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I'm receiving all distances between a random number of points in a 2 dimensional coordinate system.
How can I visualize this as coordinates on a map in my browser?
In case there are many solutions I just want to see the first possible one that my algorithm can come up with.
So here's an extremely easy example:
PointCount = 3
Distances:
0-1 = 2
0-2 = 4
1-2 = 2
Does anyone know an easy way (existing solution/framework maybe) to do it using whatever is out there to make it easier to implement?
I was thinking maybe using the html canvas element for drawing, but I don't know how to create an algorithm that could come up with possible coordinates for those points.
The above example is simplified -
Real distance values could look like this:
(0) (1) (2) (3)
(0) 0 2344 3333 10000
(1) 0 3566 10333
(2) 0 12520
I'm not sure this is relevant for SO, but anyway...
The way to do this is quite simply to place the points one by one using the data:
Pick a random location for the first point (let's say it's 0,0).
The second point is on a circle with radius d(0,1) with the first point as its center, so you can pick any point on the circle. Let's pick (d(0,1),0).
The third point is at the intersection of a circle with radius d(0,2) and center point 1, and a circle with radius d(1,2) and center point 2. You will get either 0, 1, 2 or an infinity of solutions. If the data comes from real points, 0 shouldn't happen. 1 and infinity are edge cases, but you should still handle them. Pick any of the solutions.
The fourth point is at the intersection of 3 circles. Unless you're very unlucky (but you should account for it), there should be only one solution.
Continue like this until all points have been placed.
Note that this doesn't mean you'll get the exact locations of the original points: you can have any combination of a translation (the choice of your first point), rotation (the choice of your second point) and symmetry (the choice of your third point) making the difference.
A quick and dirty implementation (not handling quite a few cases, and tested very little):
function distance(p1, p2) {
return Math.sqrt(Math.pow(p2[0] - p1[0], 2) + Math.pow(p2[1] - p1[1], 2));
}
// adapted from https://stackoverflow.com/a/12221389/3527940
function intersection(x0, y0, r0, x1, y1, r1) {
var a, dx, dy, d, h, rx, ry;
var x2, y2;
/* dx and dy are the vertical and horizontal distances between
* the circle centers.
*/
dx = x1 - x0;
dy = y1 - y0;
/* Determine the straight-line distance between the centers. */
d = Math.sqrt((dy * dy) + (dx * dx));
/* Check for solvability. */
if (d > (r0 + r1)) {
/* no solution. circles do not intersect. */
return false;
}
if (d < Math.abs(r0 - r1)) {
/* no solution. one circle is contained in the other */
return false;
}
/* 'point 2' is the point where the line through the circle
* intersection points crosses the line between the circle
* centers.
*/
/* Determine the distance from point 0 to point 2. */
a = ((r0 * r0) - (r1 * r1) + (d * d)) / (2.0 * d);
/* Determine the coordinates of point 2. */
x2 = x0 + (dx * a / d);
y2 = y0 + (dy * a / d);
/* Determine the distance from point 2 to either of the
* intersection points.
*/
h = Math.sqrt((r0 * r0) - (a * a));
/* Now determine the offsets of the intersection points from
* point 2.
*/
rx = -dy * (h / d);
ry = dx * (h / d);
/* Determine the absolute intersection points. */
var xi = x2 + rx;
var xi_prime = x2 - rx;
var yi = y2 + ry;
var yi_prime = y2 - ry;
return [
[xi, yi],
[xi_prime, yi_prime]
];
}
function generateData(nbPoints) {
var i, j, k;
var originalPoints = [];
for (i = 0; i < nbPoints; i++) {
originalPoints.push([Math.random() * 20000 - 10000, Math.random() * 20000 - 10000]);
}
var data = [];
var distances;
for (i = 0; i < nbPoints; i++) {
distances = [];
for (j = 0; j < i; j++) {
distances.push(distance(originalPoints[i], originalPoints[j]));
}
data.push(distances);
}
//console.log("original points", originalPoints);
//console.log("distance data", data);
return data;
}
function findPointsForDistances(data, threshold) {
var points = [];
var solutions;
var solutions1, solutions2;
var point;
var i, j, k;
if (!threshold)
threshold = 0.01;
// First point, arbitrarily set at 0,0
points.push([0, 0]);
// Second point, arbitrarily set at d(0,1),0
points.push([data[1][0], 0]);
// Third point, intersection of two circles, pick any solution
solutions = intersection(
points[0][0], points[0][1], data[2][0],
points[1][0], points[1][1], data[2][1]);
//console.log("possible solutions for point 3", solutions);
points.push(solutions[0]);
//console.log("solution for points 1, 2 and 3", points);
found = true;
// Subsequent points, intersections of n-1 circles, use first two to find 2 solutions,
// the 3rd to pick one of the two
// then use others to check it's valid
for (i = 3; i < data.length; i++) {
// distances to points 1 and 2 give two circles and two possible solutions
solutions = intersection(
points[0][0], points[0][1], data[i][0],
points[1][0], points[1][1], data[i][1]);
//console.log("possible solutions for point " + (i + 1), solutions);
// try to find which solution is compatible with distance to point 3
found = false;
for (j = 0; j < 2; j++) {
if (Math.abs(distance(solutions[j], points[2]) - data[i][2]) <= threshold) {
point = solutions[j];
found = true;
break;
}
}
if (!found) {
console.log("could not find solution for point " + (i + 1));
console.log("distance data", data);
console.log("solution for points 1, 2 and 3", points);
console.log("possible solutions for point " + (i + 1), solutions);
console.log("distances to point 3",
distance(solutions[0], points[2]),
distance(solutions[1], points[2]),
data[i][2]
);
break;
}
// We have found a solution, we need to check it's valid
for (j = 3; j < i; j++) {
if (Math.abs(distance(point, points[j]) - data[i][j]) > threshold) {
console.log("Could not verify solution", point, "for point " + (i + 1) + " against distance to point " + (j + 1));
found = false;
break;
}
}
if (!found) {
console.log("stopping");
break;
}
points.push(point);
}
if (found) {
//console.log("complete solution", points);
return points;
}
}
console.log(findPointsForDistances([
[],
[2344],
[3333, 3566],
[10000, 10333, 12520],
]));
console.log(findPointsForDistances([
[],
[2],
[4, 2],
]));
console.log(findPointsForDistances([
[],
[4000],
[5000, 3000],
[3000, 5000, 4000]
]));
console.log(findPointsForDistances([
[],
[2928],
[4938, 3437],
[10557, 10726, 13535]
]));
var nbPoints, i;
for (nbPoints = 4; nbPoints < 8; nbPoints++) {
for (i = 0; i < 10; i++) {
console.log(findPointsForDistances(generateData(nbPoints)));
}
}
Fiddle here: https://jsfiddle.net/jacquesc/82aqmpnb/15/
Minimum working example. Remember that in canvas coordinates, the y value is inverted but you could do something like:
y = canvasHeight - y
If you also have negative points then if would take a little bit of extra work. Also it may be helpful in that case to draw lines and tick marks to visualize the axis.
