文章目录
-
- 问题
- Code
- 测例
- Accepted 代码:
问题
假设恰有两个多边形,它们都是凸的,其顶点以逆时针顺序给出,并且具有非零区域。此外,在一个多边形中,顶点不会在另一个多边形的两侧。如下图所示:
Code
#include <iostream>
#include <vector>
#include <math.h>
using namespace std;
const double FLOAT_EPS = 1e-10;
class Point
{
/**
* Point coordinate information
*/
public:
Point(const double x = 0, const double y = 0, const double z = 0):_x(x), _y(y) {}
Point(const Point& p) : _x( p.getX() ), _y( p.getY() ) {;}
~Point() {}
const double getX() const {return _x;}
const double getY() const {return _y;}
void setX(const double x) {_x = x;}
void setY(const double y) {_y = y;}
private:
double _x, _y;
};
double cross(const Point& p, const Point& q, const Point& r)
{
return (p.getX() - q.getX()) * (r.getY() - q.getY()) -
(p.getY() - q.getY()) * (r.getX() - q.getX());
}
// line segment p-q intersect with line A-B
void lineIntersectSeg(const Point& p, const Point& q, const Point& A, const Point& B, Point& res)
{
double a = B.getY() - A.getY();
double b = A.getX() - B.getX();
double c = B.getX() * A.getY() - A.getX() * B.getY();
double u = fabs(a * p.getX() + b * p.getY() + c);
double v = fabs(a * q.getX() + b * q.getY() + c);
res.setX((p.getX()*v + q.getX()*u)/(u+v));
res.setY((p.getY()*v + q.getY()*u)/(u+v));
}
void cutPolygon(const Point& a, const Point& b, const vector<Point>& Q, vector<Point>& res)
{
for(unsigned int i = 0; i < Q.size(); i++)
{
double left1 = cross(a, b, Q[i]), left2 = 0.0;
if(i != (int)Q.size()-1) {
left2 = cross(a, b, Q[i+1]);
}
if(left1 > -FLOAT_EPS) {
res.push_back(Q[i]);
}
if(left1 * left2 < -FLOAT_EPS) {
Point p(0.0, 0.0);
lineIntersectSeg(Q[i], Q[i+1], a, b, p);
res.push_back(p);
}
}
if(res.empty()) {
return ;
}
if(fabs(res.back().getX() - res.front().getX()) > FLOAT_EPS || fabs(res.back().getY() - res.front().getY()) > FLOAT_EPS) {
res.push_back(res.front());
}
}
double area(const vector<Point> & pts)
{
if(pts.empty()) {
return 0.0;
}
double result = 0.0;
for(unsigned int i = 0; i< pts.size()-1; ++i) {
result += (pts[i].getX() * pts[i+1].getY() - pts[i].getY() * pts[i+1].getX());
}
return fabs(result)/2.0;
}
double intersectArea(const vector<Point>& polys1, const vector<Point>& polys2)
{
vector<Point> pts1 = polys1;
vector<Point> pts2 = polys2;
pts1.push_back(pts1[0]);
pts2.push_back(pts2[0]);
vector<Point> res;
for(unsigned int i = 0; i < polys2.size(); ++i) {
res.clear();
cutPolygon(pts2[i + 1], pts2[i], pts1, res);
pts1 = res;
}
return area(res);
}
测例
可以参考网址 :Condeforces-J
Input
The first line of the input will be a single integer T, the number of test cases (1 ≤ T ≤ 20). each test case contains two integers (3 ≤ N, M ≤ 40) Then a line contains N pairs of integers xi, yi (-1000 ≤ xi, yi ≤ 1000) coordinates of the ith vertex of polygon A, followed by a line contains M pairs of integers xj, yj (-1000 ≤ xj, yj ≤ 1000) coordinates of the jth vertex of polygon B. The coordinates are separated by a single space.
Output
For each test case, print on a single line, a single number representing the area of intersection, rounded to four decimal places.
Examples
input
2
5 3
0 3 1 1 3 1 3 5 1 5
1 3 5 3 3 6
3 3
-1 -1 -2 -1 -1 -2
1 1 2 1 1 2
output
2.6667
0.0000
Accepted 代码:
#include <iostream>
#include <vector>
#include <math.h>
using namespace std;
const double FLOAT_EPS = 1e-10;
class Point
{
/**
* Point coordinate information
*/
public:
Point(const double x = 0, const double y = 0, const double z = 0):_x(x), _y(y) {}
Point(const Point& p) : _x( p.getX() ), _y( p.getY() ) {;}
~Point() {}
const double getX() const {return _x;}
const double getY() const {return _y;}
void setX(const double x) {_x = x;}
void setY(const double y) {_y = y;}
private:
double _x, _y;
};
double cross(const Point& p, const Point& q, const Point& r)
{
return (p.getX() - q.getX()) * (r.getY() - q.getY()) -
(p.getY() - q.getY()) * (r.getX() - q.getX());
}
// line segment p-q intersect with line A-B
void lineIntersectSeg(const Point& p, const Point& q, const Point& A, const Point& B, Point& res)
{
double a = B.getY() - A.getY();
double b = A.getX() - B.getX();
double c = B.getX() * A.getY() - A.getX() * B.getY();
double u = fabs(a * p.getX() + b * p.getY() + c);
double v = fabs(a * q.getX() + b * q.getY() + c);
res.setX((p.getX()*v + q.getX()*u)/(u+v));
res.setY((p.getY()*v + q.getY()*u)/(u+v));
}
void cutPolygon(const Point& a, const Point& b, const vector<Point>& Q, vector<Point>& res)
{
for(unsigned int i = 0; i < Q.size(); i++)
{
double left1 = cross(a, b, Q[i]), left2 = 0.0;
if(i != (int)Q.size()-1) {
left2 = cross(a, b, Q[i+1]);
}
if(left1 > -FLOAT_EPS) {
res.push_back(Q[i]);
}
if(left1 * left2 < -FLOAT_EPS) {
Point p(0.0, 0.0);
lineIntersectSeg(Q[i], Q[i+1], a, b, p);
res.push_back(p);
}
}
if(res.empty()) {
return ;
}
if(fabs(res.back().getX() - res.front().getX()) > FLOAT_EPS || fabs(res.back().getY() - res.front().getY()) > FLOAT_EPS) {
res.push_back(res.front());
}
}
double area(const vector<Point> & pts)
{
if(pts.empty()) {
return 0.0;
}
double result = 0.0;
for(unsigned int i = 0; i< pts.size()-1; ++i) {
result += (pts[i].getX() * pts[i+1].getY() - pts[i].getY() * pts[i+1].getX());
}
return fabs(result)/2.0;
}
double intersectArea(const vector<Point>& polys1, const vector<Point>& polys2)
{
vector<Point> pts1 = polys1;
vector<Point> pts2 = polys2;
pts1.push_back(pts1[0]);
pts2.push_back(pts2[0]);
vector<Point> res;
for(unsigned int i = 0; i < polys2.size(); ++i) {
res.clear();
cutPolygon(pts2[i + 1], pts2[i], pts1, res);
pts1 = res;
}
return area(res);
}
int main()
{
int t;
scanf("%d", &t);
while(t--) {
int n, m;
scanf("%d %d", &n, &m);
vector<Point> p, q;
for(int i = 0; i < n; i++) {
int a, b;
scanf("%d %d", &a, &b);
p.push_back(Point(a, b));
}
for(int i = 0; i < m; i++) {
int a, b;
scanf("%d %d", &a, &b);
q.push_back(Point(a, b));
}
printf("%.4f\n", intersectArea(p, q));
}
return 0;
}