二维几何基础（模板）

#include<iostream>

#include<stdio.h>

#include<cstring>

#include<algorithm>

#include<cmath>

#include<functional>

#define eps 1e-9

#include<vector>

using namespace std;

const double PI = acos(-1.0);

int dcmp( double x ){ if( abs(x) < eps ) return 0;else return x < 0?-1:1; }

struct point{

double x,y;

point( double x = 0,double y = 0 ):x(x),y(y){}

}node[112]; typedef point Vector;

struct segment{

point a,b; segment(){}

segment(point _a,point _b){a=_a,b=_b;}

};

struct circle{

point c; double r; circle(){}

circle(point _c, double _r):c(_c),r(_r) {}

point PPP(double a)const{return point(c.x+cos(a)*r,c.y+sin(a)*r);}

};

struct line{

point p,v; double ang;

line() {}

line( const point &_p, const point &_v):p(_p),v(_v){ang = atan2(v.y, v.x);}

inline bool operator < (const line &L)const{return ang < L.ang;}

};

point operator + (point a,point b){return point( a.x + b.x,a.y + b.y );}

point operator - (point a,point b){return point( a.x - b.x,a.y - b.y );}

point operator * (point a,double b){return point( a.x*b,a.y*b );}

point operator / (point a,double b){ return point( a.x/b,a.y/b );}

bool operator < (const point &a, const point &b ){return a.x < b.x || (a.x == b.x && a.y < b.y );}

bool operator == (const point &a, const point &b ){return (dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0 );}

bool operator != (const point &a,const point &b ){return a == b?false:true;}

double Dot( point a,point b ){return a.x*b.x + a.y*b.y;} // 点到点的距离；

double Length( point a ){return sqrt( Dot( a,a ) );} // 向量长度

double Angle( point a,point b ){ return acos( Dot(a,b)/Length(a)/Length(b) );} // 两个向量的角度

double D_T_D(const double ° ){ return deg/180*PI; }

// 向量旋转 rad 度数

point Rotate( point a, double rad ){

return point( a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad) );

}

// 向量的 法线向量 的单位向量

point Normal( point a ){

double L = Length(a); return point(-a.y/L,a.x/L);

}

// 叉积计算

double Cross( point a,point b ){

return a.x*b.y - a.y*b.x;

}

// 获取 两个向量叉积

double get_Mix( point a,point b,point pot ){

a.x = a.x - pot.x; a.y = a.y - pot.y;

b.x = b.x - pot.x; b.y = b.y - pot.y;

return Cross( a,b );

}

// 直线相交求交点；

point get_line_inter( point p,point v, point q,point w ){

point u = p - q;

double t = Cross(w,u)/Cross(v,w);

return p+v*t;

}

// p点到直线 的距离

double dis_p_line( point p,point a,point b ) {

point v1 = b-a, v2 = p-a;

return abs( Cross(v1,v2)/Length(v1) );

}

//点在直线上的投影

inline point GetLineProjection(const point &p,const point &a,const point &b){

point v=b-a;

return a+v*(Dot(v,p-a)/Dot(v,v));

}

// 点到线段的距离

double dis_p_segm( point p,point a,point b ){

if( a == b )return Length( p-a );

point v1 = b-a,v2 = p-a,v3 = p-b;

if( dcmp(Dot(v1,v2)) < 0 )return Length(v2);

else if( dcmp(Dot( v1,v3)) > 0 )return Length(v3);

else return abs(Cross( v1,v2 ))/Length(v1);

}

//海伦公式 三条边

double Heron(double a,double b,double c){

double p=(a+b+c)/2;

return sqrt(p*(p-a)*(p-b)*(p-c));

}

// 多边形面积 从p[0] 开始，p
结束

double ploy_area( point *p,int n ){

double area = 0;

for( int i = 1; i < n-1; i++ )

area += Cross( p[i]-p[0],p[i+1]-p[0] );

return area/2.0;

}

// 线段相交判断 先必须去掉不相交的状态；再判断方向

bool get_set( point a,point b,point c,point d ){

if( min( a.x,b.x ) <= max( c.x,d.x ) && min( a.y,b.y ) <= max( c.y,d.y ) &&

min( c.x,d.x ) <= max( a.x,b.x ) && min( c.y,d.y ) <= max( a.y,b.y ) &&

Cross( c-b,a-b )*Cross( d-b,a-b ) <= 0 &&

Cross( a-d,c-d )*Cross( b-d,c-d ) <= 0

) return true;

return false;