let canvas = document.getElementById("canvas");
let ctx = canvas.getContext("2d");
let scale = 10;
let radius = 10;
function point(x, y) {
ctx.fillRect(x*scale, y*scale, radius, radius);
}
// test
point(10, 15);
point(20, 8);
<html>
<body>
<canvas id="canvas" width=1000 height=1000></canvas>
</body>
</html>
There are plenty of libraries out there.
chartist.js is easy to use and responsive JavaS cript library. I used it last year for basic charts after trying many others but it was the only one that scaling easily in different screen sizes.
chartJS is another better looking library.
And you can use html5 canvas it's easy and fun but it will take time especially in scaling.
To scale and position, you should use the minimum and maximum values for x and y.
Good luck
I've been trying to implement collision detection between circles and polygons based on Randy Gaul's C++ Impulse Engine, following the code pretty closely, but the algorithm never returns true.
Here's the JSFiddle. (the bodies are rendered using the HTML5 Canvas API for convenience)
A snippet of the code (just collision detection):
const circPoly = (a, b) => {
let data = {},
center = a.pos;
data.contacts = [];
center = b.mat.clone().trans().mult(center.clone().sub(b.pos));
let sep = -Number.MAX_VALUE,
faceNorm = 0;
for (let i = 0; i < b.verts2.length; ++i) {
let sep2 = b.norms[i].dot(center.clone().sub(b.verts2[i]));
if (sep2 > a.radius) return data;
if (sep2 > sep) { sep = sep2; faceNorm = i; }
}
let v1 = b.verts2[faceNorm],
v2 = b.verts2[faceNorm + 1 < b.verts2.length ? faceNorm + 1 : 0];
if (sep < 0.0001) {
data.depth = a.radius;
data.norm = b.mat.clone().mult(b.norms[faceNorm]).neg();
data.contacts[0] = data.norm.clone().vmult(a.pos.clone().sadd(a.radius));
return data;
}
let dot1 = center.clone().sub(v1).dot(v2.clone().sub(v1)),
dot2 = center.clone().sub(v2).dot(v1.clone().sub(v2));
data.depth = a.radius - sep;
if (dot1 <= 0) {
if (center.dist2(v1) > a.radius * a.radius) return data;
let norm = v1.clone().sub(center);
norm = b.mat.clone().mult(norm);
norm.norm();
data.norm = norm;
v1 = b.mat.clone().mult(v1.clone().add(b.pos));
data.contacts[0] = v1;
} else if (dot2 <= 0) {
if (center.dist2(v2) > a.radius * a.radius) return data;
let norm = v2.clone().sub(center);
norm = b.mat.clone().mult(norm);
norm.norm();
data.norm = norm;
v2 = b.mat.clone().mult(v2.clone().add(b.pos));
data.contacts[0] = v2;
} else {
let norm = b.norms[faceNorm];
if (center.clone().sub(v1).dot(norm) > a.radius) return data;
norm = b.mat.clone().mult(norm);
data.norm = norm.clone().neg();
data.contacts[0] = data.norm.clone().vmult(a.pos.clone().sadd(a.radius));
}
return data;
};
Note that b.verts2 refers to the polygon's vertices in real world coordinates.
I know for a fact that there are no problems with the Vector class but as I don't exactly have very much experience with transformation matrices, that class could be the root of these errors, although the code for it is pretty much entirely derived from the Impulse Engine as well, so it should work. As mentioned before, the algorithm always returns false, even when a collision really has occurred. What am I doing wrong here? I tried taking out the early returns, but that just returns weird results like contact points with negative coordinates which obviously is not quite correct.
EDIT: Modified my vector class's perpendicular function to work the same way as the Impulse Engine's (both ways are right, but I think one is clockwise and the other one counterclockwise -- I also modified my vertices to reflect the counterclockwise-ness). Unfortunately, it still fails the test.
https://jsfiddle.net/khanfused/tv359kgL/4/
Well the are many problems and I really dont understand what you are trying to do as it seem overly complex. Eg why does matrix have trans??? and why are you using the Y up screen as the coordinate system for the transform??? (rhetorical)
In the first loop.
The first is that you are testing the distance of the normal vectors
of each vert, should be testing the vert position.
Also you are finding the distance using the vec.dot function that
returns the square of the distance. But you test for the radius, you
should be testing for if(sep2 < radius * radius)
And you have the comparison the wrong way around you should be
testing if less than radius squared (not greater than)
Then when you do detect a vert within the radius you return the data
object but forget to put the vert that was found inside the circle on
the data.contacts array.
