Computational Geometry Fundamentals (templates)

1. Polygon Area Calculation

1     DoubleS (Point p[],intN)2     {  3         DoubleAns =0; 4P[n] = p[0]; 5          for(intI=1; i<n;i++)  6Ans + = Cross (p[0],p[i],p[i+1]); 7         if(Ans <0) ans =-ans; 8         returnAns/2.0; 9}

2. Find Convex bag

1     BOOLCMP (Point a,point B)2     {  3         DoubleK =Cross (MINA,A,B); 4         if(k<0)return 0; 5         if(k>0)return 1; 6         returnDist (MINA,A) <Dist (MINA,B); 7     }  8       9     voidGraham (Point p[),intN)Ten     {   One          for(intI=1; i<n;i++)   A            if(p[i].y<p[0].y | | (P[i].y = = p[0].y && p[i].x < p[0].x)) -Swap (p[i],p[0]);  -MinA = p[0];  theP[n] = p[0];  -Sort (p+1, p+n,cmp);  -stack[0] = p[0];  -stack[1] = p[1];  +top =2;  -          for(intI=2; i<n;i++)   +         {   A              while(Top >=2&& Cross (stack[top-2],stack[top-1],p[i]) <=0) top--;  atstack[top++] =P[i];  -         }   -}

3. Center of gravity for any polygon

1Point Gravity [Point p[],intN)2     {  3 Point o,t; 4o.x = O.Y =0; 5T.x = T.y =0; 6P[n] = p[0]; 7         DoubleA =0; 8          for(intI=0; i<n; i++)  9A + = Cross (o,p[i],p[i+1]); TenA/=2.0;  One          for(intI=0; i<n; i++)   A         {   -T.x + = (p[i].x + p[i+1].x) * Cross (o,p[i],p[i+1]);  -T.y + = (p[i].y + p[i+1].Y) * Cross (o,p[i],p[i+1]);  the         }   -T.x/=6*A;  -T.y/=6*A;  -         returnT;  +}

4. Finding the coordinates of the intersection of segments

1     BOOLSegment_crossing (Segment u,segment v)/** Determine if line segments intersect*/  2     {  3              return(Max (u.a.x,u.b.x) >=min (v.a.x,v.b.x)) &&4(Max (v.a.x,v.b.x) >=min (u.a.x,u.b.x)) &&5(Max (U.A.Y,U.B.Y) >=min (V.A.Y,V.B.Y)) &&6(Max (V.A.Y,V.B.Y) >=min (U.A.Y,U.B.Y)) &&7(Cross (V.A,U.B,U.A) *cross (U.B,V.B,U.A) >=0) &&8(Cross (U.A,V.B,V.A) *cross (V.B,U.B,V.A) >=0)); 9     }  Ten        One     /** Seek the coordinates of the line intersection, or return the address of the intersection p if no intersection returns NULL*/   Apoint*CrossPoint (Segment u,segment v) -     {   - Point p;  the         if(segment_crossing (u,v)) -         {   -p.x= (V.B,U.B,U.A) *v.a.x-cross (V.A,U.B,U.A) *v.b.x)/(Cross (V.B,U.B,U.A)-Cross (V.A,U.B,U.A));  -P.y= (V.B,U.B,U.A) *v.a.y-cross (V.A,U.B,U.A) *v.b.y)/(Cross (V.B,U.B,U.A)-Cross (V.A,U.B,U.A));  +             return&p;  -         }   +         returnNULL;  A}

5. Radius and center of Triangle circumscribed Circle

1 Point circle_point (Point a,point b,point C)2     {  3         DoubleA=Dist (B,C); 4         Doubleb=Dist (A,C); 5         DoubleC=Dist (A, b); 6         Doublep= (A+B+C)/2.0; 7         DoubleS=sqrt (p* (p-a) * (p-b) * (P-c)); 8R= (a*b*c)/(4*s);//the radius of the triangular circumscribed circle is R9       Ten         Doublet1= (A.X*A.X+A.Y*A.Y-B.X*B.X-B.Y*B.Y)/2;  One         DoubleT2= (A.X*A.X+A.Y*A.Y-C.X*C.X-C.Y*C.Y)/2;  A Point Center;  -Center.x= (t1* (A.Y-C.Y)-t2* (A.Y-B.Y))/((a.x-b.x) * (A.Y-C.Y)-(a.x-c.x) * (a.y-b.y));  -Center.y= (t1* (a.x-c.x)-t2* (a.x-b.x))/((A.Y-B.Y) * (a.x-c.x)-(A.Y-C.Y) * (a.x-b.x));  the         returnCenter;  -}

6. Rotation jam to find the diameter of the convex hull, that is, the plane farthest point pair, p[] is the convex hull point set

1     DoubleRotating_calipers (Point p[],intN)2     {  3         intK =1; 4         DoubleAns =0; 5P[n] = p[0]; 6          for(intI=0; i<n;i++)  7         {  8              while(Fabs (Cross (p[i],p[i+1],p[k]) < Fabs (Cross (p[i],p[i+1],p[k+1])))  9K = (+ K1) %N; Tenans = max (ans, max (Dist (p[i],p[k)), Dist (p[i+1],p[k]));  One         }   A         returnans;  -}

7. To find the width of the convex bag

1     DoubleRotating_calipers (Point p[],intN)2     {  3         intK =1; 4         DoubleAns =0x7FFFFFFF; 5P[n] = p[0]; 6          for(intI=0; i<n;i++)  7         {  8              while(Fabs (Cross (p[i],p[i+1],p[k]) < Fabs (Cross (p[i],p[i+1],p[k+1])))  9K = (+ K1) %N; Ten             DoubleTMP = Fabs (Cross (p[i],p[i+1],p[k]));  One             DoubleD = Dist (p[i],p[i+1]);  Aans = min (ans,tmp/d);  -         }   -         returnans;  the}

Computational Geometry Fundamentals (templates)