判断多边形与多边形是否相交的方法，代码来自于OpenLayers。

　　在做GIS开发时，常常需要用到空间判断的算法。比如：判断地图中的多边形与多边形是否相交。我在项目中具体的需求就是如此，需要过滤某个区域的瓦片地图。先把瓦片地图反向解析成Envolope，然后和该区域进行比对，再做其他处理。

　　其实在已经有开源的东西GDAL+GEOS可以使用，由于编译(nmake)GEOS对于C#程序员是一件不容易的事情。因为GEOS是C++实现的，网上虽然有别人已经编译好的DLL和LIB，但是始终不能引入到ASP.NET的项目中。没时间继续研究怎么把GEOS应用到C#项目中了，就选择了开源的JS框架OpenLayers。

　　OpenLayers中确实有我需要的几何判断的方法，所以就把它的代码剥离成一个JavaScript的函数。发博，以供有类似需求的童鞋使用。

//#region 验证两个面是否相交的算法
function intersectsPolygonAndPolygon (polygon1LinearRings, polygon2LinearRings) {

// polygon1LinearRings : array[LinearRing,...]
function intersectsByPolygon (polygon1LinearRings, polygon2LinearRings) {
var intersect = false;

intersect = intersectsByLinearRings(polygon1LinearRings, polygon2LinearRings);

if(!intersect) {
// check if this poly contains points of the ring/linestring
for(i=0, len=polygon2LinearRings.length; i<len; ++i) {
var point = polygon2LinearRings[i];
intersect = containsPointByLinearRing(point, polygon1LinearRings);
if(intersect) {
break;
}
}
}

return intersect;
}

// LinearRings
function containsPointByPolygon (point, LinearRings) {
var numRings = LinearRings.length;
var contained = false;
if(numRings > 0) {
contained = containsPointByLinearRing(point, LinearRings[0]);
if( numRings > 1) {
// check interior rings
var hole;
for(var i=1; i<numRings; ++i) {
hole = containsPointByLinearRing(point, LinearRings[i]);
if(hole) {
if(hole === 1) {
// on edge
contained = 1;
} else {
// in hole
contained = false;
}
break;
}
}
}
}
return contained;
}

// LinearRing : array[pt]
// point : {x:1,y:2}
function containsPointByLinearRing (point, LinearRing) {

//limitSigDigs
function approx(num, sig) {
var fig = 0;
if (sig > 0) {
fig = parseFloat(num.toPrecision(sig));
}
return fig;
}

var digs = 14;
var px = approx(point.x, digs);
var py = approx(point.y, digs);
function getX(y, x1, y1, x2, y2) {
return (y - y2) * ((x2 - x1) / (y2 - y1)) + x2;
}

var numSeg = LinearRing.length - 1;
var start, end, x1, y1, x2, y2, cx, cy;
var crosses = 0;

for(var i=0; i<numSeg; ++i) {
start = LinearRing[i];
x1 = approx(start.x, digs);
y1 = approx(start.y, digs);
end = LinearRing[i + 1];
x2 = approx(end.x, digs);
y2 = approx(end.y, digs);

if(y1 == y2) {
// horizontal edge
if(py == y1) {
// point on horizontal line
if(x1 <= x2 && (px >= x1 && px <= x2) || // right or vert
x1 >= x2 && (px <= x1 && px >= x2)) { // left or vert
// point on edge
crosses = -1;
break;
}
}
// ignore other horizontal edges
continue;
}
cx = approx(getX(py, x1, y1, x2, y2), digs);
if(cx == px) {
// point on line
if(y1 < y2 && (py >= y1 && py <= y2) || // upward
y1 > y2 && (py <= y1 && py >= y2)) { // downward
// point on edge
crosses = -1;
break;
}
}
if(cx <= px) {
// no crossing to the right
continue;
}
if(x1 != x2 && (cx < Math.min(x1, x2) || cx > Math.max(x1, x2))) {
// no crossing
continue;
}
if(y1 < y2 && (py >= y1 && py < y2) || // upward
y1 > y2 && (py < y1 && py >= y2)) { // downward
++crosses;
}
}

var contained = (crosses == -1) ?
// on edge
1 :
// even (out) or odd (in)
!!(crosses & 1);

return contained;
}

function intersectsByLinearRings (LinearRing1, LinearRings2) {
var intersect = false;
var segs1 = getSortedSegments(LinearRing1);
var segs2 = getSortedSegments(LinearRings2);

var seg1, seg1x1, seg1x2, seg1y1, seg1y2,
seg2, seg2y1, seg2y2;
// sweep right
outer: for(var i=0, len=segs1.length; i<len; ++i) {
seg1 = segs1[i];
seg1x1 = seg1.x1;
seg1x2 = seg1.x2;
seg1y1 = seg1.y1;
seg1y2 = seg1.y2;
inner: for(var j=0, jlen=segs2.length; j<jlen; ++j) {
seg2 = segs2[j];
if(seg2.x1 > seg1x2) {
// seg1 still left of seg2
break;
}
if(seg2.x2 < seg1x1) {
// seg2 still left of seg1
continue;
}
seg2y1 = seg2.y1;
seg2y2 = seg2.y2;
if(Math.min(seg2y1, seg2y2) > Math.max(seg1y1, seg1y2)) {
// seg2 above seg1
continue;
}
if(Math.max(seg2y1, seg2y2) < Math.min(seg1y1, seg1y2)) {
// seg2 below seg1
continue;
}
if(segmentsIntersect(seg1, seg2)) {
intersect = true;
break outer;
}
}
}
return intersect;
}

