HDU-5572-An Easy Physics Problem

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ACM模版

描述

题解

计算几何问题，给定一质点的位置和速度，给定一个圆柱的圆心和半径，质点移动如果撞上圆柱则发生弹性碰撞。问这个点是否可以经过另一个质点。

这个题比较直观的想法是求角度，但是这样容易存在精度上的误差，所以可以采用求一个点关于直线的对称点来求出弹性碰撞后的轨迹，判断另一个质点是否在这个质点的运动轨迹上即可。

代码

#include <cstdio>#include <iostream>#include <algorithm>#include <cmath>using namespace std;const double EPS = 1e-8;int cmp(double x){    if (fabs(x) < EPS)    {        return 0;    }    else    {        return x > 0 ? 1 : -1;    }}typedef struct node{    double x, y;    void read()    {        scanf("%lf%lf", &x, &y);    }} point, speed;point PA, PB;speed SA;struct circle{    point o;    int r;    void read()    {        scanf("%lf%lf%d", &o.x, &o.y, &r);    }} C;node operator + (node a, node b){    return {a.x + b.x, a.y + b.y};}node operator - (node a, node b){    return {a.x - b.x, a.y - b.y};}node operator * (double p, node a){    return {a.x * p, a.y * p};}double dot(node a, node b){    return a.x * b.x + a.y * b.y;}double dis(node a){    return sqrt(dot(a, a));}double cross(node a, node b){    return a.x * b.y - b.x * a.y;}node GetLine(node P, node A, node B){    node V = B - A;    node ans = A + (dot(V, P - A) / dot(V, V)) * V;    return ans;}double d;node AngleA, AngleB, head;void GetAnglePoint(point PA, speed SA, circle C){    node A = PA, B = PA + SA;    if (dis(C.o - B) > dis(C.o - A))    {        A = PA + SA;        B = PA;    }    head = GetLine(C.o, A, B);    d = dis(head - C.o);    if (cmp(d - C.r) < 0)    {        double l = sqrt((double)C.r * C.r - d * d);        AngleA = head + l / dis(B - A) * (B - A);        AngleB = head - l / dis(B - A) * (B - A);    }}int main(){    int T;    scanf("%d", &T);    for (int ce = 1; ce <= T; ce++)    {        printf("Case #%d: ", ce);        C.read();        PA.read();        SA.read();        PB.read();        GetAnglePoint(PA, SA, C);        if (cmp(d - C.r) >= 0)        {            if (cmp(cross(PB - PA, SA)) == 0 && cmp(dot(PB - PA, SA)) > 0)            {                puts("Yes");            }            else            {                puts("No");            }            continue;        }        node N;        if (cmp(dis(AngleA - PA) - dis(AngleB - PA)) < 0)        {            N = AngleA;        }        else        {            N = AngleB;        }        int flag = 0;        if (cmp(cross(PA - PB, N - PB)) == 0 && cmp(dot(PA - PB, N - PB)) <= 0)        {            flag = 1;        }        node tmp = GetLine(PA, C.o, N);        point PA2 = PA + 2 * (tmp - PA);        speed SA2 = N - PA2;        if (cmp(cross(PB - N, SA2)) == 0 && cmp(dot(PB - N, SA2)) <= 0)        {            flag = 1;        }        if (flag)        {            puts("Yes");        }        else        {            puts("No");        }    }    return 0;}

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