nyoj 298 点的变换

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题目来源：http://acm.nyist.net/JudgeOnline/problem.php?pid=298

对所有的操作，我们可以用一个矩阵储存起来，一系列的操作，我们可以利用矩阵相乘，来储存！

平移：

关于x轴对称：

关于y轴对称：

缩放：

旋转：

例如按上述顺序操作（先平移，再关于x轴对称，再关于y轴对称，然后再缩放，最后在旋转）则可以表示为：

同样道理，这题利用这种思路可已解决问题

#include <iostream>#include <cstring>#include <cstdio>#include <cmath>using namespace std;#define PI acos(-1.0)const int MAXN = 10010;struct Node{    double x, y;}iPoint[MAXN];struct Matrix{    double iMatrix[3][3];};Matrix Multi_Mattrix(Matrix a, Matrix b){    Matrix c;    int i, j, k;    for(i = 0; i < 3; ++i)    {        for(j = 0; j < 3; ++j)        {            c.iMatrix[i][j] = 0;            for(k = 0; k < 3; ++k)                c.iMatrix[i][j] += a.iMatrix[i][k] * b.iMatrix[k][j];        }    }    return c;}int main(){    int n, m, i;    Matrix iMove, iXSymmetry, iYSymmetry, iEnlarge, iRotate;    scanf("%d%d", &n, &m);    for(i = 0; i < n; ++i)        scanf("%lf%lf", &iPoint[i].x, &iPoint[i].y);    memset(iMove.iMatrix, 0, sizeof(iMove.iMatrix));//平移    memset(iXSymmetry.iMatrix, 0, sizeof(iXSymmetry.iMatrix));//关于x轴对称    memset(iYSymmetry.iMatrix, 0, sizeof(iYSymmetry.iMatrix));//关于y轴对称    memset(iEnlarge.iMatrix, 0, sizeof(iEnlarge.iMatrix));//缩放    memset(iRotate.iMatrix, 0, sizeof(iRotate.iMatrix));//旋转    iMove.iMatrix[0][0] = iMove.iMatrix[1][1] = iMove.iMatrix[2][2] = 1;    iXSymmetry.iMatrix[0][0] = iXSymmetry.iMatrix[2][2] = 1; iXSymmetry.iMatrix[1][1] = -1;    iYSymmetry.iMatrix[1][1] = iYSymmetry.iMatrix[2][2] = 1; iYSymmetry.iMatrix[0][0] = -1;    iEnlarge.iMatrix[2][2] = iRotate.iMatrix[2][2] = 1;    Matrix tmp;    memset(tmp.iMatrix, 0, sizeof(tmp.iMatrix));    tmp.iMatrix[0][0] = tmp.iMatrix[1][1] = tmp.iMatrix[2][2] = 1;    char c;    double x, y;    while(m--)    {        getchar();        scanf("%c", &c);        switch(c)        {        case 'M':            scanf("%lf %lf", &x, &y);            iMove.iMatrix[0][2] = x;            iMove.iMatrix[1][2] = y;            tmp = Multi_Mattrix(iMove, tmp);            break ;        case 'X':            tmp = Multi_Mattrix(iXSymmetry, tmp);            break ;        case 'Y':            tmp = Multi_Mattrix(iYSymmetry, tmp);            break ;        case 'S':            scanf("%lf", &x);            iEnlarge.iMatrix[0][0] = iEnlarge.iMatrix[1][1] = x;            tmp = Multi_Mattrix(iEnlarge, tmp);            break ;        case 'R':            scanf("%lf", &x);            y = x/180 * PI;            iRotate.iMatrix[0][0] = iRotate.iMatrix[1][1] = cos(y);            iRotate.iMatrix[0][1] = -sin(y);            iRotate.iMatrix[1][0] = sin(y);            tmp = Multi_Mattrix(iRotate, tmp);            break ;        default:            break ;        }    }    Matrix res;    for(i = 0; i < n; ++i)    {        memset(res.iMatrix, 0, sizeof(res.iMatrix));        res.iMatrix[0][0] = iPoint[i].x;        res.iMatrix[1][0] = iPoint[i].y;        res.iMatrix[2][0] = 1;        res = Multi_Mattrix(tmp, res);        printf("%.1lf %.1lf\n", res.iMatrix[0][0], res.iMatrix[1][0]);    }    return 0;}

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