We Keep Coding

Rotating Point around another Point

I want to create a "spiral effect" with particles (or any entities) in Java.
I'm new to objective programming (and also Java), so I started with something easier. I firstly created a Path object that has a value of Locations[] signed to it, it gets from the user a: Start location, End location, and double value, that tells him, how much space between each location in the path he has.
private void setLocations() {
//initialize vars
Location start = getStart();
World world = start.getWorld();
Location[] locations = new Location[amount];
double x = start.getX();
double y = start.getY();
double z = start.getZ();
//loop that will set values for locations
for (int i = 0; i < amount; i++) {
locations[i] = new Location(
world,
x + dividedDistanceX * (i + 1),
y + dividedDistanceY * (i + 1),
z + dividedDistanceZ * (i + 1)
);
}
this.locations = locations;
}
Now you might be asking what is the amount? So simply it's the number of points that are created when the object is initialized. It's simple math like getting the longest distance from point to point, and then dividing it by the value of space between each point.
Now the situation gets a little more complicated, so I prepared graphics for you:)
I want to rotate points around the longest axis to form some form of a spiral, and I want from user to set the maximum distance between the starting point and the new one.
Something like this:
And another graph of the sinusoid around one vector (x, y)
Honestly, I need some help.
Here's GitHub object link
Things I know I need to do:
Get the axis around which I will rotate point (it's the longest distance between points)
Add some value to the rest values (x+something, y+something)
Add angle, that point will rotate with, (for example each point will be rotated by 22,5).

Okay, so i did it, it wasn't even that hard:
public Location[] createSpiral(double radius, float angle, Location[] path) {
final int length = path.length;
Location[] result = path.clone();
Location start = path[0];
Location end = path[length - 1];
double startX = start.getX();
double startY = start.getY();
double startZ = start.getZ();
double endX = end.getX();
double endY = end.getY();
double endZ = end.getZ();
double distanceX = setDistance(startX, endX);
double distanceY = setDistance(startY, endY);
double distanceZ = setDistance(startZ, endZ);
double highestOffset = getHighestOffset(new double[]{distanceX, distanceY, distanceZ});
if (highestOffset == abs(distanceX)) {
for (int i = 0; i < length; i++) {
double sin = radius * sin(angle * i / length);
double cos = radius * cos(angle * i / length);
result[i].setY(result[i].getY() + cos);
result[i].setZ(result[i].getZ() + sin);
}
} else if (highestOffset == abs(distanceY)) {
for (int i = 0; i < length; i++) {
double sin = radius * sin(angle * i / length);
double cos = radius * cos(angle * i / length);
result[i].setX(result[i].getX() + cos);
result[i].setZ(result[i].getZ() + sin);
}
} else if (highestOffset == abs(distanceZ)) {
for (int i = 0; i < length; i++) {
double sin = radius * sin(angle * i / length);
double cos = radius * cos(angle * i / length);
result[i].setX(result[i].getX() + cos);
result[i].setY(result[i].getY() + sin);
}
} else {
return path;
}
return result;
}
It's just
double sin = radius * sin(angle * i / length);
double cos = radius * cos(angle * i / length);
and adding those values to corresponding X, Y if Z has the highest distance from a location, etc.
The rest of the code and methods are located in the GitHub link above.

Convert 2D array to latitude/longitude points with given starting point lat/lon and scales

