js 判断平面几何图形是否重叠

1. 点线面数据格式

• 点: { x: xxx, y: xxx }
• 线: [{ x: xxx, y: xxx }, { x: xxx, y: xxx }]
• 面: [{ x: xxx, y: xxx }, { x: xxx, y: xxx }, { x: xxx, y: xxx }...]

2. 重叠情况分析：无外乎相交与包含两种情况

(1 判断相交

//判断两多边形线段是否相交
function isSegmentsIntersectant(segA, segB) {//线线
    const abc = (segA[0].x - segB[0].x) * (segA[1].y - segB[0].y) - (segA[0].y - segB[0].y) * (segA[1].x - segB[0].x);
    const abd = (segA[0].x - segB[1].x) * (segA[1].y - segB[1].y) - (segA[0].y - segB[1].y) * (segA[1].x - segB[1].x);
    if (abc * abd >= 0) {
        return false;
    }
    const cda = (segB[0].x - segA[0].x) * (segB[1].y - segA[0].y) - (segB[0].y - segA[0].y) * (segB[1].x - segA[0].x);
    const cdb = cda + abc - abd;
    return !(cda * cdb >= 0);
}

//判断两多边形边界是否相交
function isPolygonsIntersectant(plyA, plyB) {//面面
    for (let i = 0, il = plyA.length; i < il; i++) {
        for (let j = 0, jl = plyB.length; j < jl; j++) {
            const segA = [plyA[i], plyA[i === il - 1 ? 0 : i + 1]];
            const segB = [plyB[j], plyB[j === jl - 1 ? 0 : j + 1]];
            if (isSegmentsIntersectant(segA, segB)) {
                return true;
            }
        }
    }
    return false;
}

(2 判断包含

//判断点是否在另一平面图中
function isPointInPolygon(point, polygon) {

    //下述代码来源：http://paulbourke.net/geometry/insidepoly/，进行了部分修改
    //基本思想是利用射线法，计算射线与多边形各边的交点，如果是偶数，则点在多边形外，否则
    //在多边形内。还会考虑一些特殊情况，如点在多边形顶点上，点在多边形边上等特殊情况。

    var N = polygon.length;
    var boundOrVertex = true; //如果点位于多边形的顶点或边上，也算做点在多边形内，直接返回true
    var intersectCount = 0; //cross points count of x 
    var precision = 2e-10; //浮点类型计算时候与0比较时候的容差
    var p1, p2; //neighbour bound vertices
    var p = point; //测试点

    p1 = polygon[0]; //left vertex        
    for (var i = 1; i <= N; ++i) { //check all rays            
        if (p.x == p1.x && p.y == p1.y) {
            return boundOrVertex; //p is an vertex
        }

        p2 = polygon[i % N]; //right vertex            
        if (p.y < Math.min(p1.y, p2.y) || p.y > Math.max(p1.y, p2.y)) { //ray is outside of our interests                
            p1 = p2;
            continue; //next ray left point
        }

        if (p.y > Math.min(p1.y, p2.y) && p.y < Math.max(p1.y, p2.y)) { //ray is crossing over by the algorithm (common part of)
            if (p.x <= Math.max(p1.x, p2.x)) { //x is before of ray                    
                if (p1.y == p2.y && p.x >= Math.min(p1.x, p2.x)) { //overlies on a horizontal ray
                    return boundOrVertex;
                }

                if (p1.x == p2.x) { //ray is vertical                        
                    if (p1.x == p.x) { //overlies on a vertical ray
                        return boundOrVertex;
                    } else { //before ray
                        ++intersectCount;
                    }
                } else { //cross point on the left side                        
                    var xinters = (p.y - p1.y) * (p2.x - p1.x) / (p2.y - p1.y) + p1.x; //cross point of x                        
                    if (Math.abs(p.x - xinters) < precision) { //overlies on a ray
                        return boundOrVertex;
                    }

                    if (p.x < xinters) { //before ray
                        ++intersectCount;
                    }
                }
            }
        } else { //special case when ray is crossing through the vertex                
            if (p.y == p2.y && p.x <= p2.x) { //p crossing over p2                    
                var p3 = polygon[(i + 1) % N]; //next vertex                    
                if (p.y >= Math.min(p1.y, p3.y) && p.y <= Math.max(p1.y, p3.y)) { //p.y lies between p1.y & p3.y
                    ++intersectCount;
                } else {
                    intersectCount += 2;
                }
            }
        }
        p1 = p2; //next ray left point
    }

    if (intersectCount % 2 == 0) { //偶数在多边形外
        return false;
    } else { //奇数在多边形内
        return true;
    }
}
//判断两多变形是否存在点与区域的包含关系(A的点在B的区域内或B的点在A的区域内)
function isPointInPolygonBidirectional(plyA, plyB) {//面面
    let [a, b] = [false, false];
    a = plyA.some(item => isPointInPolygon(item, plyB));
    if (!a) {
        b = plyB.some(item => isPointInPolygon(item, plyA));
    }
    return a || b;
}

3. 判断多边形是否重叠

function isPolygonsOverlap(plyA, plyB) {
    return isPolygonsIntersectant(plyA, plyB) || isPointInPolygonBidirectional(plyA, plyB);
}