const double eps = 1e-8;
struct point
};typedef point vtor;
//向量的加減乘除
vtor operator + (vtor a,vtor b)
vtor operator - (point a,point b)
vtor operator * (vtor a,double p)
vtor operator / (vtor a,double p)
bool operator < (point a,point b)
int dcmp(double x)
bool operator == (point a,point b)
//向量的點積，長度，夾角
double dot(vtor a,vtor b)
double length(vtor a)
double angle(vtor a,vtor b)
//叉積，三角形面積
double cross(vtor a,vtor b)
double area2(point a,point b,point c)
//向量的旋轉,求向量的單位法線（即左轉90度，然後長度歸一）
vtor rotate(vtor a,double rad)
vtor normal(vtor a)
//直線的交點
point getlineintersection(point p,vtor v,point q,vtor w)
//點到直線的距離
double distancetoline(point p,point a,point b)
//點到線段的距離
double distancetosegment(point p,point a,point b)
//點到直線的對映
point getlineprojection(point p,point a,point b)
//判斷線段是否規範相交
bool segmentproperintersection(point a1,point a2,point b1,point b2)
//判斷點是否在一條線段上
bool onsegment(point p,point a1,point a2)
//多邊形面積
double polgonarea(point *p,int n)
和圓有關的計算
struct line
point point(double t)
};struct circle
point point(double a)
};//判斷圓與直線是否相交以及求出交點
int getlinecircleintersection(line l,circle c,double t1,double t2,vector&sol)
t1 = (-f - sqrt(delta))/(2*e); sol.push_back(l.point(t1));
t2 = (-f + sqrt(delta))/(2*e); sol.push_back(l.point(t2));
return 2;
}//判斷並求出兩圓的交點
double angle(vtor v)
int getcircleintersection(circle c1,circle c2,vector&sol)
// 圓心不重合
if (dcmp(c1.r + c2.r - d) < 0) return 0; // 相離
if (dcmp(fabs(c1.r - c2.r) - d) > 0) return 0; // 包含
double a = angle(c2.c - c1.c);
double da = acos(c1.r*c1.r + d*d - c2.r*c2.r) / (2*c1.r*d);
point p1 = c1.point(a - da), p2 = c1.point(a + da);
sol.push_back(p1);
if (p1 == p2) return 1;
sol.push_back(p2);
return 2;
}//求點到圓的切線
int gettangents(point p,circle c,vtor *v)
else
}//求兩圓的切線
int getcircletangents(circle a,circle b,point *a,point *b)
//圓心距的平方
double d2 = (a.c.x - b.c.x)*(a.c.x - b.c.x) + (a.c.y - b.c.y)*(a.c.y - b.c.y);
double rdiff = a.r - b.r;
double rsum = a.r + b.r;
double base = angle(b.c - a.c);
//重合有無限多條
if (d2 == 0 && dcmp(a.r - b.r) == 0) return -1;
//內切
if (dcmp(d2 - rdiff*rdiff) == 0)
//有外公切線
double ang = acos((a.r - b.r) / sqrt(d2));
a[cnt] = a.point(base + ang); b[cnt] = b.point(base + ang); cnt++;
a[cnt] = a.point(base - ang); b[cnt] = b.point(base - ang); cnt++;
//一條內切線
if (dcmp(d2 - rsum*rsum) == 0)
//兩條內切線
else if (dcmp(d2 - rsum*rsum) > 0)
return cnt;
}
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