I have a 2D array
int[][] data = new int[720][720];
dataReader.read(data);
Each slot in the data contains a value, for that specific coordiante. The location of the slot (e.g data[5][5] is used to get the latitude/longitude).
I tried to get the location by doing the following:
I have the following information:
LL_lat = 28.33346126086149 // lower-left lat
LL_lon = 30.757889519059812 // lower-left lon
LR_lat = 28.633821527352005 // lower-right lat
LR_lon = 39.242110331928565 // lower-right lon
UL_lat = 35.52560518009779 // upper-left lat
UL_lon = 30.757889519059812 // upper-left lon
UR_lat = 35.52560518009781 // upper-right lat
UR_lon = 39.242110331928565 // upper-right lon
projdef = +proj=merc +a=6371000 +lat_0=0 +lon_0=0
xscale = 1111.1099999999517 // Size in meters for X for each cell in the array
xsize = 720 // array size X
yscale = 1088.97060116836 // size in meters for Y for each cell in the array
ysize = 720 // array size Y
I have these two functions I made:
public static double calculateLatitude(double distance, double startPointLat) {
return startPointLat + (distance * (360 / ((Math.PI * 2) * 6357)));
}
public static double calculateLongitude(double distance, double lat, double startPointLon) {
return startPointLon + distance * 360 / (Math.PI * 2 * 6400 * Math.sin(Math.toRadians(90 - lat)));
}
I basically calculate the distance by doing cellX * xscale and pass it to the latitude function along with the starting point lat, I chose any point out of the 4 points I have (represents a square area)
But the coordinates are being very not correct, probably miscalcualting something?
Is there a better way to calculate it or whats wrong?
The array and calculation:
for (int i = 0; i < arrayData.length; i++) {
for (int j = 0; j < arrayData[0].length; j++) {
int val = arrayData[i][j];
double distX = i * xscale;
double distY = j * yscale;
double lat = RadarPhysics.calculateLatitude(distX, startPointLat);
double lon = RadarPhysics.calculateLongitude(distY, lat, startPointLat);
GeoLocation loc = new GeoLocation(lat, lon);
System.out.println(loc.toString());
}
}

Find out if the user in specific region using GPS data

I want to find out if the user in specific region using GPS data and consider with accuracy info to reduce error, because the program will prompt an alert if user definitely out of the region.
GPS sensor return latitude, longitude and accuracy(in meter), I can draw a circle using those data:
135.500908,34.661964,30.0
There're array of coordinates in sequence represent the specific region:
135.500350,34.667011
135.506101,34.666853
135.505972,34.663076
135.505135,34.663111
135.504942,34.662387
135.504084,34.662440
135.504062,34.663146
135.502968,34.663217
135.502689,34.663764
135.502431,34.664205
135.502110,34.664646
135.501680,34.665105
135.501509,34.665246
135.500844,34.665229
135.500371,34.665511
My idea is to find out if any collisions of the polygon with the circle by using line-circle collisions detection algorithm, but it looks something wrong in my code, and seems I can't directly use that info due to radius/degree, could anyone help me out? Or let me know if any more simple solution?
public static boolean possiblyInside(List<Double> arrayX, List<Double> arrayY, double locationX, double locationY, double locationAccuracy) {
if (arrayX.size() != arrayY.size()) {
throw new IllegalArgumentException("Array length not equal");
}
boolean anyCircleLineIntersection = false;
if (arrayX.size() > 1) {
for (int i = 0; i < arrayX.size(); i++) {
double p1x = i == 0 ? arrayX.get(arrayX.size() - 1) : arrayX.get(i - 1);
double p1y = i == 0 ? arrayY.get(arrayY.size() - 1) : arrayY.get(i - 1);
double p2x = arrayX.get(i);
double p2y = arrayY.get(i);
if (circleLineIntersection(p1x, p1y, p2x, p2y, locationX, locationY, locationAccuracy)) {
anyCircleLineIntersection = true;
break;
}
}
}
return anyCircleLineIntersection;
}
private static boolean circleLineIntersection(double p1X, double p1Y, double p2X, double p2Y, double centerX, double centerY, double locationAccuracy) {
double rad = (180 / Math.PI);
double r = (locationAccuracy / 1000);
p1X = p1X * rad;
p1Y = p1Y * rad;
p2X = p2X * rad;
p2Y = p2Y * rad;
centerX = centerX * rad;
centerY = centerY * rad;
// Transform to local coordinates
double localP1X = p1X - centerX;
double localP1Y = p1Y - centerY;
double localP2X = p2X - centerX;
double localP2Y = p2Y - centerY;
// Pre-calculate this value. We use it often
double pDiffX = localP2X - localP1X;
double pDiffY = localP2Y - localP1Y;
double a = (pDiffX) * (pDiffX) + (pDiffY) * (pDiffY);
double b = 2 * ((pDiffX * localP1X) + (pDiffY * localP1Y));
double c = (localP1X * localP1X) + (localP1Y * localP1Y) - (r * r);
double delta = b * b - (4 * a * c);
return delta >= 0.0;
}

There is a method called Geofencing. Google already provides such functionality for you. And you don't have to deal with all these complex calculations.
You can fire events when the user entered a specific area / exited a specific area / after staying for some time in a specific area. Or you can make different combinations.
Here is an article of how you can use Geofencing. It consists of 4 separated articles.