I am not sure what the intention of keeping the index of the most
distant vect is but then the rest of the function make zero sense to
me???? :( and I have tried to understand it.
All you need to do is
A check if any verts on the poly are closer than radius, if so then you have a intercept (or is completely inside)
Then you need to check the distance of each line segment
Can be done for each line segment with the following if you dont need the intercepts (or below that if you need intercepts) only use one or the other.
// circle is a point {x:?,y:?}
// radius = is the you know what
// p1,p2 are the start and end points of a line
checkLineCircle = function(circle,radius,p1,p2){
var v1 = {};
var v2 = {};
var v3 = {};
var u;
// get dist to end of line
v2.x = circle.x - p1.x;
v2.y = circle.y - p1.y;
// check if end points are inside the circle
if( Math.min(
Math.hypot(p2.x - circle.x, p2.y - circle.y),
Math.hypot(v2.x, v2.y)
) <= radius){
return true;
}
// get the line as a vector
v1.x = p2.x - p1.x;
v1.y = p2.y - p1.y;
// get the unit distance of the closest point on the line
u = (v2.x * v1.x + v2.y * v1.y)/(v1.y * v1.y + v1.x * v1.x);
// is this on the line segment
if(u >= 0 && u <= 1){
v3.x = v1.x * u; // get the point on the line segment
v3.y = v1.y * u;
// get the distance to that point and return true or false depending on the
// it being inside the circle
return (Math.hypot(v3.y - v2.y, v3.x - v2.x) <= radius);
}
return false; // no intercept
}
Do that for each line.To save time transform the circle center to the polygon local, rather than transform each point on the poly.
If you need the points of intercept then use the following function
// p1,p2 are the start and end points of a line
// returns an array empty if no points found or one or two points depending on the number of intercepts found
// If two points found the first point in the array is the point closest to the line start (p1)
function circleLineIntercept(circle,radius,p1,p2){
var v1 = {};
var v2 = {};
var ret = [];
var u1,u2,b,c,d;
// line as vector
v1.x = p2.x - p1.x;
v1.y = p2.y - p1.y;
// vector to circle center
v2.x = p1.x - circle.x;
v2.y = p1.y - circle.y;
// dot of line and circle
b = (v1.x * v2.x + v1.y * v2.y) * -2;
// length of line squared * 2
c = 2 * (v1.x * v1.x + v1.y * v1.y);
// some math to solve the two triangles made by the intercept points, the circle center and the perpendicular line to the line.
d = Math.sqrt(b * b - 2 * c * (v2.x * v2.x + v2.y * v2.y - radius * radius));
// will give a NaN if no solution
if(isNaN(d)){ // no intercept
return ret;
}
// get the unit distance of each intercept to the line
u1 = (b - d) / c;
u2 = (b + d) / c;
// check the intercept is on the line segment
if(u1 <= 1 && u1 >= 0){
ret.push({x:line.p1.x + v1.x * u1, y : line.p1.y + v1.y * u1 });
}
// check the intercept is on the line segment
if(u2 <= 1 && u2 >= 0){
ret.push({x:line.p1.x + v1.x * u2, y : line.p1.y + v1.y * u2});
}
return ret;
}
I will leave it up to you to do the polygon iteration.
Currently the formula I am using is below, but it is less accurate as the Vincenty formula, which you can find on this link:
http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html
My question is, can someone help simplify the javascript code so i can implement it in my formula? I am trying to learn javascript but it is a bit beyond my capabilities.
ex = lat2
ey = lon2
Im thinking the easiest way would be to run through the code and do an array of 360 degrees to calculate the ex/ey coordinates.
<script type="text/javascript">
function drawCircle(point, radius, dir, addtoBounds) {
var d2r = Math.PI / 180; // degrees to radians
var r2d = 180 / Math.PI; // radians to degrees
var earthsradius = 6378137;
var points = 360;
// find the radius in lat/lon
var rlat = (radius / earthsradius) * r2d;
var rlng = rlat / Math.cos(point.lat() * d2r);
var extp = new Array();
if (dir==1) {var start=0;var end=points+1} // one extra here makes sure we connect the
else {var start=points+1;var end=0}
for (var i=start; (dir==1 ? i < end : i > end); i=i+dir)
{
var theta = Math.PI * (i / (points/2));//i is number of points + 1
var lat1=point.lat()*d2r;
var lon1=point.lng()*d2r;
var d=radius;
var R=earthsradius;
var ex = Math.asin( Math.sin(lat1)*Math.cos(d/R) +
Math.cos(lat1)*Math.sin(d/R)*Math.cos(theta));
var ey = lon1 + Math.atan2(Math.sin(theta)*Math.sin(d/R)*Math.cos(lat1),
Math.cos(d/R)-Math.sin(lat1)*Math.sin(ex));
extp.push(new google.maps.LatLng(ex*r2d, ey*r2d));
if (addtoBounds) bounds.extend(extp[extp.length-1]);
}
// alert(extp.length);
return extp;
}
Here is the direct formula converted to php. I am trying to put this code into the google maps code. The movable type link actually has this code in javascript, but since I know php much better, I converted it over to test it out, this works perfectly.
