Finding a point exactly between two points on a map at a specific distance from one point

Question

I've been working on a mapping project and encountered a problem where I need to find a point exactly between two given points on a map, at a specific distance from one of the points. I've tried various approaches, but haven't been able to achieve the desired result.

I've researched and found a formula to calculate the distance between two points on the Earth's surface, and I've adjusted it accordingly. Now, I'm trying to use this formula to find a third point on the map that lies exactly between the two given points and is at a specific distance from one of them.

Here's what I've tried so far:

// Variable declare
let start_get_lat = 31.5387761;
let start_get_lng = 72.9696664;
let end_get_lat = 31.569235;
let end_get_lng = 72.983557;
let center = {lat: Number(start_get_lat), lng: Number(start_get_lng)};
let endLocation = {lat: Number(end_get_lat), lng: Number(end_get_lng)};

Calculate distance bw two points and

// calculate distance function 
const distance = calculateDistance(lat1, lon1, centerLat, centerLon);

Get point bwtween function and usage

function getPointBetween(startLat, startLng, endLat, endLng, distance) {
    const earthRadius = 6371000; // Earth's radius in meters

    // Convert latitudes and longitudes from degrees to radians
    const lat1 = startLat * Math.PI / 180;
    const lon1 = startLng * Math.PI / 180;
    const lat2 = endLat * Math.PI / 180;
    const lon2 = endLng * Math.PI / 180;

    // Calculate the angular distance between the points
    const delta = distance / earthRadius;

    // Calculate the intermediate point
    const A = Math.sin((1 - delta) * Math.PI / 2) + Math.sin(delta * Math.PI / 2) * Math.cos(lat1) * Math.cos(lat2);
    const B = Math.sin(delta * Math.PI / 2) * Math.sin(lon2 - lon1) * Math.cos(lat2);
    const C = Math.atan2(B, A);
    const lat3 = Math.asin(A * Math.sin(lat1) + B * Math.sin(lat2)) * 180 / Math.PI;
    const lon3 = (lon1 + Math.atan2(Math.sin(lon2 - lon1) * Math.cos(lat2), Math.cos(lat1) * Math.sin(lat2) + Math.sin(lat1) * Math.cos(lat2) * Math.cos(lon2 - lon1))) * 180 / Math.PI;

    return { lat: lat3, lng: lon3 };
}

let anyDistance = distance - 1000;
const pointBetween = getPointBetween(start_get_lat, start_get_lng, end_get_lat, end_get_lng, anyDistance);
let bwMarker = new google.maps.Marker({
    position: pointBetween,
    map: map,
    title: "Center",
    fillColor: 'blue', //
});
console.log(pointBetween);

However, while this function returns a point between the two coordinates, it does not guarantee that the point lies exactly on the line segment between them at the specified distance. The goal is to achieve a precise displacement from one of the given points.

I'm looking for insights or alternative manual calculation methods to achieve this precise displacement between two coordinates without using google map, as I need a solution that can be implemented in both front-end and back-end environments.

Any suggestions or advice would be greatly appreciated. Thank you for your time and assistance!

Answer 1

Solution for Propagating Point on Google Maps

After some experimentation, I've found a simple and effective solution for propagating a point on Google Maps towards another point. Here's the JavaScript function I came up with:

function propagatePoint(latlng1, latlng2, distanceToPropagate, totalDistanceBwPoints) {
    let ratio = distanceToPropagate / totalDistanceBwPoints;
    let newLat = latlng1[0] + (latlng2[0] - latlng1[0]) * ratio;
    let newLng = latlng1[1] + (latlng2[1] - latlng1[1]) * ratio;
    return { lat: newLat, lng: newLng };
}

I've also improved the precision of the formula to enhance accuracy:

const totalDistanceBwPoints = calculateDistance(latlng1[0], latlng1[1], latlng2[0], latlng2[1]);

function calculateDistance(lat1, lon1, lat2, lon2) {
    const earthRadius = 6371; // Radius of the Earth in kilometers
    const dLat = toRadians(lat2 - lat1);
    const dLon = toRadians(lon2 - lon1);
    const a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
        Math.cos(toRadians(lat1)) * Math.cos(toRadians(lat2)) *
        Math.sin(dLon / 2) * Math.sin(dLon / 2);
    const c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
    const distance = earthRadius * c; // Distance in kilometers

    // Calculate the percentage
    const percentage = (distance * 0.11202322513989) / 100; // 0.1121% precision percentage

    // Add the percentage to the distance
    const distanceWithPercentage = distance + percentage;

    return (distanceWithPercentage * 1000).toFixed(4);
}

This function takes the latitude and longitude coordinates of two points (latlng1 and latlng2), along with the distance to propagate distanceToPropagate and the total distance between the points totalDistanceBwPoints. It then calculates the new coordinates of the propagated point.

I've tested this function, and it works perfectly for my use case, providing almost 99% accurate results. Thanks to everyone for their interest and support!