【计算几何-点的定位】

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;
}