<?php
$lat1 = 29.10860062;
$lon1 = -95.46209717;
$a = 6378137;
$b = 6356752.314245;
$f = 1/298.257223563; // WGS-84 ellipsoid params
$brng = 32.8;
$s = 1796884.48;
$alpha1 = deg2rad($brng);
$sinAlpha1 = sin($alpha1);
$cosAlpha1 = cos($alpha1);
$tanU1 = (1-$f) * tan(deg2rad($lat1));
$cosU1 = 1 / sqrt((1 + pow($tanU1,2)));
$sinU1 = $tanU1*$cosU1;
$sigma1 = atan2($tanU1, $cosAlpha1);
$sinAlpha = $cosU1 * $sinAlpha1;
$cosSqAlpha = 1 - pow($sinAlpha,2);
$uSq = $cosSqAlpha * (pow($a,2) - pow($b,2)) / (pow($b,2));
$A = 1 + $uSq/16384*(4096+$uSq*(-768+$uSq*(320-175*$uSq)));
$B = $uSq/1024 * (256+$uSq*(-128+$uSq*(74-47*$uSq)));
$sigma = $s / ($b*$A);
$sigmaP = 2*pi;
$limit = 100;
$counter = 1;
while ( $counter <= $limit ) {
$cos2SigmaM = cos(2*$sigma1 + $sigma);
$sinSigma = sin($sigma);
$cosSigma = cos($sigma);
$deltaSigma = $B*$sinSigma*($cos2SigmaM+$B/4*($cosSigma*(-1+2*pow($cos2SigmaM,2))-$B/6*$cos2SigmaM*(-3+4*pow($sinSigma,2))*(-3+4*pow($cos2SigmaM,2))));
$sigmaP = $sigma;
$sigma = $s / ($b*$A) + $deltaSigma;
$counter = $counter+1;
};
$tmp = $sinU1*$sinSigma - $cosU1*$cosSigma*$cosAlpha1;
$lat2 = atan2($sinU1*$cosSigma + $cosU1*$sinSigma*$cosAlpha1,(1-$f)*sqrt(pow($sinAlpha,2)+ pow($tmp,2)));
$lambda = atan2($sinSigma*$sinAlpha1, $cosU1*$cosSigma - $sinU1*$sinSigma*$cosAlpha1);
$C = $f/16*$cosSqAlpha*(4+$f*(4-3*$cosSqAlpha));
$L = $lambda - (1-$C) * $f * $sinAlpha *($sigma + $C*$sinSigma*($cos2SigmaM+$C*$cosSigma*(-1+2*pow($cos2SigmaM,2))));
if (deg2rad($lon1)+$L+(3*pi)<(2*pi)) {
( $lon2 = (deg2rad($lon1)+$L+(3*pi))-pi);
} else {
( $lon2 = ((deg2rad($lon1)+$L+3*pi))%(2*pi))-pi;}
$revAz = atan2($sinAlpha, -$tmp); // final bearing, if required
?>
Since the link you provided already provides the formula in javascript the hard part is complete, you can just copy it and call it rather than rewriting it into your function. Just remember to attribute the source. I removed the variables that were not being used. Also, I just hard coded 361 into the formula since you were just assigning it to a points variable. You can change this back if you are going to be passing the number of degrees into the formula. I separated the for loops, to me this is more readable, and I dont think the way you had before was working like you intended it. When working with degrees and radians I always wrap these conversions into functions since it improves readability. To do this I hooked them up to the Number object in JavaScript using prototype as seen here:
Number.prototype.toRad = function() {
//'this' is the current number the function is acting on.
//e.g. 360.toRad() == 2PI radians
return this * Math.PI / 180;
}
Number.prototype.toDeg = function() {
return this * 180 / Math.PI;
}
Not too tough to understand, prototype allows you to extend objects in JavaScript, similar to inheritance in class based languages. There are plenty of resources online that can help clarify.
Here is the reworked drawCircle function:
function drawCircle(point, radius, dir, addtoBounds) {
//best practice is to use [] rather then new Array(),
//both do the same thing.
var extp = [];
if (dir == 1) {
for (var i = 0; i < 361; i++) {
//destVincenty function returns a object with
//lat, lon, and final bearing.
var destPoint = destVincenty(point.lat(), point.lng(), i, radius);
//add new point
extp.push(new google.maps.LatLng(destPoint.lat, destPoint.lon));
if (addtoBounds) bounds.extend(extp[extp.length - 1]);
}
}
else {
for (var i = 361; i > 0; i--) {
var destPoint = destVincenty(point.lat(), point.lng(), i, radius);
extp.push(new google.maps.LatLng(destPoint.lat, destPoint.lon));
if (addtoBounds) bounds.extend(extp[extp.length - 1]);
}
}
return extp;
}
here is a fiddle of it working.
I am working on a sort of itinerary mapper for packaged vacations, and I'm really happy with what I've done so far; I have the directions api implemented with a custom renderer, so I can take driving directions, and plot my own polyline complete with directional arrows that aren't google's awful ones spaced along the path. I am not exactly a math expert, and I am trying to figure out how I could make a path parallel to another path. For example, the itinerary goes from city 1 to city 2, and then back to city 1.
I want to offset the trip back to city 1's polyline, so that it mirrors the path, but travels parallel to it. Ideally, I would like to when I create the path, check for intersecting points in other paths, and if any are found, offset the path at those points only. This would be a better implementation, because you could for instance parallel the path only where it happens to intersect another one, like when it meets another path only for a short time.
I found this code for API2 from bill chadwick
The link is here: http://wtp2.appspot.com/ParallelLines.htm
Update: Somehow managed to convert this old v2 script to get it working in v3, but I'm experiencing some troubles...
