js判断点是否在平面几何图形内(基于百度地图方法)

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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. 方法详解

//判断点是否在平面中
function isPointInPolygon(point, polygon) {//点面
    //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.equals(p1)) {
            return boundOrVertex; //p is an vertex
        }

        p2 = polygon[i % N]; //right vertex            
        if (p.x < Math.min(p1.x, p2.x) || p.x > Math.max(p1.x, p2.x)) { //ray is outside of our interests                
            p1 = p2;
            continue; //next ray left point
        }
        if (p.x > Math.min(p1.x, p2.x) && p.x < Math.max(p1.x, p2.x)) { //ray is crossing over by the algorithm (common part of)
            if (p.y <= Math.max(p1.y, p2.y)) { //x is before of ray                    
                if (p1.x == p2.x && p.y >= Math.min(p1.y, p2.y)) { //overlies on a horizontal ray
                    return boundOrVertex;
                }

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

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