几何模板.docx

1、几何模板大几何模板大几何模板 1(1)凸包 2(2)判断两条线段是否相交(平行，不平行) 4(3)三角形的外接圆(已知不在同一直线上的三点求经过三点的圆) 4(4)三角形的垂心内心重心中垂线 6(5)求直线的交点 10(6)根据线段两端点的坐标求垂直平分线上除中点外的另一点 11(7)根据两点坐标求直线方程 11(8)差积的应用 12(9)三角形的面积公式 12(10)三角形的内接圆 12(11)多边形的面积(适合凹多边形) 13(12)判断点是否在线段上 14(13)平面上两个点之间的距离 14(14)p点关于直线L的对称点 14(15)判断一个矩形是否在另一个矩形中 15(16)直线和圆的

2、交点+点关于线的对称点+点到线的距离+直线方程 16(17)判断点是否在多边形内 21(18)N点中三个点组成三角形面积最大 28(19)扇形的重心 31(20)多边形的重心 32(21)判断N点是否共面 33(22)求共线的点最多为多少 34(23)N个矩形的相交的面积 36(24)三角形外接圆+圆的参数方程 38(25)判断线段是否有交点并求交点 43(26)简单多边形的核 46(27)线段重叠+投影 50(28)二分+圆的参数方程 53(29)Pick公式 54(30)根据经度纬度求球面距离 56(31)两圆切线的交点 58(31)两圆切线的交点(32)线段与三角形的交 60(33)最近

3、最远点对 68-(1)凸包/*凸包cug_1038*/#include #include struct point int x, y; pp; point p100005; int stack100005, top; int dis(point a, point b) return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); int multi(point b, point c, point a) return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x); void

4、 swap(point p, int s, int t) point tmp; tmp = ps; ps = pt; pt = tmp; int cmp(const void *a, const void *b) point *c = (point *)a; point *d = (point *)b; double k = multi(*c, *d, pp); if(k = dis(*d, pp) return 1; else return -1; void Graham(point p, int n, int stack, int &top) int i, u; u = 0; for(i

5、= 1;i n;i+) if(pi.y = pu.y & pi.x pu.x) u = i; else if(pi.y pu.y) u = i; swap(p, 0, u); pp = p0; qsort(p + 1, n - 1, sizeof(p0), cmp); stack0 = 0; stack1 = 1; top = 1; for(i = 2;i = 0) if(top = 0) break; top-; top+; stacktop = i; int main() int ca, i, j, n; int area; scanf(%d, &ca); for(i = 1;i = ca

6、;i+) scanf(%d, &n); for(j = 0;j n;j+) scanf(%d%d, &pj.x, &pj.y); Graham(p, n, stack, top); area = 0; for(j = 1;j = min(s2.x, e2.x) & (max(s2.x, e2.x) = min(s1.x, e1.x) & (max(s1.y, e1.y) = min(s2.y, e2.y) & (max(s2.y, e2.y) = min(s1.y, e1.y) & (multi(s2, e1, s1) * multi(e1, e2, s1) = 0) & (multi(s1,

7、 e2, s2) * multi(e2, e1, s2) = 0) ) return true; return false; (3)三角形的外接圆(已知不在同一直线上的三点求经过三点的圆)/*三角形的外接圆pku_1329*/#include #include const double eps = 1e-6;typedef struct TPoint double x; double y;TPoint;typedef struct TTriangle TPoint t3;TTriangle;typedef struct TCircle TPoint centre; double r;TCirc

8、le;double distance(TPoint p1, TPoint p2) /计算平面上两个点之间的距离 return sqrt(p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y); double triangleArea(TTriangle t) /已知三角形三个顶点的坐标，求三角形的面积 return fabs(t.t0.x * t.t1.y + t.t1.x * t.t2.y + t.t2.x * t.t0.y - t.t1.x * t.t0.y - t.t2.x * t.t1.y - t.t0.x * t.t2

9、.y) / 2; TCircle circumcircleOfTriangle(TTriangle t) /三角形的外接圆 TCircle tmp; double a, b, c, c1, c2; double xA, yA, xB, yB, xC, yC; a = distance(t.t0, t.t1); b = distance(t.t1, t.t2); c = distance(t.t2, t.t0); /根据S = a * b * c / R / 4;求半径R tmp.r = a * b * c / triangleArea(t) / 4; xA = t.t0.x; yA = t.t

10、0.y; xB = t.t1.x; yB = t.t1.y; xC = t.t2.x; yC = t.t2.y; c1 = (xA * xA + yA * yA - xB * xB - yB * yB) / 2; c2 = (xA * xA + yA * yA - xC * xC - yC * yC) / 2; tmp.centre.x = -(c1 * (yA - yC) - c2 * (yA - yB) / (xA - xB) * (yA - yC) - (xA - xC) * (yA - yB); tmp.centre.y = -(c1 * (xA - xC) - c2 * (xA -

11、xB) / (yA - yB) * (xA - xC) - (yA - yC) * (xA - xB); return tmp; int main() TTriangle t; TCircle circle; double c, d, e; while(scanf(%lf%lf%lf%lf%lf%lf, &t.t0.x, &t.t0.y, &t.t1.x, &t.t1.y, &t.t2.x, &t.t2.y) != EOF) circle = circumcircleOfTriangle(t); / printf(%lf %lf %lfn, circle.centre.x, circle.ce

12、ntre.y, circle.r); if(fabs(circle.centre.x) eps) printf(x2); else if(circle.centre.x 0) printf(x - %.3lf)2 + , -circle.centre.x); else printf(x + %.3lf)2 + , circle.centre.x); if(fabs(circle.centre.y) eps) printf(y2 = ); else if(circle.centre.y 0) printf(y - %.3lf)2 = , -circle.centre.y); else print