It is more than doubling the original number of points, and following the path, but really throwing them in randomly. Screenshot here:
The class I converted is here:
function BDCCParallelLines(points, color, weight, opacity, opts, gapPx) {
console.log('Pllel COnstructor Initialized');
this.gapPx = gapPx;
this.points = points;
this.color = color;
this.weight = weight;
this.opacity = opacity;
this.opts = opts;
this.line1 = null;
this.line2 = null;
this.lstnZoom = null;
}
BDCCParallelLines.prototype = new google.maps.OverlayView();
BDCCParallelLines.prototype.onAdd = function() {
console.log('Pllel Initialized');
this.prj = map.getProjection();
var self = this;
this.lstnZoom = google.maps.event.addListener(map, "zoom_changed", function() {
self.recalc();
});
this.recalc();//first draw
}
BDCCParallelLines.prototype.onRemove = function() {
if(this.line2)
this.line2.setMap(null);
if(this.line1)
this.line1.setMap(null);
if(this.lstnZoom != null)
google.maps.event.removeListener(this.lstnZoom);
}
BDCCParallelLines.prototype.copy = function() {
return new BDCCParallelLines(this.points,this.color,this.weight,this.opacity,this.opts,this.gapPx);
}
BDCCParallelLines.prototype.draw = function(force) {
return; //do nothing
}
/**
* #param {google.maps.Map} map
* #param {google.maps.LatLng} latlng
* #param {int} z
* #return {google.maps.Point}
*/
BDCCParallelLines.prototype.latLngToPoint = function(latlng, z){
var normalizedPoint = map.getProjection().fromLatLngToPoint(latlng); // returns x,y normalized to 0~255
var scale = Math.pow(2, z);
var pixelCoordinate = new google.maps.Point(normalizedPoint.x * scale, normalizedPoint.y * scale);
return pixelCoordinate;
};
/**
* #param {google.maps.Map} map
* #param {google.maps.Point} point
* #param {int} z
* #return {google.maps.LatLng}
*/
BDCCParallelLines.prototype.pointToLatlng = function(point, z){
var scale = Math.pow(2, z);
var normalizedPoint = new google.maps.Point(point.x / scale, point.y / scale);
var latlng = map.getProjection().fromPointToLatLng(normalizedPoint);
return latlng;
};
BDCCParallelLines.prototype.recalc = function() {
var distallowance;
console.log('recalc called');
var zoom = map.getZoom();
distallowance = 1.6;
if(zoom > 6){
distallowance = 1.3;
if(zoom > 9){
distallowance = .7;
if( zoom > 13){
distallowance = .2;
if( zoom > 15){
distallowance = .0001;
}
}
}
}
console.log('Zoom Level: ' + zoom);
console.log('Allowance = ' + distallowance);
var pts1 = new Array();//left side of center
//shift the pts array away from the centre-line by half the gap + half the line width
var o = (this.gapPx + this.weight)/2;
var p2l,p2r;
for (var i=1; i<this.points.length; i++){
var p1lm1;
var p1rm1;
var p2lm1;
var p2rm1;
var thetam1;
var p1 = this.latLngToPoint(this.points[i-1], zoom)
var p2 = this.latLngToPoint(this.points[i], zoom)
var theta = Math.atan2(p1.x-p2.x,p1.y-p2.y);
theta = theta + (Math.PI/2);
var dl = Math.sqrt(((p1.x-p2.x)*(p1.x-p2.x))+((p1.y-p2.y)*(p1.y-p2.y)));
if(theta > Math.PI)
theta -= Math.PI*2;
var dx = Math.round(o * Math.sin(theta));
var dy = Math.round(o * Math.cos(theta));
var p1l = new google.maps.Point(p1.x+dx,p1.y+dy);
var p1r = new google.maps.Point(p1.x-dx,p1.y-dy);
p2l = new google.maps.Point(p2.x+dx,p2.y+dy);
p2r = new google.maps.Point(p2.x-dx,p2.y-dy);
if(i==1){ //first point
pts1.push(this.pointToLatlng(p1l,zoom));
}
else{ // mid this.points
if(distbetweentwo(this.points[i-1], this.points[i]) > distallowance){
if(theta == thetam1){
// adjacent segments in a straight line
pts1.push(this.pointToLatlng(p1l,zoom));
}
else{
var pli = this.intersect(p1lm1,p2lm1,p1l,p2l);
var pri = this.intersect(p1rm1,p2rm1,p1r,p2r);
var dlxi = (pli.x-p1.x);
var dlyi = (pli.y-p1.y);
var drxi = (pri.x-p1.x);
var dryi = (pri.y-p1.y);
var di = Math.sqrt((drxi*drxi)+(dryi*dryi));
var s = o / di;
var dTheta = theta - thetam1;
if(dTheta < (Math.PI*2))
dTheta += Math.PI*2;
if(dTheta > (Math.PI*2))
dTheta -= Math.PI*2;
if(dTheta < Math.PI){
//intersect point on outside bend
pts1.push(this.pointToLatlng(p2lm1,zoom));
pts1.push(this.pointToLatlng(new google.maps.Point(p1.x+(s*dlxi),p1.y+(s*dlyi)),zoom));
pts1.push(this.pointToLatlng(p1l,zoom));
}
else if (di < dl){
pts1.push(this.pointToLatlng(pli,zoom));
}
else{
pts1.push(this.pointToLatlng(p2lm1,zoom));
pts1.push(this.pointToLatlng(p1l,zoom));
}
}
}
else{
//console.log(distbetweentwo(this.points[i-1], this.points[i]));
}
}
p1lm1 = p1l;
p1rm1 = p1r;
p2lm1 = p2l;
p2rm1 = p2r;
thetam1 = theta;
//end loop
}
pts1.push(this.pointToLatlng(p2l,zoom));//final point
// console.log(pts1);
if(this.line1)
this.line1.setMap(null);
this.line1 = new google.maps.Polyline({
strokeColor: this.color,
strokeOpacity: this.opacity,
strokeWeight: this.weight,
map: map,
path: pts1 });
this.line1.setMap(map);
}
BDCCParallelLines.prototype.intersect = function(p0,p1,p2,p3)
{
// this function computes the intersection of the sent lines p0-p1 and p2-p3
// and returns the intersection point,
var a1,b1,c1, // constants of linear equations
a2,b2,c2,
det_inv, // the inverse of the determinant of the coefficient matrix
m1,m2; // the slopes of each line
var x0 = p0.x;
var y0 = p0.y;
var x1 = p1.x;
var y1 = p1.y;
var x2 = p2.x;
var y2 = p2.y;
var x3 = p3.x;
var y3 = p3.y;
// compute slopes, note the cludge for infinity, however, this will
// be close enough
if ((x1-x0)!=0)
m1 = (y1-y0)/(x1-x0);
else
m1 = 1e+10; // close enough to infinity
if ((x3-x2)!=0)
m2 = (y3-y2)/(x3-x2);
else
m2 = 1e+10; // close enough to infinity
// compute constants
a1 = m1;
a2 = m2;
b1 = -1;
b2 = -1;
c1 = (y0-m1*x0);
c2 = (y2-m2*x2);
// compute the inverse of the determinate
det_inv = 1/(a1*b2 - a2*b1);
// use Kramers rule to compute xi and yi
var xi=((b1*c2 - b2*c1)*det_inv);
var yi=((a2*c1 - a1*c2)*det_inv);
return new google.maps.Point(Math.round(xi),Math.round(yi));
}
This is working to a point... It is working as well as the original implementation. The entire path is recalculated on a zoom basis, and I kind of hacked the function to skip very short paths(weird angles) at higher zoom levels, it more closely follows the path the more you zoom in.