Thank you for Todor Kostov's answer.
I know Android has provided Geofencing API, but it is not a perfect fit for my situation due to its implementation and limitations, and I would like to sync the algorithm with iOS version app as well. (Even I know the algorithm are not good as iOS or Android provided, and it also looks a bit silly).
Finally, I solved the problem in this way:
Ensure current location not inside the polygon (use point-in-polygon algorithm)
Loop through all line segment of the region polygon, find out the
closest coordinate(PointA) to the current location(PointB)
Calculate the distance between PointA and PointB, convert it to meter(X)
If X > location accuracy (also in meter), the user is definitely out of the particular region
p.s. I'm not good at math and geolocation, point out if any incorrect
public static boolean possiblyInside(List<Double> arrayX, List<Double> arrayY, double locationX, double locationY, double locationAccuracy) {
if (arrayX.size() != arrayY.size()) {
throw new IllegalArgumentException("Array length not equal");
}
if (arrayX.size() < 3) {
return false;
}
double minimumDistance = Double.MAX_VALUE;
for (int i = 0; i < arrayX.size(); i++) {
double p1x = i == 0 ? arrayX.get(arrayX.size() - 1) : arrayX.get(i - 1);
double p1y = i == 0 ? arrayY.get(arrayY.size() - 1) : arrayY.get(i - 1);
double p2x = arrayX.get(i);
double p2y = arrayY.get(i);
Coordinate closest = getClosestPointOnLine(p1x, p1y, p2x, p2y, locationX, locationY);
double currentDistance = distanceMeterBetweenPoints(closest.latitude, closest.longitude, locationX, locationY);
if (currentDistance < minimumDistance) {
minimumDistance = currentDistance;
}
}
return (minimumDistance <= locationAccuracy);
}
private static Coordinate getClosestPointOnLine(double sx1, double sy1, double sx2, double sy2, double px, double py) {
double xDelta = sx2 - sx1;
double yDelta = sy2 - sy1;
if ((xDelta == 0) && (yDelta == 0)) {
throw new IllegalArgumentException("Line start equals line end");
}
double u = ((px - sx1) * xDelta + (py - sy1) * yDelta) / (xDelta * xDelta + yDelta * yDelta);
final Coordinate closestPoint;
if (u < 0.0) {
closestPoint = new Coordinate(sx1, sy1);
} else if (u > 1.0) {
closestPoint = new Coordinate(sx2, sy2);
} else {
closestPoint = new Coordinate((int) Math.round(sx1 + u * xDelta), (int) Math.round(sy1 + u * yDelta));
}
return closestPoint;
}
public static double distanceMeterBetweenPoints(double aX, double aY, double bX, double bY) {
double rad = Math.PI / 180;
int r = 6371;
double dLat = (aX - bX) * rad;
double dLng = (aY - bY) * rad;
double x = Math.pow(Math.sin(dLat / 2), 2) + Math.cos(aX * rad) * Math.cos(bX * rad) * Math.pow(Math.sin(dLng / 2), 2);
double y = 2 * Math.atan2(Math.sqrt(x), Math.sqrt(1 - x));
return r * y * 1000;
}

find closest marker to my current location

I have an arrayList of markers and I want to find the closest marker to my current location.
I had no idea how to find that marker so I searched and found same problem in here.
Google Maps Api v3 - find nearest markers
then I tried to convert those code to java but it doesn't work now.
closest doesn't change and always it is -1.
Is there any better solution for this problem or I can make the following code usable?
public void findNearMarker(){
double pi = Math.PI;
int R = 6371; //equatorial radius
double[] distances = new double[2];
double d = 0;
int i;
int closest = -1;
for ( i = 0; i == markerArrayList.size(); i++){
double lat2 = markerArrayList.get(i).getPosition().latitude;
double lon2 = markerArrayList.get(i).getPosition().longitude;
double chLat = lat2 - currentLocation.getLatitude();
double chLon = lon2 - currentLocation.getLongitude();
double dLat = chLat*(pi/180);
double dLon = chLon*(pi/180);
double rLat1 = currentLocation.getLatitude()*(pi/180);
double rLat2 = lat2 * (pi/180);
double a = Math.sin(dLat/2) * Math.sin(dLat/2) + Math.sin(dLon/2)
* Math.sin(dLon /2) * Math.cos(rLat1) * Math.cos(rLat2);
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
d = R * c;
distances[i] = d;
if (closest == -1 || d< distances[closest]){
closest = i;
}
}
}