13、f(y + %.3lf)2 = , circle.centre.y); printf(%.3lf2n, circle.r); c = 2 * circle.centre.x; d = 2 * circle.centre.y; e = circle.centre.x * circle.centre.x + circle.centre.y * circle.centre.y - circle.r * circle.r; printf(x2 + y2 ); /if(fabs(c) eps) if(c 0) printf(- %.3lfx , -c); else printf(+ %.3lfx , c

14、); if(d 0) printf(- %.3lfy , -d); else printf(+ %.3lfy , d); if(e 0) printf(- %.3lf = 0n, -e); else printf(+ %.3lf = 0n, e); printf(n); return 0; (4)三角形的垂心内心重心中垂线/*cug_1011_垂心内心重心中垂线.cpp*/#include #include using namespace std;const double eps = 1e-6; struct point double x, y;void K() /到三边距离和最短 void

15、L(double a, double b, double c, double A, double B, double C) /垂线的交点 double t1, t2, t3; t1 = c * cos(A) / cos(M_PI / 2 - C); t2 = c * cos(B) / cos(M_PI / 2 - C); t3 = a * cos(C) / cos(M_PI / 2 - A); t1 += t2 + t3; printf(%.3lfn, t1); struct TLine double a, b, c;TLine lineFromSegment(point p1, point

16、p2) /线段所在直线,返回直线方程的三个系统 TLine tmp; tmp.a = p2.y - p1.y; tmp.b = p1.x - p2.x; tmp.c = p2.x * p1.y - p1.x * p2.y; return tmp;point LineInter(TLine l1, TLine l2) /求两直线得交点坐标 point tmp; if(fabs(l1.b) -eps) printf(%.3lf , b + c); return ; else if(B - 2 * M_PI / 3 -eps) printf(%.3lf , a + c); return ; else

17、 if(C - 2 * M_PI / 3 -eps) printf(%.3lf , a + b); return ; point pa, pb, pc, pc1, pa1; pa.x = 0, pa.y = 0; pb.x = c, pb.y = 0; pc.x = b * cos(A); pc.y = b * sin(A); pc1.x = c * cos(-M_PI / 3); pc1.y = c * sin(-M_PI / 3); pa1.x = a * cos(2 * M_PI / 3 - B) + c; pa1.y = a * sin(2 * M_PI / 3 - B); TLine

18、 l1, l2; l1 = lineFromSegment(pa, pa1); l2 = lineFromSegment(pc, pc1); point f = LineInter(l1, l2); printf(%.3lf , dis(pa, f) + dis(pb, f) + dis(pc, f); void I(double a, double b, double c, double A, double B, double C) /角平分线的交点到三顶点的距离和 double t, ans; t = (a + b - c) / 2; ans = t / cos(C / 2) + (b -

19、 t) / cos(A / 2) + (a - t) / cos(B / 2); printf(%.3lf , ans);void G(double a, double b, double c, double A, double B, double C) /中线的交点 double t1, t2, t3; t1 = sqrt(b / 2) * (b / 2) + a * a - 2 * a * b / 2 * cos(C); t2 = sqrt(a / 2) * (a / 2) + c * c - 2 * a * c / 2 * cos(B); t3 = sqrt(c / 2) * (c /

20、2) + b * b - 2 * b * c / 2 * cos(A); t1 += t2 + t3; printf(%.3lf , t1 * 2 / 3); void O(double a, double b, double c, double A, double B, double C) /垂线的交点 double t = (A + C - B) / 2; printf(%.3lfn, 3 * b / 2 / cos(t); int main() int i, ca; double a, b, c; double A, B, C; cin ca; for(i = 1;i a b c; A

21、= (b * b + c * c - a * a) / 2 / b / c; B = (a * a + c * c - b * b) / 2 / a / c; C = (a * a + b * b - c * c) / 2 / a / b; A = acos(A), B = acos(B), C = acos(C); F(a, b, c, A, B, C); I(a, b, c, A, B, C); G(a, b, c, A, B, C); O(a, b, c, A, B, C); return 0;=-(5)求直线的交点/*求直线的交点，注意平形的情况无解，避免RE*/TPoint Line

22、Inter(TLine l1, TLine l2) /求两直线得交点坐标 TPoint tmp; double a1 = l1.a; double b1 = l1.b; double c1 = l1.c; double a2 = l2.a; double b2 = l2.b; double c2 = l2.c; /注意这里b1 = 0 if(fabs(b1) eps) tmp.x = -c1 / a1; tmp.y = (-c2 - a2 * tmp.x) / b2; else tmp.x = (c1 * b2 - b1 * c2) / (b1 * a2 - b2 * a1); tmp.y =

23、 (-c1 - a1 * tmp.x) / b1; /cout 交点坐标 endl; /cout a1 * tmp.x + b1 * tmp.y + c1 endl; /cout a2 * tmp.x + b2 * tmp.y + c2 endl; return tmp;(6)根据线段两端点的坐标求垂直平分线上除中点外的另一点TPoint GetOtherPoint(TPoint pre, TPoint tmp) /*根据线段两端点的坐标求垂直平分线上除中点外的另一点*/ double kx, ky; TPoint other, mid; mid.x = (pre.x + tmp.x) / 2; mid.y = (pre.y + tmp.y) / 2; kx = pre.x - tmp.x; ky = pre.y - tmp.y; if(fabs(kx) eps) other.y = mid.y; other.x = 1.0; if(fabs(other.x - mid.x) eps) other.x = 2.0; else if(fabs(ky) eps) other.x = mid.x; other.y = 1.0; if(fabs(other.y - mid.y) eps) other.y = 2.0; else double k