I would rather just have a fixed distance offset that is not recalculated, as it is pretty intensive... There are many programs which accomplish this feat, rhino3d, autocad, illustrator... I feel like it would be great for driving directions for google maps itself, an offsetting of the path so you can distinguish the return trip and the original trip.
If anybody has done anything similar to this in JS even if its not for google maps specifically, I would love to see it. Links I am investigating:
http://processingjs.nihongoresources.com/bezierinfo/
http://www.groupsrv.com/computers/about21532.html
Offsetting paths in general is a pretty tricky buisness. This paper (scientific paper alert) gives a good description of the steps taken for 'professional' offset algorithms.
http://cgcad.thss.tsinghua.edu.cn/~yongjh/papers/CiI2007V58N03P0240.pdf
You don't seem to want anything as fancy as in the demo. From what I gather you just want the same polyline, only shifted some pixels to the right and maybe some to the top so it doesn't overlap.
The code you posted has a latLngToPoint function and pointToLatLng function. I think the directions you get from Google are LatLng, so you can convert those to Points, increase the x and y property, and convert it back to a LatLng and draw your Polyline.
This should get you a line that exactly follows the original line. But, it wont look as fancy as the one in the demo. Since it wont be adding any points to smooth the line.
I am trying to create a Google Map where the user can plot the route he walked/ran/bicycled and see how long he ran. The GPolyline class with it’s getLength() method is very helpful in this regard (at least for Google Maps API V2), but I wanted to add markers based on distance, for example a marker for 1 km, 5 km, 10 km, etc., but it seems that there is no obvious way to find a point on a polyline based on how far along the line it is. Any suggestions?
Having answered a similar problem a couple of months ago on how to tackle this on the server-side in SQL Server 2008, I am porting the same algorithm to JavaScript using the Google Maps API v2.
For the sake of this example, let's use a simple 4-point polyline, with a total length of circa 8,800 meters. The snippet below will define this polyline and will render it on the map:
var map = new GMap2(document.getElementById('map_canvas'));
var points = [
new GLatLng(47.656, -122.360),
new GLatLng(47.656, -122.343),
new GLatLng(47.690, -122.310),
new GLatLng(47.690, -122.270)
];
var polyline = new GPolyline(points, '#f00', 6);
map.setCenter(new GLatLng(47.676, -122.343), 12);
map.addOverlay(polyline);
Now before we approach the actual algorithm, we will need a function that returns the destination point when given a start point, an end point, and the distance to travel along that line, Luckily, there are a few handy JavaScript implementations by Chris Veness at Calculate distance, bearing and more between Latitude/Longitude points.
In particular I have adapted the following two methods from the above source to work with Google's GLatLng class:
Destination point given distance and bearing from start point
Bearing
These were used to extend Google's GLatLng class with a method moveTowards(), which when given another point and a distance in meters, it will return another GLatLng along that line when the distance is travelled from the original point towards the point passed as a parameter.
GLatLng.prototype.moveTowards = function(point, distance) {
var lat1 = this.lat().toRad();
var lon1 = this.lng().toRad();
var lat2 = point.lat().toRad();
var lon2 = point.lng().toRad();
var dLon = (point.lng() - this.lng()).toRad();
// Find the bearing from this point to the next.
var brng = Math.atan2(Math.sin(dLon) * Math.cos(lat2),
Math.cos(lat1) * Math.sin(lat2) -
Math.sin(lat1) * Math.cos(lat2) *
Math.cos(dLon));
var angDist = distance / 6371000; // Earth's radius.
// Calculate the destination point, given the source and bearing.
lat2 = Math.asin(Math.sin(lat1) * Math.cos(angDist) +
Math.cos(lat1) * Math.sin(angDist) *
Math.cos(brng));
lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(angDist) *
Math.cos(lat1),
Math.cos(angDist) - Math.sin(lat1) *
Math.sin(lat2));
if (isNaN(lat2) || isNaN(lon2)) return null;
return new GLatLng(lat2.toDeg(), lon2.toDeg());
}
Having this method, we can now tackle the problem as follows:
Iterate through each point of the path.
Find the distance between the current point in the iteration to the next point.
If the distance in point 2 is greater the distance we need to travel on the path:
...then the destination point is between this point and the next. Simply apply the moveTowards() method to the current point, passing the next point and the distance to travel. Return the result and break the iteration.
Else:
...the destination point is further in the path from the next point in the iteration. We need to subtract the distance between this point and the next point from the total distance to travel along the path. Continue through the iteration with the modified distance.