function getSortedSegments(points) {
var numSeg = points.length - 1;
var segments = new Array(numSeg), point1, point2;
for(var i=0; i<numSeg; ++i) {
point1 = points[i];
point2 = points[i + 1];
if(point1.x < point2.x) {
segments[i] = {
x1: point1.x,
y1: point1.y,
x2: point2.x,
y2: point2.y
};
} else {
segments[i] = {
x1: point2.x,
y1: point2.y,
x2: point1.x,
y2: point1.y
};
}
}
// more efficient to define this somewhere static
function byX1(seg1, seg2) {
return seg1.x1 - seg2.x1;
}
return segments.sort(byX1);
}

function segmentsIntersect(seg1, seg2, options) {
var point = options && options.point;
var tolerance = options && options.tolerance;
var intersection = false;
var x11_21 = seg1.x1 - seg2.x1;
var y11_21 = seg1.y1 - seg2.y1;
var x12_11 = seg1.x2 - seg1.x1;
var y12_11 = seg1.y2 - seg1.y1;
var y22_21 = seg2.y2 - seg2.y1;
var x22_21 = seg2.x2 - seg2.x1;
var d = (y22_21 * x12_11) - (x22_21 * y12_11);
var n1 = (x22_21 * y11_21) - (y22_21 * x11_21);
var n2 = (x12_11 * y11_21) - (y12_11 * x11_21);
if(d == 0) {
// parallel
if(n1 == 0 && n2 == 0) {
// coincident
intersection = true;
}
} else {
var along1 = n1 / d;
var along2 = n2 / d;
if(along1 >= 0 && along1 <= 1 && along2 >=0 && along2 <= 1) {
// intersect
if(!point) {
intersection = true;
} else {
// calculate the intersection point
var x = seg1.x1 + (along1 * x12_11);
var y = seg1.y1 + (along1 * y12_11);
intersection = { 'x':x, 'y':y };
}
}
}
if(tolerance) {
var dist;
if(intersection) {
if(point) {
var segs = [seg1, seg2];
var seg, x, y;
// check segment endpoints for proximity to intersection
// set intersection to first endpoint within the tolerance
outer: for(var i=0; i<2; ++i) {
seg = segs[i];
for(var j=1; j<3; ++j) {
x = seg["x" + j];
y = seg["y" + j];
dist = Math.sqrt(
Math.pow(x - intersection.x, 2) +
Math.pow(y - intersection.y, 2)
);
if(dist < tolerance) {
intersection.x = x;
intersection.y = y;
break outer;
}
}
}

}
} else {
// no calculated intersection, but segments could be within
// the tolerance of one another
var segs = [seg1, seg2];
var source, target, x, y, p, result;
// check segment endpoints for proximity to intersection
// set intersection to first endpoint within the tolerance
outer: for(var i=0; i<2; ++i) {
source = segs[i];
target = segs[(i+1)%2];
for(var j=1; j<3; ++j) {
p = {x: source["x"+j], y: source["y"+j]};
result = distanceToSegment(p, target);
if(result.distance < tolerance) {
if(point) {
intersection = { 'x':p.x, 'y':p.y };
} else {
intersection = true;
}
break outer;
}
}
}
}
}
return intersection;
};

function distanceToSegment(point, segment) {
var result = distanceSquaredToSegment(point, segment);
result.distance = Math.sqrt(result.distance);
return result;
};

function distanceSquaredToSegment(point, segment) {
var x0 = point.x;
var y0 = point.y;
var x1 = segment.x1;
var y1 = segment.y1;
var x2 = segment.x2;
var y2 = segment.y2;
var dx = x2 - x1;
var dy = y2 - y1;
var along = ((dx * (x0 - x1)) + (dy * (y0 - y1))) /
(Math.pow(dx, 2) + Math.pow(dy, 2));
var x, y;
if(along <= 0.0) {
x = x1;
y = y1;
} else if(along >= 1.0) {
x = x2;
y = y2;
} else {
x = x1 + along * dx;
y = y1 + along * dy;
}
return {
distance: Math.pow(x - x0, 2) + Math.pow(y - y0, 2),
x: x, y: y,
along: along
};
}

return intersectsByPolygon(polygon1LinearRings, polygon2LinearRings);
}
//#endregion

View Code



　　　　　　　　　　　　　　　　[图1] 相交的情况。



　　　　　　　　　　　　　　　　[图2] 不相交的情况。

本示例采用HTML+JAVASCRIPT编写，如需要源码请点击 例子 下载。