POJ 3675 裸的题了。直接上模板就行了。注意的是，求出的是有向面积，有可能是负数。
#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <cstring>
#include <algorithm>
#include <string>
#include <set>
#include <functional>
#include <numeric>
#include <sstream>
#include <stack>
#define CL(arr, val) memset(arr, val, sizeof(arr))
#define REP(i, n)for((i) = 0; (i) < (n); ++(i))
#define FOR(i, l, h)for((i) = (l); (i) <= (h); ++(i))
#define FORD(i, h, l)for((i) = (h); (i) >= (l); --(i))
#define L(x)(x) << 1
#define R(x)(x) << 1 | 1
#define MID(l, r)(l + r) >> 1
#define Min(x, y)x < y ? x : y
#define Max(x, y)x < y ? y : x
#define E(x)(1 << (x))
#define iabs(x) (x) < 0 ? -(x) : (x)
#define OUT(x)printf("%I64d
", x)
#define lowbit(x)(x)&(-x)
#define Read()freopen("data.in", "r", stdin)
#define Write()freopen("data.out", "w", stdout);
const double eps = 1e-8;
typedef long long LL;
const int inf = ~0u>>2;
using namespace std;
inline double max (double a, double b) { if (a > b) return a; else return b; }
inline double min (double a, double b) { if (a < b) return a; else return b; }
inline int fi (double a){
if (a > eps) return 1;
else if (a >= -eps) return 0;
else return -1;
}
class Vector{
public:
double x, y;
Vector (void) {}
Vector (double x0, double y0) : x(x0), y(y0) {}
double operator * (const Vector& a) const { return x * a.y - y * a.x; }
double operator % (const Vector& a) const { return x * a.x + y * a.y; }
Vector verti (void) const { return Vector(-y, x); }
double length (void) const { return sqrt(x * x + y * y); }
Vector adjust (double len) {
double ol = len / length();
return Vector(x * ol, y * ol);
}
Vector oppose (void) { return Vector(-x, -y); }
};
class point{
public:
double x, y;
point (void) {}
point (double x0, double y0) : x(x0), y(y0) {}
Vector operator - (const point& a) const { return Vector(x - a.x, y - a.y); }
point operator + (const Vector& a) const { return point(x + a.x, y + a.y); }
};
class segment{
public:
point a, b;
segment (void) {}
segment (point a0, point b0) : a(a0), b(b0) {}
point intersect (const segment& s) const {
Vector v1 = s.a - a, v2 = s.b - a, v3 = s.b - b, v4 = s.a - b;
double s1 = v1 * v2, s2 = v3 * v4;
double se = s1 + s2;
s1 /= se, s2 /= se;
return point(a.x * s2 + b.x * s1, a.y * s2 + b.y * s1);
}
point pverti (const point& p) const {
Vector t = (b - a).verti();
segment uv(p, p + t);
return intersect(uv);
}
bool on_segment (const point& p) const {
if (fi(min(a.x, b.x) - p.x) <= 0 && fi(p.x - max(a.x, b.x)) <= 0 &&
fi(min(a.y, b.y) - p.y) <= 0 && fi(p.y - max(a.y, b.y)) <= 0) return true;
else return false;
}
};
double radius;
point polygon[110];
double kuras_area (point a, point b, double cx, double cy){
point ori(cx, cy);
int sgn = fi((b - ori) * (a - ori));
double da = (a - ori).length(), db = (b - ori).length();
int ra = fi(da - radius), rb = fi(db - radius);
double angle = acos(((b - ori) % (a - ori)) / (da * db));
segment t(a, b); point h, u; Vector seg;
double ans, dlt, mov, tangle;
if (fi(da) == 0 || fi(db) == 0) return 0;
else if (sgn == 0) return 0;
else if (ra <= 0 && rb <= 0) return fabs((b - ori) * (a - ori)) / 2 * sgn;
else if (ra >= 0 && rb >= 0){
h = t.pverti(ori);
dlt = (h - ori).length();
if (!t.on_segment(h) || fi(dlt - radius) >= 0)
return radius * radius * (angle / 2) * sgn;
else{
ans = radius * radius * (angle / 2);
