前回の応用問題の解答例

1. 点が長方形の内部に含まれるか
   

   #include <stdio.h>
   
   struct point {
     double x;
     double y;
   };
   
   struct rect {
     struct point ul; /* 左上隅 */
     struct point lr; /* 右下隅 */
   };
   
   /* 点p1の右下に点p2がある時に限り, 真を返す */
   int is_lr(struct point p1, struct point p2){
     int result;
     if((p1.x <= p2.x) &&          /* p2 の方が右にあって */
        (p1.y >= p2.y)){           /* p2 の方が下にあるなら */
       result = 1;                 /* 真 */
     } else {                      /* そうでなければ */
       result = 0;                 /* 偽 */
     }
     return result;
   }
   
   /* 長方形rの内部に点pがあるなら, 真を返す */
   int includes(struct rect r, struct point p){
     int result;
     if(is_lr(r.ul, p) &&          /* 左上隅とpの関係 */
        is_lr(p, r.lr)){           /* pと右下隅の関係 */
       result = 1;                 /* 両方OKなら真 */
     } else {                      /* そうでなければ */
       result = 0;                 /* 偽 */
     }
     return result;
   }
   
   int main(void){
     struct rect r1 = {{1.0, 2.0}, {3.0, 1.0}};
     struct point p1 = {2.0, 1.5};
     struct point p2 = {4.0, 1.5};
   
     printf("for p1: %d\n", includes(r1, p1));
     printf("for p2: %d\n", includes(r1, p2));
   
     return 0;
   }
   

2. 二つの線分が交点を持つか
   方針だけ, 授業時間に説明します. 数式の導出は以下の通り:
   
   
   

   #include <stdio.h>
   
   struct point {
     double x;
     double y;
   };
   
   struct line {
     struct point p1;
     struct point p2;
   };
   
   /* 二つの線分が交差する時, 真を返す */
   int intersects(struct line l1, struct line l2){
     int result;
     double a, b;
     double p;
     double x, y;
   
     p = (l1.p1.y-l1.p2.y)*(l2.p1.x-l2.p2.x) -
       (l1.p1.x-l1.p2.x)*(l2.p1.y-l2.p2.y);
       
     /* printf("p: %le\n", p); */
     if(p == 0.0){
       result = 0;
     } else {
       a = ((l2.p1.x-l2.p2.x)*(l2.p2.y-l1.p2.y) -
            (l2.p1.y-l2.p2.y)*(l2.p2.x-l1.p2.x)) / p;
       b = ((l1.p1.y-l1.p2.y)*(l1.p2.x-l2.p2.x) -
            (l1.p1.x-l1.p2.x)*(l1.p2.y-l2.p2.y)) / p;
       /* printf("a: %le b: %le\n", a, b); */
       if((0.0 <= a) && (a <= 1.0) &&
          (0.0 <= b) && (b <= 1.0)){
         result = 1;
       } else {
         result = 0;
       }
     }
     /* printf("\n"); */
     return result;
   }
   
   int main(void){
     struct line l1 = {{0.0, 1.0}, {1.0, 0.0}, };
     struct line l2 = {{0.0, 0.0}, {1.0, 1.0}};
     struct line l3 = {{0.0, 2.0}, {1.0, 2.0}};
     struct line l4 = {{0.0, 1.0}, {1.0, 2.0}};
     struct line l5 = {{1.0, 1.0}, {0.0, 1.0}, };
   
     printf("for l1, l2: %d\n", intersects(l1, l2));
     printf("for l1, l3: %d\n", intersects(l1, l3));
     printf("for l2, l4: %d\n", intersects(l2, l4));
     printf("for l2, l5: %d\n", intersects(l2, l5));
   
     return 0;
   }