search by location, nothing else.
I've put this together:
https://github.com/mbramwell1/GeoFire-Android
It basically lets you do nearby searches using a location and distance:
QueryLocation queryLocation = QueryLocation.fromDegrees(latitude, longitude);
Distance searchDistance = new Distance(1.0, DistanceUnit.KILOMETERS);
geoFire.query()
.whereNearTo(queryLocation, distance)
.build()
.get();
There are more docs on the repo. Its working for me so give it a try, hopefully it will do what you need.
For Dart
///
/// Checks if these coordinates are valid geo coordinates.
/// [latitude] The latitude must be in the range [-90, 90]
/// [longitude] The longitude must be in the range [-180, 180]
/// returns [true] if these are valid geo coordinates
///
bool coordinatesValid(double latitude, double longitude) {
return (latitude >= -90 && latitude <= 90 && longitude >= -180 && longitude <= 180);
}
///
/// Checks if the coordinates of a GeopPoint are valid geo coordinates.
/// [latitude] The latitude must be in the range [-90, 90]
/// [longitude] The longitude must be in the range [-180, 180]
/// returns [true] if these are valid geo coordinates
///
bool geoPointValid(GeoPoint point) {
return (point.latitude >= -90 &&
point.latitude <= 90 &&
point.longitude >= -180 &&
point.longitude <= 180);
}
///
/// Wraps the longitude to [-180,180].
///
/// [longitude] The longitude to wrap.
/// returns The resulting longitude.
///
double wrapLongitude(double longitude) {
if (longitude <= 180 && longitude >= -180) {
return longitude;
}
final adjusted = longitude + 180;
if (adjusted > 0) {
return (adjusted % 360) - 180;
}
// else
return 180 - (-adjusted % 360);
}
double degreesToRadians(double degrees) {
return (degrees * math.pi) / 180;
}
///
///Calculates the number of degrees a given distance is at a given latitude.
/// [distance] The distance to convert.
/// [latitude] The latitude at which to calculate.
/// returns the number of degrees the distance corresponds to.
double kilometersToLongitudeDegrees(double distance, double latitude) {
const EARTH_EQ_RADIUS = 6378137.0;
// this is a super, fancy magic number that the GeoFire lib can explain (maybe)
const E2 = 0.00669447819799;
const EPSILON = 1e-12;
final radians = degreesToRadians(latitude);
final numerator = math.cos(radians) * EARTH_EQ_RADIUS * math.pi / 180;
final denom = 1 / math.sqrt(1 - E2 * math.sin(radians) * math.sin(radians));
final deltaDeg = numerator * denom;
if (deltaDeg < EPSILON) {
return distance > 0 ? 360.0 : 0.0;
}
// else
return math.min(360.0, distance / deltaDeg);
}
///
/// Defines the boundingbox for the query based
/// on its south-west and north-east corners
class GeoBoundingBox {
final GeoPoint swCorner;
final GeoPoint neCorner;
GeoBoundingBox({this.swCorner, this.neCorner});
}
///
/// Defines the search area by a circle [center] / [radiusInKilometers]
/// Based on the limitations of FireStore we can only search in rectangles
/// which means that from this definition a final search square is calculated
/// that contains the circle
class Area {
final GeoPoint center;
final double radiusInKilometers;
Area(this.center, this.radiusInKilometers):
assert(geoPointValid(center)), assert(radiusInKilometers >= 0);
factory Area.inMeters(GeoPoint gp, int radiusInMeters) {
return new Area(gp, radiusInMeters / 1000.0);
}
factory Area.inMiles(GeoPoint gp, int radiusMiles) {
return new Area(gp, radiusMiles * 1.60934);
}
/// returns the distance in km of [point] to center
double distanceToCenter(GeoPoint point) {
return distanceInKilometers(center, point);
}
}
///
///Calculates the SW and NE corners of a bounding box around a center point for a given radius;
/// [area] with the center given as .latitude and .longitude
/// and the radius of the box (in kilometers)
GeoBoundingBox boundingBoxCoordinates(Area area) {
const KM_PER_DEGREE_LATITUDE = 110.574;
final latDegrees = area.radiusInKilometers / KM_PER_DEGREE_LATITUDE;
final latitudeNorth = math.min(90.0, area.center.latitude + latDegrees);
final latitudeSouth = math.max(-90.0, area.center.latitude - latDegrees);
// calculate longitude based on current latitude
final longDegsNorth = kilometersToLongitudeDegrees(area.radiusInKilometers, latitudeNorth);
final longDegsSouth = kilometersToLongitudeDegrees(area.radiusInKilometers, latitudeSouth);
final longDegs = math.max(longDegsNorth, longDegsSouth);
return new GeoBoundingBox(
swCorner: new GeoPoint(latitudeSouth, wrapLongitude(area.center.longitude - longDegs)),
neCorner: new GeoPoint(latitudeNorth, wrapLongitude(area.center.longitude + longDegs)));
}
///
/// Calculates the distance, in kilometers, between two locations, via the
/// Haversine formula. Note that this is approximate due to the fact that
/// the Earth's radius varies between 6356.752 km and 6378.137 km.
