diff --git a/plugins/cross_link.user.js b/plugins/cross_link.user.js index 47cf87f3..87ce141e 100644 --- a/plugins/cross_link.user.js +++ b/plugins/cross_link.user.js @@ -2,7 +2,7 @@ // @id iitc-plugin-cross-links@mcben // @name IITC plugin: cross links // @category Layer -// @version 1.0.0.@@DATETIMEVERSION@@ +// @version 1.1.0.@@DATETIMEVERSION@@ // @namespace https://github.com/jonatkins/ingress-intel-total-conversion // @updateURL @@UPDATEURL@@ // @downloadURL @@DOWNLOADURL@@ @@ -21,115 +21,100 @@ window.plugin.crossLinks = function() {}; -/* Great Circle Arc Intersection - Conecpt in short: - - build a plane of each arc (p1,p2,center) - - find intersection line and intersection points on sphere - - check if a point are on both arcs - see: http://geospatialmethods.org/spheres/GCAIntersect.html -*/ -var PI = Math.PI; -var radians = PI / 180; -var near_0 = 1e-6; -function greatCircleArcIntersect(a0,a1,b0,b1) { +window.plugin.crossLinks.greatCircleArcIntersect = function(a0,a1,b0,b1) { + // based on the formula at http://williams.best.vwh.net/avform.htm#Int - function length(x, y, z) { - return Math.sqrt(x * x + y * y + z * z); - } + // method: + // check to ensure no line segment is zero length - if so, cannot cross + // check to see if either of the lines start/end at the same point. if so, then they cannot cross + // check to see if the line segments overlap in longitude. if not, no crossing + // if overlap, clip each line to the overlapping longitudes, then see if latitudes cross - // Order points - if (a1.lat < a0.lat) { var t=a1;a1=a0;a0=t;} - if (b1.lat < b0.lat) { var t=b1;b1=b0;b0=t;} + // anti-meridian handling. this code will not sensibly handle a case where one point is + // close to -180 degrees and the other +180 degrees. unwrap coordinates in this case, so one point + // is beyond +-180 degrees. this is already true in IITC + // FIXME? if the two lines have been 'unwrapped' differently - one positive, one negative - it will fail - var λ0 = a0.lat, - λ1 = a1.lat, - λ2 = b0.lat, - λ3 = b1.lat, - δλ0 = λ1 - λ0, - δλ1 = λ3 - λ2, - sλ0 = δλ0 > 180, - sλ1 = δλ1 > 180, - φ0 = a0.lng * radians, - φ1 = a1.lng * radians, - φ2 = b0.lng * radians, - φ3 = b1.lng * radians, - t; + // zero length line tests + if (a0.equals(a1)) return false; + if (b0.equals(b1)) return false; - // Check if longitude ranges overlap. - // TODO handle antimeridian crossings. - if (!sλ0 && !sλ1 && (λ0 > λ3 || λ2 > λ1)) return; + // lines have a common point + if (a0.equals(b0) || a0.equals(b1)) return false; + if (a1.equals(b0) || a1.equals(b1)) return false; - // Check for polar endpoints. - if (Math.abs(Math.abs(φ0) - PI / 2) < near_0) λ0 = λ1, δλ0 = 0, sλ0 = false; - if (Math.abs(Math.abs(φ1) - PI / 2) < near_0) λ1 = λ0, δλ0 = 0, sλ0 = false; - if (Math.abs(Math.abs(φ2) - PI / 2) < near_0) λ2 = λ3, δλ1 = 0, sλ1 = false; - if (Math.abs(Math.abs(φ3) - PI / 2) < near_0) λ3 = λ2, δλ1 = 0, sλ1 = false; - // Check for arcs along meridians. - var m0 = δλ0 < near_0 || Math.abs(δλ0 - 180) < near_0, - m1 = δλ1 < near_0 || Math.abs(δλ1 - 180) < near_0; + // check for 'horizontal' overlap in lngitude + if (Math.min(a0.lng,a1.lng) > Math.max(b0.lng,b1.lng)) return false; + if (Math.max(a0.lng,a1.lng) < Math.min(b0.lng,b1.lng)) return false; - λ0 *= radians, λ1 *= radians, λ2 *= radians, λ3 *= radians; - // Intersect two great circles and check the two intersection points against - // the longitude ranges. The intersection points are simply the cross - // product of the great-circle normals ±n1⨯n2. + // ok, our two lines have some horizontal overlap in longitude + // 1. calculate the overlapping min/max longitude + // 2. calculate each line latitude at each point + // 3. if latitudes change place between overlapping range, the lines cross - // First plane. - var cosφ, - x0 = (cosφ = Math.cos(φ0)) * Math.cos(λ0), - y0 = cosφ * Math.sin(λ0), - z0 = Math.sin(φ0), - x1 = (cosφ = Math.cos(φ1)) * Math.cos(λ1), - y1 = cosφ * Math.sin(λ1), - z1 = Math.sin(φ1), - n0x = y0 * z1 - z0 * y1, - n0y = z0 * x1 - x0 * z1, - n0z = x0 * y1 - y0 * x1, - m = length(n0x, n0y, n0z); - n0x /= m, n0y /= m, n0z /= m; + // class to hold the pre-calculated maths for a geodesic line + // TODO: move this outside this function, so it can be pre-calculated once for each line we test + var GeodesicLine = function(start,end) { + var R = 6378137; // earth radius in meters (doesn't have to be exact) + var d2r = Math.PI/180.0; + var r2d = 180.0/Math.PI; - // Second plane. - var x2 = (cosφ = Math.cos(φ2)) * Math.cos(λ2), - y2 = cosφ * Math.sin(λ2), - z2 = Math.sin(φ2), - x3 = (cosφ = Math.cos(φ3)) * Math.cos(λ3), - y3 = cosφ * Math.sin(λ3), - z3 = Math.sin(φ3), - n1x = y2 * z3 - z2 * y3, - n1y = z2 * x3 - x2 * z3, - n1z = x2 * y3 - y2 * x3, - m = length(n1x, n1y, n1z); + // maths based on http://williams.best.vwh.net/avform.htm#Int - n1x /= m, n1y /= m, n1z /= m; + // only the variables needed to calculate a latitude for a given longitude are stored in 'this' + var lat1 = start.lat * d2r; + var lat2 = end.lat * d2r; + this.lng1 = start.lng * d2r; + this.lng2 = end.lng * d2r; - var Nx = n0y * n1z - n0z * n1y, - Ny = n0z * n1x - n0x * n1z, - Nz = n0x * n1y - n0y * n1x; + var dLng = this.lng2-this.lng1; - if (length(Nx, Ny, Nz) < near_0) return; + var sinLat1 = Math.sin(lat1); + var sinLat2 = Math.sin(lat2); + var cosLat1 = Math.cos(lat1); + var cosLat2 = Math.cos(lat2); - var λ = Math.atan2(Ny, Nx); - if ( (sλ0 ^ (λ0 <= λ && λ <= λ1) || m0 && Math.abs(λ - λ0) < near_0) && (sλ1 ^ (λ2 <= λ && λ <= λ3) || m1 && Math.abs(λ - λ2) < near_0) || (Nz = -Nz, - (sλ0 ^ (λ0 <= (λ = (λ + 2 * PI) % (2 * PI) - PI) && λ <= λ1) || m0 && Math.abs(λ - λ0) < near_0) && (sλ1 ^ (λ2 <= λ && λ <= λ3) || m1 && Math.abs(λ - λ2) < near_0))) { + this.sinLat1CosLat2 = sinLat1*cosLat2; + this.sinLat2CosLat1 = sinLat2*cosLat1; - var φ = Math.asin(Nz / length(Nx, Ny, Nz)); + this.cosLat1CosLat2SinDLng = cosLat1*cosLat2*Math.sin(dLng); + } - if (m0 || m1) { - if (m1) φ0 = φ2, φ1 = φ3, λ0 = λ2, λ1 = λ3, δλ0 = δλ1; + GeodesicLine.prototype.latAtLng = function(lng) { + lng = lng * Math.PI / 180; //to radians - if (δλ0 > near_0) - return (φ0 + φ1 > 0 ^ φ < (Math.abs(λ - λ0) < near_0 ? φ0 : φ1)) ? [λ / radians, φ / radians] : null; + var lat = Math.atan ( (this.sinLat1CosLat2*Math.sin(this.lng2-lng) + this.sinLat2CosLat1*Math.sin(lng-this.lng1)) + / this.cosLat1CosLat2SinDLng); - // Ensure φ0 ≤ φ1. - if (φ1 < φ0) t = φ0, φ0 = φ1, φ1 = t; - return (Math.abs(λ - (m0 ? λ0 : λ2)) < near_0 && φ0 <= φ && φ <= φ1) ? [λ / radians, φ / radians] : null; - } + return lat * 180 / Math.PI; // return value in degrees + } - return [λ / radians, φ / radians]; - } + + // calculate the longitude of the overlapping region + var leftLng = Math.max( Math.min(a0.lng,a1.lng), Math.min(b0.lng,b1.lng) ); + var rightLng = Math.min( Math.max(a0.lng,a1.lng), Math.max(b0.lng,b1.lng) ); + + // prepare geodesic line maths + var aGeo = new GeodesicLine(a0,a1); + var bGeo = new GeodesicLine(b0,b1); + + // calculate the latitudes for each line at left + right points + var aLeftLat = aGeo.latAtLng(leftLng); + var aRightLat = aGeo.latAtLng(rightLng); + + var bLeftLat = bGeo.latAtLng(leftLng); + var bRightLat = bGeo.latAtLng(rightLng); + + // if both a are less or greater than both b, then lines do not cross + if (aLeftLat < bLeftLat && aRightLat < bRightLat) return false; + if (aLeftLat > bLeftLat && aRightLat > bRightLat) return false; + + // latitudes cross between left and right - so geodesic lines cross + return true; } @@ -140,11 +125,11 @@ window.plugin.crossLinks.testPolyLine = function (polyline, link,closed) { var b = polyline.getLatLngs(); for (var i=0;i