You may have noticed that we can easily implement the above recursively, instead of iteratively. So let's do it:
function moveAlongPath(points, distance, index) {
index = index || 0; // Set index to 0 by default.
if (index < points.length) {
// There is still at least one point further from this point.
// Construct a GPolyline to use its getLength() method.
var polyline = new GPolyline([points[index], points[index + 1]]);
// Get the distance from this point to the next point in the polyline.
var distanceToNextPoint = polyline.getLength();
if (distance <= distanceToNextPoint) {
// distanceToNextPoint is within this point and the next.
// Return the destination point with moveTowards().
return points[index].moveTowards(points[index + 1], distance);
}
else {
// The destination is further from the next point. Subtract
// distanceToNextPoint from distance and continue recursively.
return moveAlongPath(points,
distance - distanceToNextPoint,
index + 1);
}
}
else {
// There are no further points. The distance exceeds the length
// of the full path. Return null.
return null;
}
}
With the above method, if we define an array of GLatLng points, and we invoke our moveAlongPath() function with this array of points and with a distance of 2,500 meters, it will return a GLatLng on that path at 2.5km from the first point.
var points = [
new GLatLng(47.656, -122.360),
new GLatLng(47.656, -122.343),
new GLatLng(47.690, -122.310),
new GLatLng(47.690, -122.270)
];
var destinationPointOnPath = moveAlongPath(points, 2500);
// destinationPointOnPath will be a GLatLng on the path
// at 2.5km from the start.
Therefore all we need to do is to call moveAlongPath() for each check point we need on the path. If you need three markers at 1km, 5km and 10km, you can simply do:
map.addOverlay(new GMarker(moveAlongPath(points, 1000)));
map.addOverlay(new GMarker(moveAlongPath(points, 5000)));
map.addOverlay(new GMarker(moveAlongPath(points, 10000)));
Note however that moveAlongPath() may return null if we request a check point further from the total length of the path, so it will be wiser to check for the return value before passing it to new GMarker().
We can put this together for the full implementation. In this example we are dropping a marker every 1,000 meters along the 8.8km path defined earlier:
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8"/>
<title>Google Maps - Moving point along a path</title>
<script src="http://maps.google.com/maps?file=api&v=2&sensor=false"
type="text/javascript"></script>
</head>
<body onunload="GUnload()">
<div id="map_canvas" style="width: 500px; height: 300px;"></div>
<script type="text/javascript">
Number.prototype.toRad = function() {
return this * Math.PI / 180;
}
Number.prototype.toDeg = function() {
return this * 180 / Math.PI;
}
GLatLng.prototype.moveTowards = function(point, distance) {
var lat1 = this.lat().toRad();
var lon1 = this.lng().toRad();
var lat2 = point.lat().toRad();
var lon2 = point.lng().toRad();
var dLon = (point.lng() - this.lng()).toRad();
// Find the bearing from this point to the next.
var brng = Math.atan2(Math.sin(dLon) * Math.cos(lat2),
Math.cos(lat1) * Math.sin(lat2) -
Math.sin(lat1) * Math.cos(lat2) *
Math.cos(dLon));
var angDist = distance / 6371000; // Earth's radius.
// Calculate the destination point, given the source and bearing.
lat2 = Math.asin(Math.sin(lat1) * Math.cos(angDist) +
Math.cos(lat1) * Math.sin(angDist) *
Math.cos(brng));
lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(angDist) *
Math.cos(lat1),
Math.cos(angDist) - Math.sin(lat1) *
Math.sin(lat2));
if (isNaN(lat2) || isNaN(lon2)) return null;
return new GLatLng(lat2.toDeg(), lon2.toDeg());
}
function moveAlongPath(points, distance, index) {
index = index || 0; // Set index to 0 by default.
if (index < points.length) {
// There is still at least one point further from this point.
// Construct a GPolyline to use the getLength() method.
var polyline = new GPolyline([points[index], points[index + 1]]);
// Get the distance from this point to the next point in the polyline.
var distanceToNextPoint = polyline.getLength();
if (distance <= distanceToNextPoint) {
// distanceToNextPoint is within this point and the next.
// Return the destination point with moveTowards().
return points[index].moveTowards(points[index + 1], distance);
}
else {
// The destination is further from the next point. Subtract
// distanceToNextPoint from distance and continue recursively.
return moveAlongPath(points,
distance - distanceToNextPoint,
index + 1);
}
}
else {
// There are no further points. The distance exceeds the length
// of the full path. Return null.
return null;
}
}
var map = new GMap2(document.getElementById('map_canvas'));
var points = [
new GLatLng(47.656, -122.360),
new GLatLng(47.656, -122.343),
new GLatLng(47.690, -122.310),
new GLatLng(47.690, -122.270)
];
var polyline = new GPolyline(points, '#f00', 6);
var nextMarkerAt = 0; // Counter for the marker checkpoints.
var nextPoint = null; // The point where to place the next marker.
map.setCenter(new GLatLng(47.676, -122.343), 12);
// Draw the path on the map.
map.addOverlay(polyline);
// Draw the checkpoint markers every 1000 meters.
while (true) {
// Call moveAlongPath which will return the GLatLng with the next
// marker on the path.
nextPoint = moveAlongPath(points, nextMarkerAt);
if (nextPoint) {
// Draw the marker on the map.
map.addOverlay(new GMarker(nextPoint));
// Add +1000 meters for the next checkpoint.
nextMarkerAt += 1000;
}
else {
// moveAlongPath returned null, so there are no more check points.
break;
}
}
</script>
</body>
</html>
Screenshot of the above example, showing a marker every 1,000 meters:
These are the prototypes for the required functions:
google.maps.Polygon.prototype.Distance = function() {
var dist = 0;
for (var i=1; i < this.getPath().getLength(); i++) {
dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i-1));
}
return dist;
}
google.maps.LatLng.prototype.distanceFrom = function(newLatLng) {
//var R = 6371; // km (change this constant to get miles)
var R = 6378100; // meters
var lat1 = this.lat();
var lon1 = this.lng();
var lat2 = newLatLng.lat();
var lon2 = newLatLng.lng();
var dLat = (lat2-lat1) * Math.PI / 180;
var dLon = (lon2-lon1) * Math.PI / 180;
var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
Math.cos(lat1 * Math.PI / 180 ) * Math.cos(lat2 * Math.PI / 180 ) *
Math.sin(dLon/2) * Math.sin(dLon/2);
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
var d = R * c;
return d;
}
source
Possibly the best approach would be to calculate where these points are.