/// [location1] The first location given
/// [location2] The second location given
/// sreturn the distance, in kilometers, between the two locations.
///
double distanceInKilometers(GeoPoint location1, GeoPoint location2) {
const radius = 6371; // Earth's radius in kilometers
final latDelta = degreesToRadians(location2.latitude - location1.latitude);
final lonDelta = degreesToRadians(location2.longitude - location1.longitude);
final a = (math.sin(latDelta / 2) * math.sin(latDelta / 2)) +
(math.cos(degreesToRadians(location1.latitude)) *
math.cos(degreesToRadians(location2.latitude)) *
math.sin(lonDelta / 2) *
math.sin(lonDelta / 2));
final c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a));
return radius * c;
}
I just published a Flutter package based on the JS code above
https://pub.dartlang.org/packages/firestore_helpers
Yes, this is an old topic, but I want to help only on Java code. How I solved a problem with longitude? I used a code from Ryan Lee and Michael Teper.
A code:
#Override
public void getUsersForTwentyMiles() {
FirebaseFirestore db = FirebaseFirestore.getInstance();
double latitude = 33.0076665;
double longitude = 35.1011336;
int distance = 20; //20 milles
GeoPoint lg = new GeoPoint(latitude, longitude);
// ~1 mile of lat and lon in degrees
double lat = 0.0144927536231884;
double lon = 0.0181818181818182;
final double lowerLat = latitude - (lat * distance);
final double lowerLon = longitude - (lon * distance);
double greaterLat = latitude + (lat * distance);
final double greaterLon = longitude + (lon * distance);
final GeoPoint lesserGeopoint = new GeoPoint(lowerLat, lowerLon);
final GeoPoint greaterGeopoint = new GeoPoint(greaterLat, greaterLon);
Log.d(LOG_TAG, "local general lovation " + lg);
Log.d(LOG_TAG, "local lesserGeopoint " + lesserGeopoint);
Log.d(LOG_TAG, "local greaterGeopoint " + greaterGeopoint);
//get users for twenty miles by only a latitude
db.collection("users")
.whereGreaterThan("location", lesserGeopoint)
.whereLessThan("location", greaterGeopoint)
.get()
.addOnCompleteListener(new OnCompleteListener<QuerySnapshot>() {
#Override
public void onComplete(#NonNull Task<QuerySnapshot> task) {
if (task.isSuccessful()) {
for (QueryDocumentSnapshot document : task.getResult()) {
UserData user = document.toObject(UserData.class);
//here a longitude condition (myLocation - 20 <= myLocation <= myLocation +20)
if (lowerLon <= user.getUserGeoPoint().getLongitude() && user.getUserGeoPoint().getLongitude() <= greaterLon) {
Log.d(LOG_TAG, "location: " + document.getId());
}
}
} else {
Log.d(LOG_TAG, "Error getting documents: ", task.getException());
}
}
});
}
Just inside after issuing the result set the filter to longitude:
if (lowerLon <= user.getUserGeoPoint().getLongitude() && user.getUserGeoPoint().getLongitude() <= greaterLon) {
Log.d(LOG_TAG, "location: " + document.getId());
}
I hope this will help someone.
Have a nice day!
You should use GeoFire (works with Firestore). With this you can filter documents on server and read less documents from your Firestore db. This will reduce your read count as well.
Check this lib for GroFire: https://github.com/patpatchpatrick/GeoFirestore-iOS
"patpatchpatrick" made this to Swift 5 compatible.
Just do a pod install as follows:
pod 'Geofirestore', :git => 'https://github.com/patpatchpatrick/GeoFirestore-iOS'
I am using this library in one of my projects and it works fine.
