When determining a point in a straight line, two conditions need to be met, such as determining whether the qpoint is in the online segment P1P2.
1 (Q-P1) x (P2-P1) = 0; // The cross multiplication is 0.
2: Q is in the rectangle with the diagonal vertex P1 and P2. // ensure that the vertex Q is not in the extension line or reverse extension line of the P1P2 line segment.
Points in the triangle:
If point P is in the triangle, spab + SPAC + spbc = SABC
The triangle area formula is given by the cross product S = 1/2 × | crossproduct (a, B, c) |;
This method has a floating point error.
The other is to judge whether point P is on the right side of each side along the clockwise direction of the side of the triangle. If yes, it is in the triangle.
This method has no floating point error.
Only floating point errors are given below.
#include <stdio.h>#include <math.h>#include <iostream>#include <algorithm>#define eps 1e-8using namespace std;typedef struct node{ double x,y;}point;typedef struct triangle{ point A; point B; point C;};double crossProduct(point p1,point p2,point p0)//(p1-p0)X(p2-p0){ double x1,x2,y1,y2; x1=p1.x-p0.x; y1=p1.y-p0.y; x2=p2.x-p0.x; y2=p2.y-p0.y; return x1*y2-x2*y1;}bool inTriangle(triangle t,point P){ point A,B,C; A=t.A; B=t.B; C=t.C; double Sabc=fabs(crossProduct(A,B,C));printf("abc:%lf ",Sabc); double Spab=fabs(crossProduct(P,A,B));printf("pab:%lf ",Spab); double Spac=fabs(crossProduct(P,A,C));printf("pac:%lf ",Spac); double Spbc=fabs(crossProduct(P,B,C));printf("pbc:%lf ",Spbc); if(fabs(Sabc-(Spab+Spac+Spbc))<eps) return true; else return false;}bool onSegment(point Pi,point Pj,point Q){ if((Q.x-Pi.x)*(Pj.y-Pi.y)==(Pj.x-Pi.x)*(Q.y-Pi.y)&&//x1*y2=x2*y1 min(Pi.x,Pj.x)<=Q.x&&Q.x<=max(Pi.x,Pj.x)&& min(Pi.y,Pj.y)<=Q.y&&Q.y<=max(Pi.y,Pj.y)) return true; else return false;}int main(){ point p,q,r,s; scanf("%lf%lf%lf%lf",&p.x,&p.y,&q.x,&q.y);//segment p--q scanf("%lf%lf",&r.x,&r.y);//point r scanf("%lf%lf",&s.x,&s.y);//point s if(onSegment(p,q,r)) { printf("YES\n"); } else { printf("NO\n"); } triangle t; t.A=p; t.B=q; t.C=r; if(inTriangle(t,s)) { printf("YES\n"); } else { printf("NO\n"); } return 0;}
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