How do one decide the direction in Where do I Turn?

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Автор ganesh_6, история, 2 года назад, По-английски

I was solving the question http://codeforces.com/contest/227/problem/A. If the cross product is zero then obviously they are collinear since sin(x)=0 if x=2*n*PI. However, how do they decide if it is Left or Right based on the value of cross-product i.e; x1*y2-x2*y1. Please demystify this for me. Am I missing any fundamentals?

C++

#include<iostream>

using namespace std;

long long xa,xb,ya,yb,xc,yc,t;

long long cp(long long x1,long long x2,long long y1,long long y2)
{
    return x1*y2-x2*y1;
}
int main()
{
    cin>>xa>>ya>>xb>>yb>>xc>>yc;
    t=cp(xc-xa,xb-xa,yc-ya,yb-ya);
    if (t==0)
    {
        cout<<"TOWARDS"<<endl;
    }
    if (t<0)
    {
        cout<<"LEFT"<<endl;
    }
    if (t>0)
    {
        cout<<"RIGHT"<<endl;
    }
    return 0;
}

geometry

ganesh_6
2 года назад
3

Комментарии (2)

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alihotnik

2 года назад, # |

← Rev. 2 →

Function cp calculates the z-coordinate of the cross product. Then you can use the right hand rule to determine the direction (angle CAB is always less than 90) If C is to the left => Thumb will go down => z-coordinate less than 0 => t is less than 0, and vice versa

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ganesh_6

2 года назад, # ^ |

Awesome! Now I remember my school days. These are the stuff I learned in my school in Physics and maths. Looks like I need to revise a lot in the process. Thanks a ton!

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