To set a location:
let location: CLLocation = CLLocation(latitude: lat, longitude: lng)
yourCollection.setLocation(location: location, forDocumentWithID: "YourDocId") { (error) in }
To remove location:
collection.removeLocation(forDocumentWithID: "YourDocId")
To get docs:
let center = CLLocation(latitude: lat, longitude: lng)
let collection = "Your collection path"
let circleQuery = collection.query(withCenter: center, radius: Double(yourRadiusVal))
let _ = circleQuery.observe(.documentEntered, with: { (key, location) in
//Use info as per your need
})
I have used .documentEntered, you can use other available geo queries like (Document Exited, Document Moved) as per your need.
You can query using GeoPoint as well.
This is not fully tested yet it should be a bit of an improvement on Ryan Lee's answer
My calculation is more accurate and then I filter the answers to remove hits which fall within the bounding box but outside the radius
Swift 4
func getDocumentNearBy(latitude: Double, longitude: Double, meters: Double) {
let myGeopoint = GeoPoint(latitude:latitude, longitude:longitude )
let r_earth : Double = 6378137 // Radius of earth in Meters
// 1 degree lat in m
let kLat = (2 * Double.pi / 360) * r_earth
let kLon = (2 * Double.pi / 360) * r_earth * __cospi(latitude/180.0)
let deltaLat = meters / kLat
let deltaLon = meters / kLon
let swGeopoint = GeoPoint(latitude: latitude - deltaLat, longitude: longitude - deltaLon)
let neGeopoint = GeoPoint(latitude: latitude + deltaLat, longitude: longitude + deltaLon)
let docRef : CollectionReference = appDelegate.db.collection("restos")
let query = docRef.whereField("location", isGreaterThan: swGeopoint).whereField("location", isLessThan: neGeopoint)
query.getDocuments { snapshot, error in
guard let snapshot = snapshot else {
print("Error fetching snapshot results: \(error!)")
return
}
self.documents = snapshot.documents.filter { (document) in
if let location = document.get("location") as? GeoPoint {
let myDistance = self.distanceBetween(geoPoint1:myGeopoint,geoPoint2:location)
print("myDistance:\(myDistance) distance:\(meters)")
return myDistance <= meters
}
return false
}
}
}
Functions which accurately measure the distance in Meters between 2 Geopoints for filtering
func distanceBetween(geoPoint1:GeoPoint, geoPoint2:GeoPoint) -> Double{
return distanceBetween(lat1: geoPoint1.latitude,
lon1: geoPoint1.longitude,
lat2: geoPoint2.latitude,
lon2: geoPoint2.longitude)
}
func distanceBetween(lat1:Double, lon1:Double, lat2:Double, lon2:Double) -> Double{ // generally used geo measurement function
let R : Double = 6378.137; // Radius of earth in KM
let dLat = lat2 * Double.pi / 180 - lat1 * Double.pi / 180;
let dLon = lon2 * Double.pi / 180 - lon1 * Double.pi / 180;
let a = sin(dLat/2) * sin(dLat/2) +
cos(lat1 * Double.pi / 180) * cos(lat2 * Double.pi / 180) *
sin(dLon/2) * sin(dLon/2);
let c = 2 * atan2(sqrt(a), sqrt(1-a));
let d = R * c;
return d * 1000; // meters
}
The easiest way is to calculate a "geo hash" when storing the location in the database.
A geo hash is a string which represents a location down to a certain accuracy. The longer the geo hash, the closer the locations with said geo hash must be. Two location which are e.g. 100m apart may have the same 6-char geo hash but when calculating a 7-char geo hash the last char might be different.
There are plenty libraries allowing you to calculate geo hashes for any language. Just store it alongside the location and use a == query to find locations with the same geo hash.
In javascript you can simply
const db = firebase.firestore();
//Geofire
import { GeoCollectionReference, GeoFirestore, GeoQuery, GeoQuerySnapshot } from 'geofirestore';
// Create a GeoFirestore reference
const geofirestore: GeoFirestore = new GeoFirestore(db);
// Create a GeoCollection reference
const geocollection: GeoCollectionReference = geofirestore.collection('<Your_collection_name>');
const query: GeoQuery = geocollectionDrivers.near({
center: new firebase.firestore.GeoPoint(location.latitude, location.longitude),
radius: 10000
});
query.onSnapshot(gquerySnapshot => {
gquerySnapshot.forEach(res => {
console.log(res.data());
})
});
A workaround for Flutter till we have native query in Firestore to pull ordered documents based on lat/long:
https://pub.dev/packages/geoflutterfire
A plugin to store geo hashes in the Firestore and query the same.
