hdu3712 Detector Placement

题意：给一束激光，一个三棱柱，三棱柱会折射光，问这束激光最终是否会和y = 0相交；

分析：模拟题，为了方便处理折射角，事先求出每条边的向内和向外的法向量；

findpoint : 找第一交点

step1:  判断激光是否和三角形有规范相交；

step2: 第一次折射；

step3:第二次折射，可能无法折射；

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
const int N = 100+10;
const double eps = 1e-8;
const double pi = acos(-1.0);
inline int dcmp(double x) {
    return x < -eps ? -1 : x > eps;
}
inline double sqr(double x) {
    return x * x;
}

struct Point{
    double x,y;
    Point(){}
    Point(double _x,double _y):x(_x),y(_y){}
    bool operator == (const Point &p) const{
        return dcmp(x - p.x) == 0 && dcmp(y - p.y) == 0;
    }
    Point operator + (const Point &p) const{
        return Point(x + p.x, y + p.y);
    }
    Point operator - (const Point &p) const{
        return Point (x - p.x, y - p.y);
    }
    Point operator * (const double &k) const{
        return Point (x * k, y * k);
    }
    Point operator / (const double &k) const{
        return Point (x / k, y / k);
    }
    double operator * (const Point &p) const{
        return x * p.y - y * p.x;
    }
    double operator / (const Point &p) const{
        return x * p.x + y * p.y;
    }
    double len2() {
        return x * x + y * y;
    }
    double len() {
        return sqrt(len2());
    }
    Point scale(const double &k) {
        return dcmp( len() ) ? (*this) * (k / len()) : (*this);
    }
    Point turnLeft() {
        return Point(-y,x);
    }
    Point turnRight(){
        return Point(y,-x);
    }
    double Distance(const Point &p) {
        return sqrt(sqr(x - p.x) + sqr(y - p.y));
    }
    Point rotate(const Point &p,double angle, double k = 1) {
        Point vec = (*this) - p;
        double c = cos(angle * k)  , s =sin(angle * k) ;
        return p + Point(vec.x * c - vec.y * s, vec.x * s + vec.y * c);
    }
    void input(){
        scanf("%lf%lf",&x,&y);
    }
    void ot() {
        printf("%.3lf %.3lf\n",x,y);
    }
};
double Angle(Point a,Point b) {
    return (a/b) / a.len() / b.len();
}
struct Line{
    Point a,b;
    Line(){}
    Line(Point a,Point b):a(a),b(b){}
    double operator * (const Point &p) const{
        return (b - a) * (p - a);
    }
    double operator / (const Point &p) const{
        return (p - a) / (p - b);
    }
    bool IsPointOnSeg(const Point &p) {
        return dcmp( (a - p) * (b - p) ) == 0 && dcmp( (p - a) / (p - b) ) <= 0;
    }
    int LineCrossSeg(const Line &v) {//2jiao, 1 dian ,0 wu
        int d1 = dcmp( (*this) * v.a), d2 = dcmp((*this) * v.b);
        if ((d1 ^ d2) == -2) return 2;
        return (d1 == 0 || d2 == 0);
    }
    Point CrossPoint(const Line &v) {
        double s1 = v * a, s2 = v * b;
        return ( a * s2 - b * s1 ) / (s2 - s1);
    }
};
Line li[3];
int d[3];
Point a[3],b[3],c[3];
Point st,en;

double u;
int check(int i) {
    if (dcmp( (li[i].b - li[i].a) * (a[d[i]] - li[i].a) ) > 0) {
        return 1;
    }
    return 0;
}
void init(){
    for (int i = 0; i < 3; i++) {
        if (check(i)) {
            b[i] = (li[i].b - li[i].a).turnLeft();
            c[i] = (li[i].b - li[i].a).turnRight();
        }else {
            b[i] = (li[i].b - li[i].a).turnRight();
            c[i] = (li[i].b - li[i].a).turnLeft();
        }
    }
}
int ond(Point a,Point b,Point p) {
    if (dcmp((p - a) / (b - a)) >= 0) return 1;
    return 0;
}
int step1() {
    int fg = 0;
    Line line = Line(st,en);
    for (int i = 0; i < 3; i++) {
        if (line.LineCrossSeg(li[i]) == 2) {
            Point p = line.CrossPoint(li[i]);
            if (ond(st,en,p)) fg = 1;
        }
    }
    if (fg == 0) {

        Point p = line.CrossPoint(Line(Point(0,0),Point(1,0)));
        if (ond(st,en,p)) printf("%.3lf\n",p.x+eps);
        else printf("Error\n");
        return 0;
    }
    return 1;

}
void findPoint(Point &p,int &id) {
    Line line = Line(st,en);
    double dis = 1e50;
    for (int i = 0; i < 3; i++) {
        if (line.LineCrossSeg(li[i])) {
            Point tp = line.CrossPoint(li[i]);
            if (!ond(st,en,tp)) continue;
            double tdis = tp.Distance(st);
            if (tdis < dis && dcmp(tdis) != 0) {
                dis = tdis;
                p = tp;
                id = i;
            }
        }
    }
}
void step2() {
    Point p;
    int id = -1;
    findPoint(p,id);
    Point vec = en - st;
    double cs = Angle(vec,b[id]);
    double sn1 = sqrt(1 - cs * cs);
    double sn2 = sn1 / u;
    double ag = asin(sn1) - asin(sn2);
    if (dcmp(vec * b[id]) <= 0) {
        vec = (p + vec).rotate(p,-ag);
    }else vec = (p + vec).rotate(p,ag);
    st = p; en = vec;
}
void step3() {
    Point p;
    int id = -1;
    findPoint(p,id);
    Point vec = en - st;
    double cs = Angle(vec,c[id]);
    double sn1 = sqrt(1 - cs * cs);
    double sn2 = sn1 * u;
    if (sn2 > 1) {
        if (dcmp(p.y) == 0) printf("%.3lf\n",p.x+eps);
        else printf("Error\n");
        return;
    }
    double ag = asin(sn2) - asin(sn1);
    if (dcmp(vec * c[id]) >= 0) {
        vec = (p + vec).rotate(p,-ag);
    }else vec = (p + vec).rotate(p,ag);
    st = p; en = vec;
    Point an = Line(st,en).CrossPoint(Line(Point(0,0),Point(1,0)));
    if (ond(st,en,an)) {
        printf("%.3lf\n",an.x+eps);
    }else printf("Error\n");
}
void solve(){
    init();
    if (!step1()) return;
    step2();
    step3();
}
int main(){
   // cout<<Line(Point(0,0),Point(1,0)).LineCrossSeg(Line(Point(0,0),Point(1,0)))<<endl;
    int T; scanf("%d",&T);
    while (T--) {
        st.input(); en.input();
        for (int i = 0; i < 3; i++) a[i].input();
        li[0] = Line(a[0],a[1]); d[0] = 2;
        li[1] = Line(a[1],a[2]); d[1] = 0;
        li[2] = Line(a[2],a[0]); d[2] = 1;
        scanf("%lf",&u);
        solve();
    }
    return 0;
}
/*
3
0 10
0 20
-1 3 1 2 -1 1
1.325
0 10
0 0
-1 3 1 2 -1 1
1.325

0 10 0 9
0 0 0 1 1 0
1.0
*/