}

// 线段 直线 平行判断只需要对应向量平行；

bool get_pall( point a,point b,point c,point d ){

if( Cross( a-b,c-d ) == 0 )return true;

return false;

}

// 直线 重合判断 只需要 一条直线的两点都在直线方向

bool get_doub( point a,point b,point c,point d ){

if( Cross( d-b,a-b ) == 0 && Cross( c-b,a-b ) == 0 )return 1;

return 0;

}

// 获取 线段 交点；依据 叉积判断

point get_pot( point a,point b,point c,point d ){

point temp;

temp.x = ( c.x*Cross(b-a,d-a) - d.x*Cross(b-a,c-a) )/( Cross(b-a,d-a) - Cross(b-a,c-a) );

temp.y = ( c.y*Cross(b-a,d-a) - d.y*Cross(b-a,c-a) )/( Cross(b-a,d-a) - Cross(b-a,c-a) );

return temp;

}

//获取直线的交点 同时也可以是线段的交点；

point get_ppp( point a,point b,point c,point d ){

double a0 = a.y - b.y; double b0 = b.x - a.x; double c0 = a.x*b.y - b.x*a.y;

double a1 = c.y - d.y; double b1 = d.x - c.x; double c1 = c.x*d.y - d.x*c.y;

double D = a0*b1 - a1*b0; point temp;

temp.x = ( b0*c1 - b1*c0 )/D;

temp.y = ( a1*c0 - a0*c1 )/D;

return temp;

}

//点pot 是否 在线段 ab 上 只需 叉积等于0 点积等于0

bool online( point a,point b,point pot ){

if( Cross( a - pot,b - pot ) == 0 && Dot( a - pot,b - pot ) <= 0 )return 1;

return 0;

}

int top,res[1123456]; // 凸包 ( 起点 0 ) ( n 个点 ) 自己写的，，需要改进 改进；

void GRA( int n )

{

sort( node,node+n ); // 先排序

top = 1; res[0] = 0; res[1] = 1;// 从第0位开始放；前两位不管

for( int i = 2; i <= n; i++ ){

while( top && get_Mix( node[i],node[res[top]],node[res[top-1]] ) > 0 )top--;

res[++top] = i;

}

int k = top;

for( int i = n-2; i >= 0; i-- ){

while( top > k && get_Mix( node[i],node[res[top]],node[res[top-1]] ) > 0 )top--;

res[++top] = i;

}

top--; // 会添加进去最后一个点

}

//求两圆相交

int C_T_C( circle c1,circle c2,point &p1,point &p2 ){

double d = Length( c1.c- c2.c );

if( dcmp( d ) == 0 ) {

if( dcmp( c1.r-c2.r ) == 0 ) return -1;//两圆重合

return 0;

}

if( dcmp( c1.r + c2.r - d ) < 0 ) return 0;

if( dcmp( fabs( c1.r - c2.r ) - d ) > 0 ) return 0;

double a = Angle( c2.c - c1.c,point( 1,0 ) );

double da = acos(( c1.r * c1.r + d * d - c2.r * c2.r )/( 2 * c1.r * d ) );

p1 = c1.PPP( a - da ); p2 = c1.PPP( a + da );

if( p1 == p2 ) return 1;

return 2;

}

//圆与直线交点 返回交点个数

int C_T_L( line L,circle C,point &p1,point &p2){

double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y;

double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r;

double delta = f*f - 4*e*g;

if( dcmp(delta) < 0 ) return 0;//相离

if( dcmp(delta) == 0 ) {//相切

p1 = p1 = L.p + L.v*( -f/(2*e) );

return 1;

}//相交

p1 = ( L.p + L.v * ( -f-sqrt(delta) )/( 2*e ) );

p2 = ( L.p + L.v * ( -f+sqrt(delta) )/( 2*e ) );

return 2;

}

//点与圆的切线；

int get_P_C_inter( point p,circle c, point *v )

{

point u = c.c - p; double dist = Length(u);

if( dist < c.r )return 0;

else if( dcmp( dist - c.r) == 0 ){

v[0] = Rotate( u,PI/2 );

return 1;

}else {

double ang = asin( c.r/dist );

v[0] = Rotate(u,-ang);

v[1] = Rotate(u,+ang);

return 2;

}

return -1;

}

int main( )

{



return 0;

}