Limitations: limit not supported
There's a GeoFire library for Firestore called Geofirestore: https://github.com/imperiumlabs/GeoFirestore (Disclaimer: I helped develop it). It's super easy to use and offers the same features for Firestore that Geofire does for Firebase Realtime DB)

Formula of n-vector from latitude and longitude with three.js objects

I want the formula giving the n-vector (perpendicular to the globe) from latitude and longitude in a three.js scene.
My code is currently the following, based on a list of cities (in the table called "wup"):
var conegeometry = new THREE.CylinderGeometry(0, 10, 10, 500, false);
var earthRadius = 6371; // kilometres
var réduc = 0.02;
for (var iter=1;iter<1693;iter++){
var cone = new THREE.Mesh(conegeometry, conematerial);
var lat = wup[iter].Latitude*Math.PI/180;
var lon = wup[iter].Longitude*Math.PI/180;
cone.position.set (
earthRadius * réduc * Math.cos(lat) * Math.cos(lon),
earthRadius * réduc * Math.cos(lat) * Math.sin(lon),
earthRadius * réduc * Math.sin(lat));
cone.rotation.set (
Math.sin(lat),
Math.cos(lat) * Math.sin(lon),
-Math.cos(lat) * Math.cos(lon));
scene.add(cone);
}
Formulae come from this article, p 402.
My aim is to have all cities represented as cones with the top at lat/lon position and the rest below the surface of earth, and perpendicularly to the earth surface (simplified as a sphere).
Latitude and longitude come from UN cities dataset, seem very clean and classical in degrees.
Santiago Del Estero -27,79511 -64,26149
Yerevan 40,181998 44,514619
Adelaide -34,92866 138,59863
But something is wrong in the rotation formulae, and I can't find the right adjustment. Any idea?
You need to fix two things: calculation of position and calculation of rotation.
Position:
The geographical coordinate system is left-handed (longitude grows towards east). Three.js uses a right-handed coordinate system (longitude grows towards west). Therefore the longitude value needs to be inverted in your geometry. Also, the formulae you found work for coordinates with Z-axis pointing up. Three.js has the Y-axis pointing up. So you need to swap the z and y formulas. This is the correct code for position:
var lat = wup[iter].Latitude*Math.PI/180;
var lon = - wup[iter].Longitude*Math.PI/180;
cone.position.set (
earthRadius * réduc * Math.cos(lat) * Math.cos(lon),
earthRadius * réduc * Math.sin(lat),
earthRadius * réduc * Math.cos(lat) * Math.sin(lon));
Rotation:
You just need to rotate the cone by their longitude/latitude values (not sines and cosines)
cone.rotation.set ( 0, -lon, - Math.PI / 2 + lat);
I found a solution, much simpler than my initial idea. Based on this project and this example at using the instruction lookAt which avoids complicate trigonometric formulae.
I also found that my formulae for lat/lon to x, y, z where wrong, and not corresponding to the formulae used in the project shp.js which I also use.
Objects can be set at facing a given point, here the centre of the earth. But then cones are cylinders and must for a reason I do not fully understand be turned of PI/2. So this worked:
var lat = wup[iter].Latitude*Math.PI/180;
var lon = - wup[iter].Longitude*Math.PI/180;
cone.position.set (
Math.cos(lon) * 90 * Math.cos(lat),
Math.sin(lat) * 90,
Math.sin(lon) * 90 * Math.cos(lat)
);
cone.lookAt( new THREE.Vector3(0,0,0) ); //orientate the cone to the center of earth
cone.translateZ( - earthRadius * réduc); //to follow the genral contraction
cone.translateZ( coneHeight/2); //to put the top edge at lat/lon position
cone.rotateX(- Math.PI / 2 ); //because cylinders.cones are drawn horizontally

How to make clock ticks stuck to the clock border?

I try to make a clock, in swift, but now i want to make something strange. I want make border radius settable. This is the easy part (is easy because I already did that). I drew 60 ticks around the clock. The problem is that 60 ticks are a perfect circle. If I change the border radius I obtain this clock:
All ticks are made with NSBezierPath, and code for calculate position for every tick is :
tickPath.moveToPoint(CGPoint(
x: center.x + cos(angle) * point1 ,
y: center.y + sin(angle) * point1
))
tickPath.lineToPoint(CGPoint(
x: center.x + cos(angle) * point2,
y: center.y + sin(angle) * point2
))
point1 and point2 are points for 12 clock tick.
