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POc++ : check if two triangles intersect or not
 

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    <p>Problem : </p> <p>Given the vertices of two triangles, check whether both of them have any common interior point. No points on the edges or vertices are considered interior to a triangle.<br> I think this is a problem to find whether two triangles intersect or not. </p> <p>My idea is : </p> <pre><code>1. Make three line segments for each of the two triangles 2. For each pair of line segment (A,B) (where A is in triangle #1 and B is in Triangle #2) check whether they intersect or not. 3. If any pair of segments intersect, then the two triangles have a interior point. Otherwise not . </code></pre> <p>My code :</p> <pre><code>#include &lt;algorithm&gt; #include &lt;iostream&gt; #include &lt;cstdlib&gt; #include &lt;cstdio&gt; #include &lt;cmath&gt; #define READ freopen("in.txt","r",stdin) #define ui64 unsigned long long int #define i64 long long int using namespace std; class Point{ public: i64 x, y; Point() : x(0), y(0) {} Point(int a, i64 b) : x(a), y(b) {} }; class Segment{ public: Point a, b; Segment() : a(0,0), b(0,0) {} Segment(Point e, Point r) : a(e), b(r) {} Segment(const Segment &amp;s){ a = s.a; b = s.b; } i64 Direction(const Point &amp;p){ return (p.x - a.x) * (b.y - a.y) - (b.x - a.x) * (p.y - a.y); } inline bool inside(int a,int b,int c){ return a&lt;=c &amp;&amp; c&lt;=b; } bool onSegment(const Point &amp;p){ return inside(min(a.x,b.x), max(a.x,b.x), p.x) &amp;&amp; inside(min(a.y,b.y), max(a.y,b.y), p.y); } bool Intersect(Segment &amp;s){ int d1 = this-&gt;Direction(s.a); int d2 = this-&gt;Direction(s.b); int d3 = s.Direction(a); int d4 = s.Direction(b); if(((d1&gt;0 &amp;&amp; d2&lt;0) || (d1&lt;0 &amp;&amp; d2&gt;0)) &amp;&amp; ((d3&gt;0 &amp;&amp; d4&lt;0) || (d3&lt;0 &amp;&amp; d4&gt;0))) return true; //check if the two segments just touch each other but don't cross //i ignored this because as the problem said ... //No points on the edges or vertices are considered interior to a triangle. /*if(!d1 &amp;&amp; this-&gt;onSegment(s.a)) return true; if(!d2 &amp;&amp; this-&gt;onSegment(s.b)) return true; if(!d3 &amp;&amp; s.onSegment(a)) return true; if(!d4 &amp;&amp; s.onSegment(b)) return true;*/ return false; } }; Point p1[3], p2[3]; Segment s1[3], s2[3]; bool check() { for(int i=0;i&lt;3;i++) for(int j=0;j&lt;3;j++) if(s1[i].Intersect(s2[j])) return true; return false; } int main() { //READ; int t, ts=0; scanf("%d",&amp;t);//number of test cases while(t--){ //points for first triangle for(int i=0;i&lt;3;i++){ scanf("%lld %lld",&amp;p1[i].x, &amp;p1[i].y); } //points for second triangle for(int i=0;i&lt;3;i++){ scanf("%lld %lld",&amp;p2[i].x, &amp;p2[i].y); } for(int i=0;i&lt;3;i++){ s1[i] = Segment(p1[i], p1[(i+1)%3]); s2[i] = Segment(p2[i], p2[(i+1)%3]); } printf("pair %d: %s\n",++ts, check() ? "yes" : "no"); } return 0; } </code></pre> <p>However for this input .. </p> <pre><code>1 0 0 5 0 2 4 4 0 5 0 -4 16 </code></pre> <p>My program gives output</p> <pre><code>no </code></pre> <p>but the correct answer is </p> <pre><code>yes </code></pre> <p>and there are many cases for which my program doesn't work.<br> I checked my Segment class for other program and it worked fine.<br> But in this , i can't find the mistake.<br> Please help. </p> <p>Thank you.</p>
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    1. USAshwin Nanjappa
    1. USpalatok
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      1. VTUpMod
    1. COYour approach doesn't consider the case where one triangle is entirely contained within the other.
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      1. USOliver Charlesworth
    2. COthanks for pointing out. in that case, what should be my approach ?
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      1. USpalatok
    3. CObut the problem statement said : NO points on the edges or vertices are considered interior to a triangle.
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      1. USpalatok
 

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