/* 求兩圓外公切線方程式 */ /* Wei-hung Yeh 葉韋宏*/ #include #include #define INPUTFILE "c_outtan.in" /* 輸入檔檔名*/ typedef struct POINT{ double x,y; }POINT; /* center : 圓心的座標 (center.x,center.y) r : 圓的半徑 p : 圓外一點的座標 (p.x,p.y) m1,m2 : 傳回的切線斜率 */ #define ERROR 0 /* 點在圓內 */ #define ONLY_ONE_PERPENDICULAR_LINE 1 /* 點在圓上,切線垂直x軸 */ #define AMONG_ONE_IS_PERPENDICULAR 2 /* 兩條切線,其中一條垂直x軸 */ #define TWO_GENERAL_LINES 3 /* 兩條不垂直X軸的切線 */ #define ONLY_ONE_GENERAL_LINE 4 /* 點在圓上,切線不垂直X軸 */ int point2circle_slope(POINT center, double r,POINT p, double* m1, double* m2) { double a,b,c,t; double D=0; bool OnCircle=false; a = p.x - center.x; a *= a; b = p.y - center.y; b *= b; c = sqrt(a + b); if (c < r) return ERROR; else if (c == r) OnCircle = true; b = (p.y - center.y) * (center.x - p.x); a = center.x - p.x; a *= a; a -= r*r; c = p.y - center.y; c *= c; c -= r*r; if (a == 0 && !OnCircle){ *m1 = (-c) / (2 * b); return AMONG_ONE_IS_PERPENDICULAR; } else{ D = 4 * (b*b - a*c); if (D == 0){ if (p.y - center.y == 0) return ONLY_ONE_PERPENDICULAR_LINE; else{ *m1 = (-2*(p.y - center.y) * (center.x - p.x)) / (2*a); return ONLY_ONE_GENERAL_LINE; } } else{ D = sqrt(D); t = -2*(p.y - center.y) * (center.x - p.x); *m1 = (t + D) / (2*a); *m2 = (t - D) / (2*a); return TWO_GENERAL_LINES; } } } /* c1 :圓1的座標 r1 :圓1的半徑 c2 :圓2的座標 r2 :圓2的半徑 *m1 :回傳外公切線斜率(若公切線只有一條,則斜率存放在*m1) *m2 :回傳外公切線斜率 *p :兩外公切線的交點 */ #define SAME 5 /* 兩圓半徑一樣,兩外公切線不垂直X軸 */ #define TWO_ORTHOGONAL_LINES 6 /* 兩圓半徑一樣,兩外公切線垂直X軸 */ int outer_tangent(POINT c1, double r1, POINT c2, double r2, double* m1, double* m2, POINT* p) { POINT t; double tr; if (fabs(r1 - r2) >= sqrt(pow(c1.x - c2.x,2) + pow(c1.y - c2.y,2))) return ERROR; if (r1 == r2){ if (c1.x == c2.x){ p->y = c1.y; p->x = c1.x + r1; return TWO_ORTHOGONAL_LINES; } else{ *m1 = (c1.y - c2.y) / (c1.x - c2.x); p->x = c1.x + sqrt((pow(r1,2) + pow(*m1,2)) / (pow(*m1,2) + 1)); if (*m1 == 0) p->y = c1.y+r1; else p->y = -(p->x - c1.x) / *m1 + c1.y; return SAME; } } else if (r2 > r1){ t.x = c1.x; t.y = c1.y; tr = r1; c1.x = c2.x; c1.y = c2.y; r1 = r2; c2.x = t.x; c2.y = t.y; r2 = tr; } p->x = (r1*c2.x - r2*c1.x) / (r1 - r2); p->y = (r1*c2.y - r2*c2.y) / (r1 - r2); return point2circle_slope(c1,r1,*p,m1,m2); } void main(void) { POINT c1,c2,p; double r1,r2,m1,m2; FILE *in_file = fopen(INPUTFILE,"r"); int count; count = 0; while(fscanf(in_file,"%lf%lf%lf%lf%lf%lf",&c1.x,&c1.y,&r1,&c2.x,&c2.y,&r2) != EOF){ printf("Case %d:\n",++count); switch (outer_tangent(c1,r1,c2,r2,&m1,&m2,&p)){ case ERROR: printf("ERROR!\n"); break; case SAME: printf("y = %lf * (x - %lf)% + lf\n",m1,p.x,p.y); printf("y = %lf * (x - %lf)% + lf\n",m1,2*c1.x-p.x,2*c1.y-p.y); break; case TWO_ORTHOGONAL_LINES: printf("x = %lf\n",p.x); printf("x = %lf\n",2*c1.x - p.x); break; case AMONG_ONE_IS_PERPENDICULAR: printf("y = %lf * (x - %lf)% + lf\n",m1,p.x,p.y); printf("x = %lf\n",p.x); break; case TWO_GENERAL_LINES: printf("y = %lf * (x - %lf) + %lf\n",m1,p.x,p.y); printf("y = %lf * (x - %lf) + %lf\n",m2,p.x,p.y); break; } } fclose(in_file); } /* test data format: input file name: c_outtan.in Sample Input: (圓1.x 圓1.y 圓1半徑 圓2.x 圓2.y 圓2半徑) 0 0 2 0 5 2 兩圓半徑一樣,外公切線皆垂直X軸 0 0 2 5 0 2 兩圓半徑一樣,外公切線皆平行X軸 0 0 4 5 0 2 兩圓大小不一樣,有兩條外公切線 0 0 2 3 3 2 兩圓大小一樣,兩外公切線不平行也不垂直X軸 Sample OutPut: Case 1: x = 2.000000 x = -2.000000 Case 2: y = 0.000000 * (x - 2.000000)+2.000000 y = 0.000000 * (x - -2.000000)-2.000000 Case 3: y = 0.436436 * (x - 10.000000) + 0.000000 y = -0.436436 * (x - 10.000000) + 0.000000 Case 4: y = 1.000000 * (x - 1.581139)-1.581139 y = 1.000000 * (x - -1.581139)+1.581139 */