My clock background is made with bezier path:
let bezierPath = NSBezierPath(roundedRect:self.bounds, xRadius:currentRadius, yRadius:currentRadius)
currentRadius - is a settable var , so my background cam be, from a perfect circle (when corner radius = height / 2) to a square (when corner radius = 0 ).
Is any formula to calculate position for every tick so, for any border radius , in the end all ticks to be at same distance to border ?
The maths is rather complicated to explain without recourse to graphics diagrams, but basically if you consider a polar coordinates approach with the origin at the clock centre then there are two cases:
where the spoke from the origin hits the straight side of the square - easy by trigonometry
where it hits the circle arc at the corner - we use the cosine rule to solve the triangle formed by the centre of the clock, the centre of the corner circle and the point where the spoke crosses the corner. The origin-wards angle of that triangle is 45º - angleOfSpoke, and two of the sides are of known length. Solve the cosine equation as a quadratic and you have it.
This function does it:
func radiusAtAngle(angleOfSpoke: Double, radius: Double, cornerRadius: Double) -> Double {
// radius is the half-width of the square, = the full radius of the circle
// cornerRadius is, of course, the corner radius.
// angleOfSpoke is the (maths convention) angle of the spoke
// the function returns the radius of the spoke.
let theta = atan((radius - cornerRadius) / radius) // This determines which case
let modAngle = angleOfSpoke % M_PI_2 // By symmetry we need only consider the first quadrant
if modAngle <= theta { // it's on the vertical flat
return radius / cos(modAngle)
} else if modAngle > M_PI_2 - theta { // it's on the horizontal flat
return radius / cos(M_PI_2 - modAngle)
} else { // it's on the corner arc
// We are using the cosine rule to solve the triangle formed by
// the clock centre, the curved corner's centre,
// and the point of intersection of the spoke.
// Then use quadratic solution to solve for the radius.
let diagonal = hypot(radius - cornerRadius, radius - cornerRadius)
let rcosa = diagonal * cos(M_PI_4 - modAngle)
let sqrTerm = rcosa * rcosa - diagonal * diagonal + cornerRadius * cornerRadius
if sqrTerm < 0.0 {
println("Aaargh - Negative term") // Doesn't happen - use assert in production
return 0.0
} else {
return rcosa + sqrt(sqrTerm) // larger of the two solutions
}
}
}
In the diagram OP = diagonal, OA = radius, PS = PB = cornerRadius, OS = function return, BÔX = theta, SÔX = angleOfSpoke

How do I generate a random latitude and longitude within the radius of another point?

In Ruby if I have a particular latitude and longitude, how can I generate a relatively random sample of points within a given radius or near another point?
{ latitude: 37.7905576, longitude: -122.3989885 }
Theory
The circumference of the earth at equator = 40,076 km. The equator is divided into 360 degrees of longitude, so each degree at the equator represents approximately 111.32 km. Moving away from the equator towards a pole this distance decreases to zero at the pole.
1 degree aproximates to 111.32 km at equator.
96.41km at 30 degrees N/S
78.71 km at 45 degrees N/S
55.66 km at 60 degrees N/S
28.82 km at 75 degrees N/S
Therefor just adding or subtracting a random distance from the coordinates will not produce a "circle" . To avoid this we can generate a series of points and eliminating those outside the radius by using either Haversine,Spherical Law Of Cosines or Equirectangular projection.
As the latter uses only the common trig functions cos() I will use it to illustrate. Using php as I don't have Ruby
Application
function Equirectangular($lat1,$lng1,$lat2,$lng2){
$x = deg2rad($lng2-$lng1) * cos(deg2rad($lat1+$lat2)/2);
$y = deg2rad($lat1-$lat2);
$R = 6372.8; // gives d in km
$distance = sqrt($x*$x + $y*$y) * $R;
return $distance;
}
$centerLat = 37.7905576;
$centerLng = -122.3989885;
for ($i = 0; $i <= 200; $i++) {
$lat = rand(0,40000)/2;//Random between 0 & 2 =radius +- 2 degrees 222.62 km
$lng = rand(0,40000)/2;
$lat2 = $centerLat+ ($lat/10000);
$lng2 = $centerLng+ ($lng/10000);
echo $lat2." ".$lng2."";
if (Equirectangular($centerLat,$centerLng,$lat2,$lng2)< 200){//200 km
echo " In";
}else{
echo " Out";
}
echo "<br>";
}

Calculating new longitude, latitude from old + n meters

I want to create 2 new longitude and 2 new latitudes based on a coordinate and a distance in meters, I want to create a nice bounding box around a certain point. It is for a part of a city and max ±1500 meters. I therefore don't think the curvature of earth has to be taken into account.