As a basic algorithm you could iterate over all the points in the Polyline, and calculate the cumulative distance - if the next segment puts you over your distance, you can interpolate the point where the distance has been reached - then simply add a point of interest to your map for that.
I have used Martin Zeitler method to work with Google Map V3 and its working fine.
function init() {
var mapOptions = {
zoom: 15,
center: new google.maps.LatLng(-6.208437004433984, 106.84543132781982),
suppressInfoWindows: true,
};
// Get all html elements for map
var mapElement = document.getElementById('map1');
// Create the Google Map using elements
map = new google.maps.Map(mapElement, mapOptions);
var nextMarkerAt = 0; // Counter for the marker checkpoints.
var nextPoint = null; // The point where to place the next marker.
while (true) {
var routePoints = [ new google.maps.LatLng(47.656, -122.360),
new google.maps.LatLng(47.656, -122.343),
new google.maps.LatLng(47.690, -122.310),
new google.maps.LatLng(47.690, -122.270)];
nextPoint = moveAlongPath(routePoints, nextMarkerAt);
if (nextPoint) {
//Adding marker from localhost
MarkerIcon = "http://192.168.1.1/star.png";
var marker = new google.maps.Marker
({position: nextPoint,
map: map,
icon: MarkerIcon
});
// Add +1000 meters for the next checkpoint.
nextMarkerAt +=1000;
}
else {
// moveAlongPath returned null, so there are no more check points.
break;
}
}
}
Number.prototype.toRad = function () {
return this * Math.PI / 180;
}
Number.prototype.toDeg = function () {
return this * 180 / Math.PI;
}
function moveAlongPath(point, distance, index) {
index = index || 0; // Set index to 0 by default.
var routePoints = [];
for (var i = 0; i < point.length; i++) {
routePoints.push(point[i]);
}
if (index < routePoints.length) {
// There is still at least one point further from this point.
// Construct a GPolyline to use the getLength() method.
var polyline = new google.maps.Polyline({
path: [routePoints[index], routePoints[index + 1]],
strokeColor: '#FF0000',
strokeOpacity: 0.8,
strokeWeight: 2,
fillColor: '#FF0000',
fillOpacity: 0.35
});
// Get the distance from this point to the next point in the polyline.
var distanceToNextPoint = polyline.Distance();
if (distance <= distanceToNextPoint) {
// distanceToNextPoint is within this point and the next.
// Return the destination point with moveTowards().
return moveTowards(routePoints, distance,index);
}
else {
// The destination is further from the next point. Subtract
// distanceToNextPoint from distance and continue recursively.
return moveAlongPath(routePoints,
distance - distanceToNextPoint,
index + 1);
}
}
else {
// There are no further points. The distance exceeds the length
// of the full path. Return null.
return null;
}
}
function moveTowards(point, distance,index) {
var lat1 = point[index].lat.toRad();
var lon1 = point[index].lng.toRad();
var lat2 = point[index+1].lat.toRad();
var lon2 = point[index+1].lng.toRad();
var dLon = (point[index + 1].lng - point[index].lng).toRad();
// Find the bearing from this point to the next.
var brng = Math.atan2(Math.sin(dLon) * Math.cos(lat2),
Math.cos(lat1) * Math.sin(lat2) -
Math.sin(lat1) * Math.cos(lat2) *
Math.cos(dLon));
var angDist = distance / 6371000; // Earth's radius.
// Calculate the destination point, given the source and bearing.
lat2 = Math.asin(Math.sin(lat1) * Math.cos(angDist) +
Math.cos(lat1) * Math.sin(angDist) *
Math.cos(brng));
lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(angDist) *
Math.cos(lat1),
Math.cos(angDist) - Math.sin(lat1) *
Math.sin(lat2));
if (isNaN(lat2) || isNaN(lon2)) return null;
return new google.maps.LatLng(lat2.toDeg(), lon2.toDeg());
}
google.maps.Polyline.prototype.Distance = function () {
var dist = 0;
for (var i = 1; i < this.getPath().getLength(); i++) {
dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i - 1));
}
return dist;
}
google.maps.LatLng.prototype.distanceFrom = function (newLatLng) {
//var R = 6371; // km (change this constant to get miles)
var R = 6378100; // meters
var lat1 = this.lat();
var lon1 = this.lng();
var lat2 = newLatLng.lat();
var lon2 = newLatLng.lng();
var dLat = (lat2 - lat1) * Math.PI / 180;
var dLon = (lon2 - lon1) * Math.PI / 180;
var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
Math.cos(lat1 * Math.PI / 180) * Math.cos(lat2 * Math.PI / 180) *
Math.sin(dLon / 2) * Math.sin(dLon / 2);
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
var d = R * c;
return d;
}
I wanted to port Daniel Vassalo's answer to iOS, but it wasn't worked properly and some markers were misplaced until I changed
var dLon = (point.lng() - this.lng()).toRad();
to
var dLon = point.lng().toRad() - this.lng().toRad();
So if anyone having a trouble to figure out why are the markers are misplaced, try this and maybe it will help.