ACM_计算几何_源码

------------------------------------------------------------------------------------------------------------------------------------------ (1)凸包/*凸包cug_1038*/#include <stdio.h>#include <stdlib.h>struct point{int x, y;}pp;point p[100005];int stack[100005], top;int dis(point a, point b){return ((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));}int multi(point b, point c, point a){return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);}void swap(point p[], int s, int t){point tmp;tmp = p[s];p[s] = p[t];p[t] = tmp;}int cmp(const void *a, const void *b){point *c = (point *)a;point *d = (point *)b;double k = multi(*c, *d, pp);if(k < 0) return 1;else if(k == 0 && dis(*c, pp) >= dis(*d, pp)) return 1;else return -1;}void Graham(point p[], int n, int stack[], int &top){int i, u;u = 0;for(i = 1;i < n;i++){if(p[i].y == p[u].y && p[i].x < p[u].x) u = i;else if(p[i].y < p[u].y) u = i;}swap(p, 0, u);pp = p[0];qsort(p + 1, n - 1, sizeof(p[0]), cmp);stack[0] = 0;stack[1] = 1;top = 1;for(i = 2;i < n;i++){while(multi(p[i], p[stack[top]], p[stack[top - 1]]) >= 0){if(top == 0) break;top--;}top++;stack[top] = i;}}int main(){int ca, i, j, n;int area;scanf("%d", &ca);for(i = 1;i <= ca;i++){scanf("%d", &n);for(j = 0;j < n;j++){scanf("%d%d", &p[j].x, &p[j].y);}Graham(p, n, stack, top);area = 0;for(j = 1;j <= top - 1;j++){area += abs(multi(p[stack[0]], p[stack[j]], p[stack[j + 1]])); }printf("%.1lf\n", (double)area / 2);}return 0;}--------------------------------------------------------------------------------------------------------------------- (2)判断两条线段是否相交(平行，不平行)bool isIntersected(TPoint s1, TPoint e1, TPoint s2, TPoint e2){//判断线段是否相交//1.快速排斥试验判断以两条线段为对角线的两个矩形是否相交//2.跨立试验if((max(s1.x, e1.x) >= min(s2.x, e2.x)) &&(max(s2.x, e2.x) >= min(s1.x, e1.x)) &&(max(s1.y, e1.y) >= min(s2.y, e2.y)) &&(max(s2.y, e2.y) >= min(s1.y, e1.y)) &&(multi(s2, e1, s1) * multi(e1, e2, s1) >= 0) &&(multi(s1, e2, s2) * multi(e2, e1, s2) >= 0)) return true;return false;}(3)三角形的外接圆(已知不在同一直线上的三点求经过三点的圆)/*三角形的外接圆pku_1329*/#include <stdio.h>#include <math.h>const double eps = 1e-6;typedef struct TPoint{double x;double y;}TPoint;typedef struct TTriangle{TPoint t[3];}TTriangle;typedef struct TCircle{TPoint centre;double r;}TCircle;double distance(TPoint p1, TPoint p2){//计算平面上两个点之间的距离return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y)); }double triangleArea(TTriangle t){//已知三角形三个顶点的坐标，求三角形的面积return fabs(t.t[0].x * t.t[1].y + t.t[1].x * t.t[2].y + t.t[2].x * t.t[0].y - t.t[1].x * t.t[0].y - t.t[2].x * t.t[1].y - t.t[0].x * t.t[2].y) / 2; }TCircle circumcircleOfTriangle(TTriangle t){//三角形的外接圆TCircle tmp;double a, b, c, c1, c2;double xA, yA, xB, yB, xC, yC;a = distance(t.t[0], t.t[1]);b = distance(t.t[1], t.t[2]);c = distance(t.t[2], t.t[0]);//根据S = a * b * c / R / 4;求半径Rtmp.r = a * b * c / triangleArea(t) / 4;xA = t.t[0].x; yA = t.t[0].y;xB = t.t[1].x; yB = t.t[1].y;xC = t.t[2].x; yC = t.t[2].y;c1 = (xA * xA + yA * yA - xB * xB - yB * yB) / 2;c2 = (xA * xA + yA * yA - xC * xC - yC * yC) / 2;tmp.centre.x = -(c1 * (yA - yC) - c2 * (yA - yB)) /((xA - xB) * (yA - yC) - (xA - xC) * (yA - yB));tmp.centre.y = -(c1 * (xA - xC) - c2 * (xA - xB)) /((yA - yB) * (xA - xC) - (yA - yC) * (xA - xB));return tmp;}int main(){TTriangle t;TCircle circle;double c, d, e;while(scanf("%lf%lf%lf%lf%lf%lf", &t.t[0].x, &t.t[0].y,&t.t[1].x, &t.t[1].y, &t.t[2].x, &t.t[2].y) != EOF){circle = circumcircleOfTriangle(t);// printf("%lf %lf %lf\n", circle.centre.x, circle.centre.y, circle.r);if(fabs(circle.centre.x) < eps) printf("x^2");else if(circle.centre.x < 0) printf("(x - %.3lf)^2 + ", -circle.centre.x);else printf("(x + %.3lf)^2 + ", circle.centre.x);if(fabs(circle.centre.y) < eps) printf("y^2 = ");else if(circle.centre.y < 0) printf("(y - %.3lf)^2 = ", -circle.centre.y);else printf("(y + %.3lf)^2 = ", circle.centre.y);printf("%.3lf^2\n", circle.r);c = 2 * circle.centre.x;d = 2 * circle.centre.y;e = circle.centre.x * circle.centre.x +circle.centre.y * circle.centre.y - circle.r * circle.r;printf("x^2 + y^2 ");//if(fabs(c) < eps)if(c < 0) printf("- %.3lfx ", -c);else printf("+ %.3lfx ", c);if(d < 0) printf("- %.3lfy ", -d);else printf("+ %.3lfy ", d);if(e < 0) printf("- %.3lf = 0\n", -e);else printf("+ %.3lf = 0\n", e);printf("\n");}return 0;}(4)三角形的垂心内心重心中垂线/*cug_1011_垂心内心重心中垂线.cpp*/#include <iostream>#include <cmath>using namespace std;const double eps = 1e-6;struct point{double x, y;};void K(){//到三边距离和最短}void L(double a, double b, double c, double A, double B, double C){ //垂线的交点double t1, t2, t3;t1 = c * cos(A) / cos(M_PI / 2 - C);t2 = c * cos(B) / cos(M_PI / 2 - C);t3 = a * cos(C) / cos(M_PI / 2 - A);t1 += t2 + t3;printf("%.3lf\n", t1);}struct TLine{double a, b, c;};TLine lineFromSegment(point p1, point p2){//线段所在直线,返回直线方程的三个系统TLine tmp;tmp.a = p2.y - p1.y;tmp.b = p1.x - p2.x;tmp.c = p2.x * p1.y - p1.x * p2.y;return tmp;}point LineInter(TLine l1, TLine l2){//求两直线得交点坐标point tmp;if(fabs(l1.b) < eps){tmp.x = -l1.c / l1.a;tmp.y = (-l2.c - l2.a * tmp.x) / l2.b;}else{tmp.x = (l1.c * l2.b - l1.b * l2.c) / (l1.b * l2.a - l2.b * l1.a); tmp.y = (-l1.c - l1.a * tmp.x) / l1.b;}return tmp;}double dis(point a, point b){return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));}void F(double a, double b, double c, double A, double B, double C) {//到三顶点的距离和最短, 费马点/*当三角形最大的顶角小于120度的时候，三角形内一点到三顶点之间的距离最小是与三顶点夹角都成120度的点P当最到顶点大于等于120度，该顶点取最小值补充一下，当三角形的最大角小于120度时，费尔码点在三角形内，作法有多种，可以从任二办向外作等边三角形，联接正三角形的顶点和原三角形的对角，两者的联线即所求。