Given are the (x,y) coordinates of the endpoints of two adjacent sides of a parallelogram. Find the (x,y) coordinates of the fourth point.
Input
Each line of input contains eight floating point numbers: the (x,y) coordinates of one of the endpoints of the first side followed by the (x,y) coordinates of the other endpoint of the first side, followed by the (x,y) coordinates of one of the endpoints of the second side followed by the (x,y) coordinates of the other endpoint of the second side. All coordinates are in meters, to the nearest mm. All coordinates are between -10000 and +10000.
Output
For each line of input, print the (x,y) coordinates of the fourth point of the parallelogram in meters, to the nearest mm, separated by a single space.
Sample Input
0.000 0.000 0.000 1.000 0.000 1.000 1.000 1.000 1.000 0.000 3.500 3.500 3.500 3.500 0.000 1.000 1.866 0.000 3.127 3.543 3.127 3.543 1.412 3.145Sample Output
1.000 0.000 -2.500 -2.500 0.151 -0.398
The meaning of the question: Give you two adjacent sides of a parallelogram, let you find the coordinates of the fourth point.
Analysis of ideas: a relatively basic computational geometry problem, as long as the vector sums of the vectors are
equal, the positions of equal points can be solved There are 4 cases, which are 1 3, 1 4, 2 3, 2 4 respectively.
Code example:
struct point { double x, y; point(double _x=0, double _y=0):x(_x), y(_y){} // point - point = vector point operator-(const point &v){ return point(x-v.x, y-v.y); } }; int dcmp(double x){ if (fabs(x)<eps) return 0; else return x<0?-1:1; } bool operator == (const point &a, const point &b){ return (dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0); } typedef point Vector; // Vector represents a vector point p[10]; int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); while(~scanf("%lf%lf", &p[1].x, &p[1].y)){ for(int i = 2; i <= 4; i++) { scanf("%lf%lf", &p[i].x, &p[i].y); } if (p[2] == p[3]) { Vector v = p[4] - p[3]; printf("%.3f %.3f\n", v.x+p[1].x, v.y+p[1].y); } if (p[2] == p[4]){ Vector v = p[3] - p[4]; printf("%.3f %.3f\n", v.x+p[1].x, v.y+p[1].y); } if (p[1] == p[3]){ Vector v = p[4]-p[3]; printf("%.3f %.3f\n", v.x+p[2].x, v.y+p[2].y); } if (p[1] == p[4]){ Vector v = p[3] - p[4]; printf("%.3f %.3f\n", v.x+p[2].x, v.y+p[2].y); } } return 0; }