first you need to import the location class of the android sdk
import android.location.Location;
ArrayList<Marker> markers = new ArrayList<>();
markers = sortListbyDistance(markers, currentLocation.getLocation());
public static ArrayList<Marker> sortListbyDistance(ArrayList<Marker> markers, final LatLng location){
Collections.sort(markers, new Comparator<Marker>() {
#Override
public int compare(Marker marker2, Marker marker1) {
//
if(getDistanceBetweenPoints(marker1.getLocation(),location)>getDistanceBetweenPoints(marker2.getLocation(),location)){
return -1;
} else {
return 1;
}
}
});
return markers;
}
public static float getDistanceBetweenPoints(double firstLatitude, double firstLongitude, double secondLatitude, double secondLongitude) {
float[] results = new float[1];
Location.distanceBetween(firstLatitude, firstLongitude, secondLatitude, secondLongitude, results);
return results[0];
}
and to get the nearest marker just get first item in markers, cheers :)

If you follow
Comparing two locations using their Longitude and Latitude
/** calculates the distance between two locations in MILES */
private double distance(double lat1, double lng1, double lat2, double lng2) {
double earthRadius = 3958.75; // in miles, change to 6371 for kilometer output
double dLat = Math.toRadians(lat2-lat1);
double dLng = Math.toRadians(lng2-lng1);
double sindLat = Math.sin(dLat / 2);
double sindLng = Math.sin(dLng / 2);
double a = Math.pow(sindLat, 2) + Math.pow(sindLng, 2)
* Math.cos(Math.toRadians(lat1)) * Math.cos(Math.toRadians(lat2));
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
double dist = earthRadius * c;
return dist; // output distance, in MILES
}
loop through your list with this function and get the lowest return value.
You can also use the Maps API
Location locationA = new Location("point A");
locationA.setLatitude(latA);
locationA.setLongitude(lngA);
Location locationB = new Location("point B");
locationB.setLatitude(latB);
locationB.setLongitude(lngB);
float distance = locationA.distanceTo(locationB);

Convert latitude/longitude point to a pixels (x,y) on mercator projection

I'm trying to convert a lat/long point into a 2d point so that I can display it on an image of the world-which is a mercator projection.
I've seen various ways of doing this and a few questions on stack overflow-I've tried out the different code snippets and although I get the correct longitude to pixel, the latitude is always off-seems to be getting more reasonable though.
I need the formula to take into account the image size, width etc.
I've tried this piece of code:
double minLat = -85.05112878;
double minLong = -180;
double maxLat = 85.05112878;
double maxLong = 180;
// Map image size (in points)
double mapHeight = 768.0;
double mapWidth = 991.0;
// Determine the map scale (points per degree)
double xScale = mapWidth/ (maxLong - minLong);
double yScale = mapHeight / (maxLat - minLat);
// position of map image for point
double x = (lon - minLong) * xScale;
double y = - (lat + minLat) * yScale;
System.out.println("final coords: " + x + " " + y);
The latitude seems to be off by about 30px in the example I'm trying. Any help or advice?
Update
Based on this question:Lat/lon to xy
I've tried to use the code provided but I'm still having some problems with latitude conversion, longitude is fine.
int mapWidth = 991;
int mapHeight = 768;
double mapLonLeft = -180;
double mapLonRight = 180;
double mapLonDelta = mapLonRight - mapLonLeft;
double mapLatBottom = -85.05112878;
double mapLatBottomDegree = mapLatBottom * Math.PI / 180;
double worldMapWidth = ((mapWidth / mapLonDelta) * 360) / (2 * Math.PI);
double mapOffsetY = (worldMapWidth / 2 * Math.log((1 + Math.sin(mapLatBottomDegree)) / (1 - Math.sin(mapLatBottomDegree))));
double x = (lon - mapLonLeft) * (mapWidth / mapLonDelta);
double y = 0.1;
if (lat < 0) {
lat = lat * Math.PI / 180;
y = mapHeight - ((worldMapWidth / 2 * Math.log((1 + Math.sin(lat)) / (1 - Math.sin(lat)))) - mapOffsetY);
} else if (lat > 0) {
lat = lat * Math.PI / 180;
lat = lat * -1;
y = mapHeight - ((worldMapWidth / 2 * Math.log((1 + Math.sin(lat)) / (1 - Math.sin(lat)))) - mapOffsetY);
System.out.println("y before minus: " + y);
y = mapHeight - y;
} else {
y = mapHeight / 2;
}
System.out.println(x);
System.out.println(y);
When using the original code if the latitude value is positive it returned a negative point, so I modified it slightly and tested with the extreme latitudes-which should be point 0 and point 766, it works fine. However when I try a different latitude value ex: 58.07 (just north of the UK) it displays as north of Spain.