tangle = acos(dlt / radius);
ans -= radius * radius * tangle;
ans += radius * sin(tangle) * dlt;
return ans * sgn;
}
}
else{
h = t.pverti(ori);
dlt = (h - ori).length();
seg = b - a;
mov = sqrt(radius * radius - dlt * dlt);
seg = seg.adjust(mov);
if (t.on_segment(h + seg)) u = h + seg;
else u = h + seg.oppose();
if (ra == 1) swap(a, b);
ans = fabs((a - ori) * (u - ori)) / 2;
tangle = acos(((u - ori) % (b - ori)) / ((u - ori).length() * (b - ori).length()));
ans += radius * radius * (tangle / 2);
return ans * sgn;
}
}
const double pi = acos(-1.0);
int main (){
int n;
while(scanf("%lf",&radius)!=EOF){
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%lf%lf",&polygon[i].x,&polygon[i].y);
}
double ans=0;
for(int i=0;i<n;i++){
ans+=kuras_area(polygon[i],polygon[(i+1)%n],0,0);
}
printf("%.2lf
",fabs(ans));
}
}
HDU 3982。很明显，求出切割的半平面交之后就可以得出一个多边形。然后求多边形与圆面积相交部分即可。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const double eps = 1e-6;
typedef long long LL;
const int inf = ~0u>>2;
const int MAXN=4222;
inline double max (double a, double b) { if (a > b) return a; else return b; }
inline double min (double a, double b) { if (a < b) return a; else return b; }
inline int fi (double a){
if (a > eps) return 1;
else if (a >= -eps) return 0;
else return -1;
}
struct Point {
double x,y;
Point(double xx,double yy){x=xx; y=yy;}
Point(){}
}convex[MAXN],cherry;
class Vector{
public:
double x, y;
Vector (void) {}
Vector (double x0, double y0) : x(x0), y(y0) {}
double operator * (const Vector& a) const { return x * a.y - y * a.x; } //向量叉乘
double operator % (const Vector& a) const { return x * a.x + y * a.y; } //向量点乘
Vector verti (void) const { return Vector(-y, x); }
double length (void) const { return sqrt(x * x + y * y); }
Vector adjust (double len) {
double ol = len / length();
return Vector(x * ol, y * ol);
}
Vector oppose (void) { return Vector(-x, -y); }
};
class point{
public:
double x, y;
point (void) {}
point (double x0, double y0) : x(x0), y(y0) {}
Vector operator - (const point& a) const { return Vector(x - a.x, y - a.y); }
point operator + (const Vector& a) const { return point(x + a.x, y + a.y); }
void _copy(Point t){
x=t.x; y=t.y;
}
};
class segment{
public:
point a, b;
segment (void) {}
segment (point a0, point b0) : a(a0), b(b0) {}
point intersect (const segment& s) const {
Vector v1 = s.a - a, v2 = s.b - a, v3 = s.b - b, v4 = s.a - b;
double s1 = v1 * v2, s2 = v3 * v4;
double se = s1 + s2;
s1 /= se, s2 /= se;
return point(a.x * s2 + b.x * s1, a.y * s2 + b.y * s1);
}
point pverti (const point& p) const {
Vector t = (b - a).verti();
segment uv(p, p + t);
return intersect(uv);
}
bool on_segment (const point& p) const {
if (fi(min(a.x, b.x) - p.x) <= 0 && fi(p.x - max(a.x, b.x)) <= 0 &&
fi(min(a.y, b.y) - p.y) <= 0 && fi(p.y - max(a.y, b.y)) <= 0) return true;
else return false;
}
};
double radius;
point polygon[MAXN];//多边形
double kuras_area (point a, point b, double cx, double cy){
point ori(cx, cy);
int sgn = fi((b - ori) * (a - ori));
double da = (a - ori).length(), db = (b - ori).length();
int ra = fi(da - radius), rb = fi(db - radius);
double angle = acos(((b - ori) % (a - ori)) / (da * db));
segment t(a, b); point h, u; Vector seg;
double ans, dlt, mov, tangle;
if (fi(da) == 0 || fi(db) == 0) return 0;
else if (sgn == 0) return 0;
