【计算几何-点的定位】

小鱼儿 2022-06-09 14:19 189阅读 0赞

1.二维坐标系，输入点的坐标(xi, yi)，判断点是否在三角形内  
判断原理：若点p在三角形内，Sabc = Spab + Spac + Spbc；

struct point{
       /*记录点的信息*/
        double x;
        double y;
    };
    
    struct v{
       /*记录边的信息*/
        point star;/*边的起点*/
        point en;/*边的终点*/
    };
    
    struct triangle{
       /*记录三角形信息*/
        point A;/*三角形的顶点A*/
        point B;/*三角形的顶点B*/
        point C;/*三角形的顶点C*/
    };
    triangle tre[104];
    int tr;
    
    
    
    double crossProduct(v * v1, v * v2);/*向量叉积*/
    bool inTrianle(triangle t, point P);/*判断点是否在三角形内*/
    
    
    double crossProduct(v * v1, v * v2){
        v vt1, vt2;
        double result = 0;
        vt1.star.x = 0;
        vt1.star.y = 0;
        vt1.en.x = v1->en.x - v1->star.x;
        vt1.en.y = v1->en.y - v1->star.y;
    
        vt2.star.x = 0;
        vt2.star.y = 0;
        vt2.en.x = v2->en.x - v2->star.x;
        vt2.en.y = v2->en.y - v2->star.y;
    
        result = vt1.en.x * vt2.en.y - vt2.en.x * vt1.en.y;
        return result;
    }
    bool inTrianle(triangle t, point p){
        v AB, AC, BC, PA, PB, PC;
        AB.star = t.A;
        AB.en = t.B;
        AC.star = t.A;
        AC.en = t.C;
        BC.star = t.B;
        BC.en = t.C;
        PA.star = p;
        PA.en = t.A;
        PB.star = p;
        PB.en = t.B;
        PC.star = p;
        PC.en = t.C;
    
        double Sabc = fabs(crossProduct(&AB, &AC));
        double Spab = fabs(crossProduct(&PA, &PB));
        double Spac = fabs(crossProduct(&PA, &PC));
        double Spbc = fabs(crossProduct(&PB, &PC));
        if(Sabc == Spab + Spac + Spbc)
            return true;
        else
            return false;
    }

2.二维坐标系，输入点坐标(xi, yi)，判断点是否在圆内  
判断原理：若点在圆内，则点到圆心的距离小于等于半径

struct circle{
        int x;/*圆心的横坐标*/
        int y;/*圆心的纵坐标*/
        int r;/*圆的半径*/
    };
    circle cir[104];
    int ci;
    
    bool inCircle(circle t, int x, int y);/*判断点是否在圆内*/
    
    bool inCircle(circle t, int x, int y){
        int ans = (x-t.x)*(x-t.x) + (y-t.y)*(y-t.y);
        if(ans <= t.r*t.r)
            return true;
        else
            return false;
    }