The Mercator map projection is a special limiting case of the Lambert Conic Conformal map projection with
the equator as the single standard parallel. All other parallels of latitude are straight lines and the meridians
are also straight lines at right angles to the equator, equally spaced. It is the basis for the transverse and
oblique forms of the projection. It is little used for land mapping purposes but is in almost universal use for
navigation charts. As well as being conformal, it has the particular property that straight lines drawn on it are
lines of constant bearing. Thus navigators may derive their course from the angle the straight course line
makes with the meridians. [1.]
The formulas to derive projected Easting and Northing coordinates from spherical latitude φ and longitude λ
are:
E = FE + R (λ – λₒ)
N = FN + R ln[tan(π/4 + φ/2)]
where λO is the longitude of natural origin and FE and FN are false easting and false northing.
In spherical Mercator those values are actually not used, so you can simplify the formula to
Pseudo code example, so this can be adapted to every programming language.
latitude = 41.145556; // (φ)
longitude = -73.995; // (λ)
mapWidth = 200;
mapHeight = 100;
// get x value
x = (longitude+180)*(mapWidth/360)
// convert from degrees to radians
latRad = latitude*PI/180;
// get y value
mercN = ln(tan((PI/4)+(latRad/2)));
y = (mapHeight/2)-(mapWidth*mercN/(2*PI));
Sources:
OGP Geomatics Committee, Guidance Note Number 7, part 2: Coordinate Conversions and Transformation
Derivation of the Mercator projection
National Atlas: Map Projections
Mercator Map projection
EDIT
Created a working example in PHP (because I suck at Java)
https://github.com/mfeldheim/mapStuff.git
EDIT2
Nice animation of the Mercator projection
https://amp-reddit-com.cdn.ampproject.org/v/s/amp.reddit.com/r/educationalgifs/comments/5lhk8y/how_the_mercator_projection_distorts_the_poles/?usqp=mq331AQJCAEoAVgBgAEB&amp_js_v=0.1

