首先判斷要檢測的點是否在邊上

然后再判斷射線是否經過一個線段的端點，如果經過低端點不計數，經過高端點計數

#include <vector> #include <string> #include <iostream> #include <cmath> #include <stdio.h>using namespace std;const double eps = 1e-10;const int N = 103;bool lessEqual(double a, double b) {//<=return a < b + eps; }bool largerEqual(double a, double b) {// >=return a + eps > b; }bool equal(double a, double b) {return fabs(a-b) < eps; }struct point {double x;double y;point(){}point(double a, double b) :x(a),y(b) {} };point ps[N]; int num; int m;//(b-a)X(c-a) //如果b在c的右手邊，為正； //b在c的左手邊，為負 //a,b,c共線，0 double x_multi(point &a, point &b, point &c) {return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y); }//(b-a)X(c-a) //夾角小于90，正 //大于90，負 //等于90，0 double dot_multi(point &a, point &b, point &c) {return (b.x - a.x) * (c.x - a.x) + (b.y - a.y) * (c.y - a.y); }bool onSegment(point &a, point &b, point &c) {//c點是否在線段ab之間double max_x = max(a.x, b.x);double max_y = max(a.y, b.y);double min_x = min(a.x, b.x);double min_y = min(a.y, b.y);if (equal(x_multi(a,b,c),0.0) && lessEqual(c.x,max_x) && largerEqual(c.x, min_x) && lessEqual(c.y, max_y) && largerEqual(c.y, min_y))return true;return false; }bool onLine(point &a, point &b, point &c) {//已知a,b,c共線double max_x = max(a.x, b.x);double max_y = max(a.y, b.y);double min_x = min(a.x, b.x);double min_y = min(a.y, b.y);if (lessEqual(c.x,max_x) && largerEqual(c.x, min_x) && lessEqual(c.y, max_y) && largerEqual(c.y, min_y))return true;return false; }bool segmentIntersect(point &a, point &b, point &c, point &d) {//兩條線段是否相交double d1 = x_multi(a,b,d);double d2 = x_multi(a,b,c);double d3 = x_multi(c,d,a);double d4 = x_multi(c,d,b);if (d1*d2 < 0 && d3 * d4 <0)return true;if (equal(d1,0.0) && onLine(a,b,d))return true;if (equal(d2,0.0) && onLine(a,b,c))return true;if (equal(d3,0.0) && onLine(c,d,a))return true;if (equal(d4,0.0) && onLine(c,d,b))return true;return false; }bool isInside(point &pt) {int count = 0;point end(1e9,pt.y);for (int i = 0; i < num; ++i) {int j = (i+1)%num;if (onSegment(ps[i], ps[j], pt))return true;if (!equal(ps[i].y, ps[j].y)) {point low = ps[i];if (low.y > ps[j].y)low = ps[j];if (onSegment(pt,end,low))//較低端點不計算continue;if (segmentIntersect(pt,end,ps[i],ps[j]))++count;/*int tmp = -1;if (onSegment(pt,end,ps[i]))tmp = i;else if (onSegment(pt,end,ps[j]))tmp = j;if(tmp != -1 && equal(ps[tmp].y, max(ps[i].y,ps[j].y)))++count;else if (tmp == -1 && segmentIntersect(ps[i],ps[j],pt,end))++count;*/}}return count % 2==1; }int main() {int ind = 1;while (scanf("%d", &num) && num !=0) {scanf("%d", &m);for (int i = 0; i < num ; ++i){scanf("%lf%lf",&ps[i].x, &ps[i].y);}if (ind !=1)cout<<endl;cout<<"Problem "<<ind<<":"<<endl;++ind;for (int i = 0; i < m; ++i) {point pt;scanf("%lf%lf", &pt.x, &pt.y);if (isInside(pt))cout<<"Within"<<endl;elsecout<<"Outside"<<endl;}} }

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