1 //pku_1266_三角形外接圆+圆的参数方程.cpp
2 #include <stdio.h>
3 #include <math.h>
4
5 const double eps = 1e-6;
6 const double pi = acos(-1);
7 const double inf = 9999999.0;
8
9 typedef struct TPoint
10 {
11 double x, y;
12 }TPoint;
13
14 typedef struct TCircle
15 {
16 TPoint c;
17 double r;
18 }TCircle;
19
20 typedef struct TTriangle
21 {
22 TPoint t[3];
23 }TTriangle;
24
25 double max(double x, double y)
26 {
27 if(x > y) return x;
28 else return y;
29 }
30
31 double min(double x, double y)
32 {
33 if(x < y) return x;
34 else return y;
35 }
36
37 double distance(TPoint p1, TPoint p2)
38 {
39 return sqrt((p1.x - p2.x) * (p1.x - p2.x)
40 + (p1.y - p2.y) * (p1.y - p2.y));
41 }
42
43 double triangleArea(TTriangle t)
44 {
45 //已知三角形三个顶点的坐标，求三角形的面积
46 return fabs(t.t[0].x * t.t[1].y + t.t[1].x * t.t[2].y
47 + t.t[2].x * t.t[0].y - t.t[1].x * t.t[0].y
48 - t.t[2].x * t.t[1].y - t.t[0].x * t.t[2].y) / 2;
49 }
50
51 TCircle circumcircleOfTriangle(TTriangle t)
52 {
53 //三角形的外接圆
54 TCircle tmp;
55 double a, b, c, c1, c2;
56 double xA, yA, xB, yB, xC, yC;
57 a = distance(t.t[0], t.t[1]);
58 b = distance(t.t[1], t.t[2]);
59 c = distance(t.t[2], t.t[0]);
60 //根据S = a * b * c / R / 4;求半径R
61 tmp.r = a * b * c / triangleArea(t) / 4;
62
63 xA = t.t[0].x; yA = t.t[0].y;
64 xB = t.t[1].x; yB = t.t[1].y;
65 xC = t.t[2].x; yC = t.t[2].y;
66 c1 = (xA * xA + yA * yA - xB * xB - yB * yB) / 2;
67 c2 = (xA * xA + yA * yA - xC * xC - yC * yC) / 2;
68
69 tmp.c.x = (c1 * (yA - yC) - c2 * (yA - yB)) /
70 ((xA - xB) * (yA - yC) - (xA - xC) * (yA - yB));
71 tmp.c.y = (c1 * (xA - xC) - c2 * (xA - xB)) /
72 ((yA - yB) * (xA - xC) - (yA - yC) * (xA - xB));
73
74 return tmp;
75 }
76
77 double Get_angle(TPoint p, TCircle c)
78 {
79 double ans;
80 ans = acos((p.x - c.c.x) / c.r);
81 if(p.y < c.c.y){
82 if(ans >= M_PI / 2){
83 ans = (M_PI - ans) + M_PI;
84 }
85 else {
86 ans = 2 * M_PI - ans;
87 }
88 }
89 return ans;
90 }
91
92 double swap(double &a, double &b)
93 {
94 double c;
95 c = a;
96 a = b;
97 b = c;
98 }
99
100 int UP(double a)
101 {
102 int a0;
103 if(a >= 0){
104 a0 = int(a);
105 if(fabs(a0 - a) < eps) return a0;
106 else return a0 + 1;
107 }
108 else {
109 a0 = (int)a;
110 if(fabs(a0 - 1 - a) < eps) return a0 - 1;
111 return a0;
112 }
113 }
114
115 int DOWN(double a)
116 {
117 int a0;
118 if(a >= 0){
119 a0 = (int)a;
120 if(fabs(a - (a0 + 1)) < eps) return a0 + 1;
121 return a0;
122 }
123 else {
124 a0 = (int)a;
125 if(fabs(a0 - a) < eps) return a0;
126 else return a0 - 1;
127 }
128 }
129
130 int main()
131 {
132 TCircle c;
133 TTriangle t;
134 TPoint p1, p2, p3;
135 double a1, a2, a3, tmp;
136 int max_x, min_x, max_y, min_y;
137 scanf("%lf%lf", &p1.x, &p1.y);
138 scanf("%lf%lf%lf%lf", &p2.x, &p2.y, &p3.x, &p3.y);
139 t.t[0] = p1;
140 t.t[1] = p2;
141 t.t[2] = p3;
142 c = circumcircleOfTriangle(t);
143 a1 = Get_angle(p1, c);
144 a2 = Get_angle(p2, c);
145 a3 = Get_angle(p3, c);
146 if(a1 > a2) swap(a1, a2);
147 //讨论
148 if(a3 >= a1 && a3 <= a2){
149 tmp = 0;
150 if(tmp >= a1 && tmp <= a2){
151 max_x = UP(c.c.x + c.r);
152 }
153 else max_x = UP(max(p1.x, p2.x));
154 tmp = pi / 2;
155 if(tmp >= a1 && tmp <= a2){
156 max_y = UP(c.c.y + c.r);
157 }
158 else max_y = UP(max(p1.y, p2.y));
159 tmp = pi;
160 if(tmp >= a1 && tmp <= a2){
161 min_x = DOWN(c.c.x - c.r);
162 }
163 else min_x = DOWN(min(p1.x, p2.x));
164 tmp = pi * 3 / 2;
165 if(tmp >= a1 && tmp <= a2){
166 min_y = DOWN(c.c.y - c.r);
167 }
168 else min_y = DOWN(min(p1.y, p2.y));
169 }
170 else {
171 tmp = 0;
172 if(tmp <= a1 || tmp >= a2){
173 max_x = UP(c.c.x + c.r);
174 }
175 else max_x = UP(max(p1.x, p2.x));
176 tmp = pi / 2;
177 if(tmp <= a1 || tmp >= a2){
178 max_y = UP(c.c.y + c.r);
179 }
180 else max_y = UP(max(p1.y, p2.y));
181 tmp = pi;
182 if(tmp <= a1 || tmp >= a2){
183 min_x = DOWN(c.c.x - c.r);
184 }
185 else min_x = DOWN(min(p1.x, p2.x));
186 tmp = pi * 3 / 2;
187 if(tmp <= a1 || tmp >= a2){
188 min_y = DOWN(c.c.y - c.r);
189 }
190 else min_y = DOWN(min(p1.y, p2.y));
191 }
192 printf("%d\n", (max_x - min_x) * (max_y - min_y));
193 return 0;
194 }