You cannot merely transpose from longitude/latitude to x/y like that because the world isn't flat. Have you look at this post? Converting longitude/latitude to X/Y coordinate
UPDATE - 1/18/13
I decided to give this a stab, and here's how I do it:-
public class MapService {
// CHANGE THIS: the output path of the image to be created
private static final String IMAGE_FILE_PATH = "/some/user/path/map.png";
// CHANGE THIS: image width in pixel
private static final int IMAGE_WIDTH_IN_PX = 300;
// CHANGE THIS: image height in pixel
private static final int IMAGE_HEIGHT_IN_PX = 500;
// CHANGE THIS: minimum padding in pixel
private static final int MINIMUM_IMAGE_PADDING_IN_PX = 50;
// formula for quarter PI
private final static double QUARTERPI = Math.PI / 4.0;
// some service that provides the county boundaries data in longitude and latitude
private CountyService countyService;
public void run() throws Exception {
// configuring the buffered image and graphics to draw the map
BufferedImage bufferedImage = new BufferedImage(IMAGE_WIDTH_IN_PX,
IMAGE_HEIGHT_IN_PX,
BufferedImage.TYPE_INT_RGB);
Graphics2D g = bufferedImage.createGraphics();
Map<RenderingHints.Key, Object> map = new HashMap<RenderingHints.Key, Object>();
map.put(RenderingHints.KEY_INTERPOLATION, RenderingHints.VALUE_INTERPOLATION_BICUBIC);
map.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
map.put(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
RenderingHints renderHints = new RenderingHints(map);
g.setRenderingHints(renderHints);
// min and max coordinates, used in the computation below
Point2D.Double minXY = new Point2D.Double(-1, -1);
Point2D.Double maxXY = new Point2D.Double(-1, -1);
// a list of counties where each county contains a list of coordinates that form the county boundary
Collection<Collection<Point2D.Double>> countyBoundaries = new ArrayList<Collection<Point2D.Double>>();
// for every county, convert the longitude/latitude to X/Y using Mercator projection formula
for (County county : countyService.getAllCounties()) {
Collection<Point2D.Double> lonLat = new ArrayList<Point2D.Double>();
for (CountyBoundary countyBoundary : county.getCountyBoundaries()) {
// convert to radian
double longitude = countyBoundary.getLongitude() * Math.PI / 180;
double latitude = countyBoundary.getLatitude() * Math.PI / 180;
Point2D.Double xy = new Point2D.Double();
xy.x = longitude;
xy.y = Math.log(Math.tan(QUARTERPI + 0.5 * latitude));
// The reason we need to determine the min X and Y values is because in order to draw the map,
// we need to offset the position so that there will be no negative X and Y values
minXY.x = (minXY.x == -1) ? xy.x : Math.min(minXY.x, xy.x);
minXY.y = (minXY.y == -1) ? xy.y : Math.min(minXY.y, xy.y);
lonLat.add(xy);
}
countyBoundaries.add(lonLat);
}
// readjust coordinate to ensure there are no negative values
for (Collection<Point2D.Double> points : countyBoundaries) {
for (Point2D.Double point : points) {
point.x = point.x - minXY.x;
point.y = point.y - minXY.y;
// now, we need to keep track the max X and Y values
maxXY.x = (maxXY.x == -1) ? point.x : Math.max(maxXY.x, point.x);
maxXY.y = (maxXY.y == -1) ? point.y : Math.max(maxXY.y, point.y);
}
}
int paddingBothSides = MINIMUM_IMAGE_PADDING_IN_PX * 2;
// the actual drawing space for the map on the image
int mapWidth = IMAGE_WIDTH_IN_PX - paddingBothSides;
int mapHeight = IMAGE_HEIGHT_IN_PX - paddingBothSides;
// determine the width and height ratio because we need to magnify the map to fit into the given image dimension
double mapWidthRatio = mapWidth / maxXY.x;
double mapHeightRatio = mapHeight / maxXY.y;
// using different ratios for width and height will cause the map to be stretched. So, we have to determine
// the global ratio that will perfectly fit into the given image dimension
double globalRatio = Math.min(mapWidthRatio, mapHeightRatio);
// now we need to readjust the padding to ensure the map is always drawn on the center of the given image dimension
double heightPadding = (IMAGE_HEIGHT_IN_PX - (globalRatio * maxXY.y)) / 2;
double widthPadding = (IMAGE_WIDTH_IN_PX - (globalRatio * maxXY.x)) / 2;
// for each country, draw the boundary using polygon
for (Collection<Point2D.Double> points : countyBoundaries) {
Polygon polygon = new Polygon();
for (Point2D.Double point : points) {
int adjustedX = (int) (widthPadding + (point.getX() * globalRatio));
// need to invert the Y since 0,0 starts at top left
int adjustedY = (int) (IMAGE_HEIGHT_IN_PX - heightPadding - (point.getY() * globalRatio));
polygon.addPoint(adjustedX, adjustedY);
}
g.drawPolygon(polygon);
}
// create the image file
ImageIO.write(bufferedImage, "PNG", new File(IMAGE_FILE_PATH));
}
}
RESULT: Image width = 600px, Image height = 600px, Image padding = 50px
RESULT: Image width = 300px, Image height = 500px, Image padding = 50px

