计算几何 2017.4.5

2、UVa 11178 Morley's Theorem

参考：《算法竞赛入门经典-训练指南》P259

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <set>#include <cmath>#include <cctype>#include <ctime>#include <cassert>using namespace std;#define REP(i, n) for (int i = 0; i < (n); ++i)struct Point {  double x, y;  Point(double x = 0.0, double y = 0.0):x(x),y(y) {}};typedef Point Vector;const double INF = 1e20;const double eps = 1e-10;const double PI = acos(-1.0);Point A, B, C, D, E, F;int N;Point operator + (const Point& a, const Vector& b) { return Point{a.x + b.x, a.y + b.y}; }Vector operator - (const Point& a, const Point& b) { return Vector(a.x - b.x, a.y - b.y); }Vector operator * (const Vector& a, double k) { return Vector{a.x * k, a.y * k}; }double dot(const Vector& a, const Vector& b) { return a.x * b.x + a.y * b.y; }double length(const Vector& a) { return sqrt(dot(a, a)); }double angle(const Vector& a, const Vector& b) { return acos(dot(a, b) / length(a) / length(b)); }double cross(const Vector& a, const Vector& b) { return a.x * b.y - a.y * b.x; }Point read_point() { double x, y; scanf("%lf %lf", &x, &y); return Point{x, y}; }Point line_intersection(const Point& p, const Vector& v, const Point& q, const Vector& w) {    Vector u = p - q; double t = cross(w, u) / cross(v, w); return p + v * t;}Vector rotate(const Vector& a, double rad) {    return Vector{a.x * cos(rad) - a.y * sin(rad), a.x * sin(rad) + a.y * cos(rad)};}Point get_D(Point a, Point b, Point c) {    Vector v1 = c - b; double a1 = angle(v1, a - b); v1 = rotate(v1, a1 / 3.0);    Vector v2 = b - c; double a2 = angle(a - c, v2); v2 = rotate(v2, -a2 / 3.0);    return line_intersection(b, v1, c, v2);}int main() {#ifdef __AiR_H    freopen("in.txt", "r", stdin);//    freopen("out.txt", "w", stdout);#endif // __AiR_H    scanf("%d", &N);    while (N--) {        A = read_point(); B = read_point(); C = read_point();        D = get_D(A, B, C); E = get_D(B, C, A); F = get_D(C, A, B);        printf("%.6f %.6f %.6f %.6f %.6f %.6f\n", D.x, D.y, E.x, E.y, F.x, F.y);    }#ifdef __AiR_H    printf("Time used = %.2fs\n", (double)clock() / CLOCKS_PER_SEC);#endif // __AiR_H    return 0;}

3、POJ 1269 Intersecting Lines

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <set>#include <cmath>#include <cctype>#include <ctime>#include <cassert>using namespace std;#define REP(i, n) for (int i = 0; i < (n); ++i)struct Point {  double x, y;  Point(double x = 0.0, double y = 0.0):x(x),y(y) {}};typedef Point Vector;struct Seg { Point a, b; };const double INF = 1e20;const double eps = 1e-10;const double PI = acos(-1.0);int T;Seg A, B;Point operator + (const Point& a, const Vector& b) { return Point(a.x + b.x, a.y + b.y); }Vector operator - (const Point& a, const Point& b) { return Vector(a.x - b.x, a.y - b.y); }Vector operator * (const Vector& a, double k) { return Vector(a.x * k, a.y * k); }double cross(const Vector& a, const Vector& b) { return a.x * b.y - a.y * b.x; }Point read_point() { double x, y; scanf("%lf %lf", &x, &y); return Point(x, y); }Seg read_seg() { return Seg{read_point(), read_point()}; }bool is_parallel(const Seg& p, const Seg& q) {    return (abs((p.a.y - p.b.y) * (q.a.x - q.b.x) - (p.a.x - p.b.x) * (q.a.y - q.b.y)) < eps) ? true : false;}Point line_intersection(const Point& p, const Vector& v, const Point& q, const Vector& w) {    Vector u = p - q; double t = cross(w, u) / cross(v, w); return p + v * t;}int main() {#ifdef __AiR_H    freopen("in.txt", "r", stdin);//    freopen("out.txt", "w", stdout);#endif // __AiR_H    scanf("%d", &T);    printf("INTERSECTING LINES OUTPUT\n");    while (T--) {        A = read_seg(); B = read_seg();        if (is_parallel(A, B)) {            if (is_parallel(A, Seg{A.a, B.a})) { printf("LINE\n"); }            else { printf("NONE\n"); }        } else {            Point ans = line_intersection(A.a, A.b - A.a, B.a, B.b - B.a);            printf("POINT %.2f %.2f\n", ans.x, ans.y);        }    }    printf("END OF OUTPUT\n");#ifdef __AiR_H    printf("Time used = %.2fs\n", (double)clock() / CLOCKS_PER_SEC);#endif // __AiR_H    return 0;}