else if (ra <= 0 && rb <= 0) return fabs((b - ori) * (a - ori)) / 2 * sgn;
else if (ra >= 0 && rb >= 0){
h = t.pverti(ori);
dlt = (h - ori).length();
if (!t.on_segment(h) || fi(dlt - radius) >= 0)
return radius * radius * (angle / 2) * sgn;
else{
ans = radius * radius * (angle / 2);
tangle = acos(dlt / radius);
ans -= radius * radius * tangle;
ans += radius * sin(tangle) * dlt;
return ans * sgn;
}
}
else{
h = t.pverti(ori);
dlt = (h - ori).length();
seg = b - a;
mov = sqrt(radius * radius - dlt * dlt);
seg = seg.adjust(mov);
if (t.on_segment(h + seg)) u = h + seg;
else u = h + seg.oppose();
if (ra == 1) swap(a, b);
ans = fabs((a - ori) * (u - ori)) / 2;
tangle = acos(((u - ori) % (b - ori)) / ((u - ori).length() * (b - ori).length()));
ans += radius * radius * (tangle / 2);
return ans * sgn;
}
}
const double pi = acos(-1.0);
struct Line {
Point a,b;
double ang;
}line[MAXN/2],st[MAXN/2];
int n,cnt;
double operator *(const Point x,const Point y){
return x.x*y.y-x.y*y.x;
}
Point operator -(Point x,const Point y){
x.x-=y.x; x.y-=y.y;
return x;
}
Point operator * (const Line &x,const Line &y){ //交点
double a1=(y.b-x.a)*(y.a-x.a),a2=(y.a-x.b)*(y.b-x.b);
Point r;
r.x=(x.a.x*a2+x.b.x*a1)/(a2+a1);
r.y=(x.a.y*a2+x.b.y*a1)/(a2+a1);
return r;
}
bool operator ==(const Point &a,const Point &b){
return fabs(a.x-b.x)<eps&&fabs(a.y-b.y)<eps;
}
bool operator <(const Line &x,const Line &y){
if(fabs(x.ang-y.ang)<eps)
return (y.b-x.a)*(x.b-y.a)>eps;
return x.ang <y.ang;
}
bool JudgeOut(const Line &x,const Point &p){
return (p-x.a)*(x.b-x.a)>eps;
}
bool Parellel(const Line &x,const Line &y){
return fabs((x.b-x.a)*(y.b-y.a))<eps;
}
void HplaneI(){
sort(line,line+n);
int top=1,bot=0,tmp=1;
for(int i=1;i<n;i++){
if(line[i].ang-line[i-1].ang>eps) line[tmp++]=line[i];
}
n=tmp;
st[0]=line[0],st[1]=line[1];
for(int i=2;i<n;i++){
if(Parellel(st[top],st[top-1])||Parellel(st[bot],st[bot+1]))return ;
while(bot<top&&JudgeOut(line[i],st[top]*st[top-1])) top--;
while(bot<top&&JudgeOut(line[i],st[bot]*st[bot+1])) bot++;
st[++top]=line[i];
}
while(bot<top&&JudgeOut(st[bot],st[top]*st[top-1])) top--;
while(bot<top&&JudgeOut(st[top],st[bot]*st[bot+1])) bot++;
if(top<=bot+1) return ;
st[++top]=st[bot]; cnt=0;
for(int i=bot;i<top;i++){
polygon[cnt++]._copy(st[i]*st[i+1]);
}
}
int main(){
int T,icase=0;
scanf("%d",&T);
while(T--){
scanf("%lf%d",&radius,&n);
for(int i=0;i<n;i++){
scanf("%lf%lf%lf%lf",&line[i].a.x,&line[i].a.y,&line[i].b.x,&line[i].b.y);
}
scanf("%lf%lf",&cherry.x,&cherry.y);
for(int i=0;i<n;i++){
if((line[i].a-cherry)*(line[i].b-cherry)<0){
swap(line[i].a,line[i].b);
}
line[i].ang=atan2(line[i].b.y-line[i].a.y,line[i].b.x-line[i].a.x);
}
line[n].a=Point(-radius,-radius); line[n].b=Point(radius,-radius); line[n++].ang=0;
line[n].a=Point(radius,-radius); line[n].b=Point(radius,radius); line[n++].ang=pi/2;
line[n].a=Point(radius,radius); line[n].b=Point(-radius,radius); line[n++].ang=pi;
line[n].a=Point(-radius,radius); line[n].b=Point(-radius,-radius); line[n++].ang=-pi/2;
cnt=0;
HplaneI();
double ans=0;
for(int i=0;i<cnt;i++){
// printf("%lf %lf
",polygon[i].x,polygon[i].y);
ans+=kuras_area(polygon[i],polygon[(i+1)%cnt],0,0);
}
printf("Case %d: ",++icase);
printf("%.5lf",fabs(fabs(ans)-pi*radius*radius)<eps?100:fabs(ans)/(pi*radius*radius)*100);
puts("%");
}
return 0;
}