Java version of original Google Maps JavaScript API v3 java script code is as following, it works with no problem
public final class GoogleMapsProjection2
{
private final int TILE_SIZE = 256;
private PointF _pixelOrigin;
private double _pixelsPerLonDegree;
private double _pixelsPerLonRadian;
public GoogleMapsProjection2()
{
this._pixelOrigin = new PointF(TILE_SIZE / 2.0,TILE_SIZE / 2.0);
this._pixelsPerLonDegree = TILE_SIZE / 360.0;
this._pixelsPerLonRadian = TILE_SIZE / (2 * Math.PI);
}
double bound(double val, double valMin, double valMax)
{
double res;
res = Math.max(val, valMin);
res = Math.min(res, valMax);
return res;
}
double degreesToRadians(double deg)
{
return deg * (Math.PI / 180);
}
double radiansToDegrees(double rad)
{
return rad / (Math.PI / 180);
}
PointF fromLatLngToPoint(double lat, double lng, int zoom)
{
PointF point = new PointF(0, 0);
point.x = _pixelOrigin.x + lng * _pixelsPerLonDegree;
// Truncating to 0.9999 effectively limits latitude to 89.189. This is
// about a third of a tile past the edge of the world tile.
double siny = bound(Math.sin(degreesToRadians(lat)), -0.9999,0.9999);
point.y = _pixelOrigin.y + 0.5 * Math.log((1 + siny) / (1 - siny)) *- _pixelsPerLonRadian;
int numTiles = 1 << zoom;
point.x = point.x * numTiles;
point.y = point.y * numTiles;
return point;
}
PointF fromPointToLatLng(PointF point, int zoom)
{
int numTiles = 1 << zoom;
point.x = point.x / numTiles;
point.y = point.y / numTiles;
double lng = (point.x - _pixelOrigin.x) / _pixelsPerLonDegree;
double latRadians = (point.y - _pixelOrigin.y) / - _pixelsPerLonRadian;
double lat = radiansToDegrees(2 * Math.atan(Math.exp(latRadians)) - Math.PI / 2);
return new PointF(lat, lng);
}
public static void main(String []args)
{
GoogleMapsProjection2 gmap2 = new GoogleMapsProjection2();
PointF point1 = gmap2.fromLatLngToPoint(41.850033, -87.6500523, 15);
System.out.println(point1.x+" "+point1.y);
PointF point2 = gmap2.fromPointToLatLng(point1,15);
System.out.println(point2.x+" "+point2.y);
}
}
public final class PointF
{
public double x;
public double y;
public PointF(double x, double y)
{
this.x = x;
this.y = y;
}
}

JAVA only?
Python code here! Refer to Convert latitude/longitude point to a pixels (x,y) on mercator projection
import math
from numpy import log as ln
# Define the size of map
mapWidth = 200
mapHeight = 100
def convert(latitude, longitude):
# get x value
x = (longitude + 180) * (mapWidth / 360)
# convert from degrees to radians
latRad = (latitude * math.pi) / 180
# get y value
mercN = ln(math.tan((math.pi / 4) + (latRad / 2)))
y = (mapHeight / 2) - (mapWidth * mercN / (2 * math.pi))
return x, y
print(convert(41.145556, 121.2322))
Answer:
(167.35122222222225, 24.877939817552335)

public static String getTileNumber(final double lat, final double lon, final int zoom) {
int xtile = (int)Math.floor( (lon + 180) / 360 * (1<<zoom) ) ;
int ytile = (int)Math.floor( (1 - Math.log(Math.tan(Math.toRadians(lat)) + 1 / Math.cos(Math.toRadians(lat))) / Math.PI) / 2 * (1<<zoom) ) ;
if (xtile < 0)
xtile=0;
if (xtile >= (1<<zoom))
xtile=((1<<zoom)-1);
if (ytile < 0)
ytile=0;
if (ytile >= (1<<zoom))
ytile=((1<<zoom)-1);
return("" + zoom + "/" + xtile + "/" + ytile);
}
}

I'm new here, just to write, as I've been following the community for some years. I'm happy to be able to contribute.
Well, it took me practically a day in search of that and your question encouraged me to continue the search.
I arrived at the following function, which works! Credits for this article: https://towardsdatascience.com/geotiff-coordinate-querying-with-javascript-5e6caaaf88cf
var bbox = [minLong, minLat, maxLong, maxLat];
var pixelWidth = mapWidth;
var pixelHeight = mapHeight;
var bboxWidth = bbox[2] - bbox[0];
var bboxHeight = bbox[3] - bbox[1];
var convertToXY = function(latitude, longitude) {
var widthPct = ( longitude - bbox[0] ) / bboxWidth;
var heightPct = ( latitude - bbox[1] ) / bboxHeight;
var x = Math.floor( pixelWidth * widthPct );
var y = Math.floor( pixelHeight * ( 1 - heightPct ) );
return { x, y };
}