4、POJ 1127 Jack Straws

参考：《挑战程序设计竞赛》《算法竞赛入门经典-训练指南 》

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <set>#include <cmath>#include <cctype>#include <ctime>#include <cassert>using namespace std;#define REP(i, n) for (int i = 0; i < (n); ++i)struct Point {  double x, y;  Point(double x = 0.0, double y = 0.0):x(x),y(y) {}};typedef Point Vector;struct Seg { Point a, b; };const double INF = 1e20;const double eps = 1e-10;const double PI = acos(-1.0);int n;bool vis[20], G[20][20];bool flag = false;Point operator + (const Point& a, const Vector& b) { return Point(a.x + b.x, a.y + b.y); }Vector operator - (const Point& a, const Point& b) { return Vector(a.x - b.x, a.y - b.y); }Vector operator * (const Vector& a, double k) { return Vector(a.x * k, a.y * k); }double dot(const Vector& a, const Vector& b) { return a.x * b.x + a.y * b.y; }double cross(const Vector& a, const Vector& b) { return a.x * b.y - a.y * b.x; }Point read_point() { double x, y; scanf("%lf %lf", &x, &y); return Point(x, y); }Seg read_seg() { return Seg{read_point(), read_point()}; }int dcmp(double x) { if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }bool on_seg(const Point& a, const Seg& p) {    return dcmp(cross(p.a - a, p.b - a)) == 0 && dcmp(dot(p.a - a, p.b - a)) <= 0;}bool is_seg_intersect(const Seg& p, const Seg& q) {    double c1 = cross(p.b - p.a, q.a - p.a), c2 = cross(p.b - p.a, q.b - p.a);    double c3 = cross(q.b - q.a, p.a - q.a), c4 = cross(q.b - q.a, p.b - q.a);    if (dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0) { return true; }    return on_seg(p.a, q) || on_seg(p.b, q) || on_seg(q.a, p) || on_seg(q.b, p);}void dfs(int u, int v) {    if (flag) { return; }    if (u == v) { flag = true; return; }    REP(i, n) if (!vis[i] && G[u][i]) { vis[i] = true; dfs(i, v); }}int main() {#ifdef __AiR_H    freopen("in.txt", "r", stdin);//    freopen("out.txt", "w", stdout);#endif // __AiR_H    int a, b; Seg seg[20];    while (scanf("%d", &n) && n != 0) {        memset(G, false, sizeof(G));        REP(i, n) { seg[i] = read_seg(); }        for (int i = 0; i < n - 1; ++i) for (int j = i + 1; j < n; ++j) {            if (is_seg_intersect(seg[i], seg[j])) { G[i][j] = true; G[j][i] = true; }        }        while (scanf("%d %d", &a, &b) && !(a == 0 && b == 0)) {            --a; --b; memset(vis, false, sizeof(vis)); flag = false; dfs(a, b);            if (flag) { printf("CONNECTED\n"); }            else { printf("NOT CONNECTED\n"); }        }    }#ifdef __AiR_H    printf("Time used = %.2fs\n", (double)clock() / CLOCKS_PER_SEC);#endif // __AiR_H    return 0;}

5、POJ 2624 4th Point

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <set>#include <cmath>#include <cctype>#include <ctime>#include <cassert>using namespace std;#define REP(i, n) for (int i = 0; i < (n); ++i)struct Point {  double x, y;  Point(double x = 0.0, double y = 0.0):x(x),y(y) {}};typedef Point Vector;struct Seg { Point a, b; };const double INF = 1e20;const double eps = 1e-10;const double PI = acos(-1.0);Point A, B, C, D;Point operator + (const Point& a, const Vector& b) { return Point(a.x + b.x, a.y + b.y); }Vector operator - (const Point& a, const Point& b) { return Vector(a.x - b.x, a.y - b.y); }Vector operator * (const Vector& a, double k) { return Vector(a.x * k, a.y * k); }int dcmp(double x) { if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }int main() {#ifdef __AiR_H    freopen("in.txt", "r", stdin);//    freopen("out.txt", "w", stdout);#endif // __AiR_H    while (scanf("%lf %lf %lf %lf %lf %lf %lf %lf", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y, &D.x, &D.y) != EOF) {        Point ans, A_t, B_t, C_t;        if (dcmp(A.x - C.x) == 0 && dcmp(A.y - C.y) == 0) { A_t = B; B_t = A; C_t = D; }        else if (dcmp(B.x - C.x) == 0 && dcmp(B.y - C.y) == 0) { A_t = A; B_t = B; C_t = D; }        else if (dcmp(A.x - D.x) == 0 && dcmp(A.y - D.y) == 0) { A_t = B; B_t = A; C_t = C; }        else { A_t = A; B_t = B; C_t = C; }        ans = A_t + (C_t - B_t);        printf("%.3f %.3f\n", ans.x, ans.y);    }#ifdef __AiR_H    printf("Time used = %.2fs\n", (double)clock() / CLOCKS_PER_SEC);#endif // __AiR_H    return 0;}