From c7c5df713443834c69c4c6d417a7feed69a35c7a Mon Sep 17 00:00:00 2001 From: McBen Date: Tue, 10 Jun 2014 17:37:11 +0200 Subject: [PATCH] cross-links: replaced intersection approximation (inside polygons has to be rewritten) --- plugins/cross_link.user.js | 191 ++++++++++++++++++++++++------------- 1 file changed, 126 insertions(+), 65 deletions(-) diff --git a/plugins/cross_link.user.js b/plugins/cross_link.user.js index a6b304dd..f120dffc 100644 --- a/plugins/cross_link.user.js +++ b/plugins/cross_link.user.js @@ -25,52 +25,113 @@ window.plugin.crossLinks.STYLE_LINECOLLISION = {color: '#f22', weight: 4}; window.plugin.crossLinks.STYLE_INSIDEPOLY = {color: '#ff2', weight: 4}; -function relativeCCW(x1,y1,x2,y2, px, py) { - // code from java.awt - x2 -= x1; - y2 -= y1; - px -= x1; - py -= y1; +// Great Circle Arc Intersection +// http://geospatialmethods.org/spheres/GCAIntersect.html +function intersect(a, b) { + var PI = Math.PI, + radians = PI / 180, + ε = 1e-6; - var ccw = px * y2 - py * x2; + var λ0 = a[0][0], + λ1 = a[1][0], + λ2 = b[0][0], + λ3 = b[1][0], + δλ0 = λ1 - λ0, + δλ1 = λ3 - λ2, + aδλ0 = Math.abs(δλ0), + aδλ1 = Math.abs(δλ1), + sλ0 = aδλ0 > 180, + sλ1 = aδλ1 > 180, + φ0 = a[0][1] * radians, + φ1 = a[1][1] * radians, + φ2 = b[0][1] * radians, + φ3 = b[1][1] * radians, + t; - if (ccw == 0.0) { - ccw = px * x2 + py * y2; + // Ensure λ0 ≤ λ1 and λ2 ≤ λ3. + if (δλ0 < 0) t = λ0, λ0 = λ1, λ1 = t, t = φ0, φ0 = φ1, φ1 = t; + if (δλ1 < 0) t = λ2, λ2 = λ3, λ3 = t, t = φ2, φ2 = φ3, φ3 = t; - if (ccw > 0.0) { - px -= x2; - py -= y2; - ccw = px * x2 + py * y2; + // Check if longitude ranges overlap. + // TODO handle antimeridian crossings. + if (!sλ0 && !sλ1 && (λ0 > λ3 || λ2 > λ1)) return; - if (ccw < 0.0) { - ccw = 0.0; - } - } - } - return (ccw < 0.0) ? -1 : ((ccw > 0.0) ? 1 : 0); - } + // Check for polar endpoints. + if (Math.abs(Math.abs(φ0) - PI / 2) < ε) λ0 = λ1, aδλ0 = δλ0 = 0, sλ0 = false; + if (Math.abs(Math.abs(φ1) - PI / 2) < ε) λ1 = λ0, aδλ0 = δλ0 = 0, sλ0 = false; + if (Math.abs(Math.abs(φ2) - PI / 2) < ε) λ2 = λ3, aδλ1 = δλ1 = 0, sλ1 = false; + if (Math.abs(Math.abs(φ3) - PI / 2) < ε) λ3 = λ2, aδλ1 = δλ1 = 0, sλ1 = false; -function linesIntersect(x1,y1,x2,y2,x3,y3,x4,y4) { - // code from java.awt - return ( (relativeCCW(x1, y1, x2, y2, x3, y3) * relativeCCW(x1, y1, x2, y2, x4, y4) <= 0) - && (relativeCCW(x3, y3, x4, y4, x1, y1) * relativeCCW(x3, y3, x4, y4, x2, y2) <= 0)); + // Check for arcs along meridians. + var m0 = aδλ0 < ε || Math.abs(aδλ0 - 180) < ε, + m1 = aδλ1 < ε || Math.abs(aδλ1 - 180) < ε; + + 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. + + // 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; + + // 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); + + n1x /= m, n1y /= m, n1z /= m; + + var Nx = n0y * n1z - n0z * n1y, + Ny = n0z * n1x - n0x * n1z, + Nz = n0x * n1y - n0y * n1x; + + if (length(Nx, Ny, Nz) < ε) return; + + var λ = Math.atan2(Ny, Nx); + if ((sλ0 ^ (λ0 <= λ && λ <= λ1) || m0 && Math.abs(λ - λ0) < ε) && (sλ1 ^ (λ2 <= λ && λ <= λ3) || m1 && Math.abs(λ - λ2) < ε) || (Nz = -Nz, + (sλ0 ^ (λ0 <= (λ = (λ + 2 * PI) % (2 * PI) - PI) && λ <= λ1) || m0 && Math.abs(λ - λ0) < ε) && (sλ1 ^ (λ2 <= λ && λ <= λ3) || m1 && Math.abs(λ - λ2) < ε))) { + var φ = Math.asin(Nz / length(Nx, Ny, Nz)); + if (m0 || m1) { + if (m1) φ0 = φ2, φ1 = φ3, λ0 = λ2, λ1 = λ3, aδλ0 = aδλ1; + if (aδλ0 > ε) return φ0 + φ1 > 0 ^ φ < (Math.abs(λ - λ0) < ε ? φ0 : φ1) ? [λ / radians, φ / radians] : null; + // Ensure φ0 ≤ φ1. + if (φ1 < φ0) t = φ0, φ0 = φ1, φ1 = t; + return Math.abs(λ - (m0 ? λ0 : λ2)) < ε && φ0 <= φ && φ <= φ1 ? [λ / radians, φ / radians] : null; + } + return [λ / radians, φ / radians]; + } } -function isCrossing(p1,p2,q1,q2) { - return linesIntersect( p1.lat,p1.lng,p2.lat,p2.lng, - q1.lat,q1.lng,q2.lat,q2.lng); +function length(x, y, z) { + return Math.sqrt(x * x + y * y + z * z); } -window.plugin.crossLinks.testLine = function (drawline, link) { +window.plugin.crossLinks.testPolyLine = function (polyline, link) { + var a= [[link[0].lat,link[0].lng],[link[1].lat,link[1].lng]]; + for (var i=0;i