So I have 50.0452345 (x) and 4.3242234 (y) and I want to know x + 500 meters, x - 500 meters, y - 500 meters, y + 500 meters
I found many algorithms but almost all seem to deal with the distance between points.
The number of kilometers per degree of longitude is approximately
(pi/180) * r_earth * cos(theta*pi/180)
where theta is the latitude in degrees and r_earth is approximately 6378 km.
The number of kilometers per degree of latitude is approximately the same at all locations, approx
(pi/180) * r_earth = 111 km / degree
So you can do:
new_latitude = latitude + (dy / r_earth) * (180 / pi);
new_longitude = longitude + (dx / r_earth) * (180 / pi) / cos(latitude * pi/180);
As long as dx and dy are small compared to the radius of the earth and you don't get too close to the poles.
The accepted answer is perfectly right and works. I made some tweaks and turned into this:
double meters = 50;
// number of km per degree = ~111km (111.32 in google maps, but range varies
// between 110.567km at the equator and 111.699km at the poles)
//
// 111.32km = 111320.0m (".0" is used to make sure the result of division is
// double even if the "meters" variable can't be explicitly declared as double)
double coef = meters / 111320.0;
double new_lat = my_lat + coef;
// pi / 180 ~= 0.01745
double new_long = my_long + coef / Math.cos(my_lat * 0.01745);
Hope this helps too.
For latitude do:
var earth = 6378.137, //radius of the earth in kilometer
pi = Math.PI,
m = (1 / ((2 * pi / 360) * earth)) / 1000; //1 meter in degree
var new_latitude = latitude + (your_meters * m);
For longitude do:
var earth = 6378.137, //radius of the earth in kilometer
pi = Math.PI,
cos = Math.cos,
m = (1 / ((2 * pi / 360) * earth)) / 1000; //1 meter in degree
var new_longitude = longitude + (your_meters * m) / cos(latitude * (pi / 180));
The variable your_meters can contain a positive or a negative value.
I had to spend about two hours to work out the solution by #nibot , I simply needed a method to create a boundary box given its center point and width/height (or radius) in kilometers:
I don't fully understand the solution mathematically/ geographically.
I tweaked the solution (by trial and error) to get the four coordinates. Distances in km, given the current position and distance we shift to the new position in the four coordinates:
North:
private static Position ToNorthPosition(Position center, double northDistance)
{
double r_earth = 6378;
var pi = Math.PI;
var new_latitude = center.Lat + (northDistance / r_earth) * (180 / pi);
return new Position(new_latitude, center.Long);
}
East:
private static Position ToEastPosition(Position center, double eastDistance)
{
double r_earth = 6378;
var pi = Math.PI;
var new_longitude = center.Long + (eastDistance / r_earth) * (180 / pi) / Math.Cos(center.Lat * pi / 180);
return new Position(center.Lat, new_longitude);
}
South:
private static Position ToSouthPosition(Position center, double southDistance)
{
double r_earth = 6378;
var pi = Math.PI;
var new_latitude = center.Lat - (southDistance / r_earth) * (180 / pi);
return new Position(new_latitude, center.Long);
}
West:
private static Position ToWestPosition(Position center, double westDistance)
{
double r_earth = 6378;
var pi = Math.PI;
var new_longitude = center.Long - (westDistance / r_earth) * (180 / pi) / Math.Cos(center.Lat * pi / 180);
return new Position(center.Lat, new_longitude);
}
Have you checked out: How do I find the lat/long that is x km north of a given lat/long ?
These calculations are annoying at best, I've done many of them. The haversine formula will be your friend.
Some reference: http://www.movable-type.co.uk/scripts/latlong.html
Posting this method for sake of completeness.
Use this method "as it is" to:
Move any (lat,long) point by given meters in either axis.
