判斷一個點是否在一個多邊形內

/** 
 * 判斷點是否在多邊形內 
 * @param point 檢測點 
 * @param pts   多邊形的頂點 
 * @return      點在多邊形內返回true,不然返回false 
 */  
public static boolean IsPtInPoly(Point2D.Double point, List<Point2D.Double> pts){  
      
    int N = pts.size();  
    boolean boundOrVertex = true; //若是點位於多邊形的頂點或邊上，也算作點在多邊形內，直接返回true  
    int intersectCount = 0;//cross points count of x   
    double precision = 2e-10; //浮點類型計算時候與0比較時候的容差  
    Point2D.Double p1, p2;//neighbour bound vertices  
    Point2D.Double p = point; //當前點  
      
    p1 = pts.get(0);//left vertex          
    for(int i = 1; i <= N; ++i){//check all rays              
        if(p.equals(p1)){  
            return boundOrVertex;//p is an vertex  
        }  
          
        p2 = pts.get(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                          
                    double 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                      
                Point2D.Double p3 = pts.get((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){//偶數在多邊形外  
        return false;  
    } else { //奇數在多邊形內  
        return true;  
    }  
      
}  

測試:

// 測試一個點是否在多邊形內  
public static void main(String[] args) {  
      
    Point2D.Double point = new Point2D.Double(116.404072, 39.916605);  
      
    List<Point2D.Double> pts = new ArrayList<Point2D.Double>();  
    pts.add(new Point2D.Double(116.395, 39.910));  
    pts.add(new Point2D.Double(116.394, 39.914));  
    pts.add(new Point2D.Double(116.403, 39.920));  
    pts.add(new Point2D.Double(116.402, 39.914));  
    pts.add(new Point2D.Double(116.410, 39.913));  
      
    if(IsPtInPoly(point, pts)){  
        System.out.println("點在多邊形內");  
    }else{  
        System.out.println("點在多邊形外");  
    }  
}