Python method to move any point by defined meters.
def translate_latlong(lat,long,lat_translation_meters,long_translation_meters):
''' method to move any lat,long point by provided meters in lat and long direction.
params :
lat,long: lattitude and longitude in degrees as decimal values, e.g. 37.43609517497065, -122.17226450150885
lat_translation_meters: movement of point in meters in lattitude direction.
positive value: up move, negative value: down move
long_translation_meters: movement of point in meters in longitude direction.
positive value: left move, negative value: right move
'''
earth_radius = 6378.137
#Calculate top, which is lat_translation_meters above
m_lat = (1 / ((2 * math.pi / 360) * earth_radius)) / 1000;
lat_new = lat + (lat_translation_meters * m_lat)
#Calculate right, which is long_translation_meters right
m_long = (1 / ((2 * math.pi / 360) * earth_radius)) / 1000; # 1 meter in degree
long_new = long + (long_translation_meters * m_long) / math.cos(lat * (math.pi / 180));
return lat_new,long_new
Working Python code to offset coordinates by 10 metres.
def add_blur(lat, long):
meters = 10
blur_factor = meters * 0.000006279
new_lat = lat + blur_factor
new_long = long + blur_factor / math.cos(lat * 0.018)
return new_lat, new_long
if you don't have to be very exact then: each 10000 meters is about 0.1 for latitude and longitude.
for example I want to load locations 3000 meters around point_A from my database:
double newMeter = 3000 * 0.1 / 10000;
double lat1 = point_A.latitude - newMeter;
double lat2 = point_A.latitude + newMeter;
double lon1 = point_A.longitude - newMeter;
double lon1 = point_A.longitude + newMeter;
Cursor c = mDb.rawQuery("select * from TABLE1 where lat >= " + lat1 + " and lat <= " + lat2 + " and lon >= " + lon1 + " and lon <= " + lon2 + " order by id", null);
public double MeterToDegree(double meters, double latitude)
{
return meters / (111.32 * 1000 * Math.Cos(latitude * (Math.PI / 180)));
}
var meters = 50;
var coef = meters * 0.0000089;
var new_lat = map.getCenter().lat.apply() + coef;
var new_long = map.getCenter().lng.apply() + coef / Math.cos(new_lat * 0.018);
map.setCenter({lat:new_lat, lng:new_long});
See from Official Google Maps Documentation (link below) as they solve on easy/simple maps the problems with distance by countries :)
I recommended this solution to easy/simply solve issue with boundaries that you can know which area you're solving the problem with boundaries (not recommended globally)
Note:
Latitude lines run west-east and mark the position south-north of a point. Lines of latitude are called parallels and in total there are 180 degrees of latitude. The distance between each degree of latitude is about 69 miles (110 kilometers).
The distance between longitudes narrows the further away from the equator. The distance between longitudes at the equator is the same as latitude, roughly 69 miles (110 kilometers) . At 45 degrees north or south, the distance between is about 49 miles (79 kilometers). The distance between longitudes reaches zero at the poles as the lines of meridian converge at that point.
Original source 1
Original source 2
Official Google Maps Documentation: Code Example: Autocomplete Restricted to Multiple Countries
See the part of their code how they solve problem with distance center + 10 kilometers by +/- 0.1 degree
function initMap(): void {
const map = new google.maps.Map(
document.getElementById("map") as HTMLElement,
{
center: { lat: 50.064192, lng: -130.605469 },
zoom: 3,
}
);
const card = document.getElementById("pac-card") as HTMLElement;
map.controls[google.maps.ControlPosition.TOP_RIGHT].push(card);
const center = { lat: 50.064192, lng: -130.605469 };
// Create a bounding box with sides ~10km away from the center point
const defaultBounds = {
north: center.lat + 0.1,
south: center.lat - 0.1,
east: center.lng + 0.1,
west: center.lng - 0.1,
};
const input = document.getElementById("pac-input") as HTMLInputElement;
const options = {
bounds: defaultBounds,
componentRestrictions: { country: "us" },
fields: ["address_components", "geometry", "icon", "name"],
origin: center,
strictBounds: false,
types: ["establishment"],
};
This is what I did in VBA that seems to be working for me. Calculation is in feet not meters though
Public Function CalcLong(OrigLong As Double, OrigLat As Double, DirLong As String, DirLat As String, DistLong As Double, DistLat As Double)
Dim FT As Double
Dim NewLong, NewLat As Double
FT = 1 / ((2 * WorksheetFunction.Pi / 360) * 20902230.971129)
If DirLong = "W" Then
NewLat = CalcLat(OrigLong, OrigLat, DirLong, DirLat, DistLong, DistLat)
NewLong = OrigLong - ((FT * DistLong) / Cos(NewLat * (WorksheetFunction.Pi / 180)))
CalcLong = NewLong
Else
NewLong = OrigLong + ((FT * DistLong) / Math.Cos(CalcLat(OrigLong, OrigLat, DirLong, DirLat, DistLong, DistLat) * (WorksheetFunction.Pi / 180)))
CalcLong = NewLong
End If
End Function
Public Function CalcLat(OrigLong As Double, OrigLat As Double, DirLong As String, DirLat As String, DistLong As Double, DistLat As Double) As Double
Dim FT As Double
Dim NewLat As Double
FT = 1 / ((2 * WorksheetFunction.Pi / 360) * 20902230.971129)
If DirLat = "S" Then
NewLat = (OrigLat - (FT * DistLat))
CalcLat = NewLat
Else
NewLat = (OrigLat + (FT * DistLat))
CalcLat = NewLat
End If
End Function
Original poster said:
"So I have 50.0452345 (x) and 4.3242234 (y) and I want to know x + 500 meters..."
I will assume the units of the x and y values he gave there were in meters (and not degrees Longitude, Latitude). If so then he is stating measurements to 0.1 micrometer, so I will assume he needs similar accuracy for the translated output. I also will assume by "+500 meters" etc. he meant
the direction to be due North-South and due East-West.
He refers to a reference point:
"2 new latitudes based on a coordinate";
but he did not give the Longitude and Latitude,
so to explain the procedure concretely I will give
the Latitudes and Longitudes for the corners of the
500 meter box he requested around the point
[30 degrees Longitude,30 degrees Latitude].
The exact solution on the surface of the GRS80 Ellipsoid is
given with the following set of functions
(I wrote these for the free-open-source-mac-pc math program called "PARI"
which allows any number of digits precision to be setup):
\\=======Arc lengths along Latitude and Longitude and the respective scales:
dms(u)=[truncate(u),truncate((u-truncate(u))*60),((u-truncate(u))*60-truncate((u-truncate(u))*60))*60];
SpinEarthRadiansPerSec=7.292115e-5;\
GMearth=3986005e8;\
J2earth=108263e-8;\
re=6378137;\
ecc=solve(ecc=.0001,.9999,eccp=ecc/sqrt(1-ecc^2);qecc=(1+3/eccp^2)*atan(eccp)-3/eccp;ecc^2-(3*J2earth+4/15*SpinEarthRadiansPerSec^2*re^3/GMearth*ecc^3/qecc));\
e2=ecc^2;\
b2=1-e2;\
b=sqrt(b2);\
fl=1-b;\
rfl=1/fl;\
U0=GMearth/ecc/re*atan(eccp)+1/3*SpinEarthRadiansPerSec^2*re^2;\
HeightAboveEllipsoid=0;\
reh=re+HeightAboveEllipsoid;\
longscale(lat)=reh*Pi/648000/sqrt(1+b2*(tan(lat))^2);
latscale(lat)=reh*b*Pi/648000/(1-e2*(sin(lat))^2)^(3/2);
longarc(lat,long1,long2)=longscale(lat)*648000/Pi*(long2-long1);
latarc(lat1,lat2)=(intnum(th=lat1,lat2,sqrt(1-e2*(sin(th))^2))+e2/2*sin(2*lat1)/sqrt(1-e2*(sin(lat1))^2)-e2/2*sin(2*lat2)/sqrt(1-e2*(sin(lat2))^2))*reh;
\\=======
I then plugged the reference point [30,30]
into those functions at the PARI command prompt
and had PARI solve for the point +/- 500 meters away
from it, giving the two new Longitudes and
two new Latitudes that the original poster asked for.
Here is the input and output showing that:
? dms(solve(x=29,31,longarc(30*Pi/180,30*Pi/180,x*Pi/180)+500))
cpu time = 1 ms, real time = 1 ms.
%1172 = [29, 59, 41.3444979398934670450280297216509190843055]
? dms(solve(x=29,31,longarc(30*Pi/180,30*Pi/180,x*Pi/180)-500))
cpu time = 1 ms, real time = 1 ms.
%1173 = [30, 0, 18.6555020601065329549719702783490809156945]
? dms(solve(x=29,31,latarc(30*Pi/180,x*Pi/180)+500))
cpu time = 1,357 ms, real time = 1,358 ms.
%1174 = [29, 59, 43.7621925447500548285775757329518579545513]
? dms(solve(x=29,31,latarc(30*Pi/180,x*Pi/180)-500))
cpu time = 1,365 ms, real time = 1,368 ms.
%1175 = [30, 0, 16.2377963202802863245716034907838199823349]
?

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