【例2】openGL （HDU 3320）。

Problem Description
Jiaoshou selected a course about “openGL” this semester. He was quite interested in modelview, which is a part of “openGL”. Just using three functions, it could make the model to move, rotate and largen or lessen. But he was puzzled with the theory of the modelview. He didn’t know a vertex after several transformations where it will be.

Now, He tells you the position of the vertex and the transformations. Please help Jiaoshou find the position of the vertex after several transformations.

Input
The input will start with a line giving the number of test cases, T.
Each case will always begin with “glBegin(GL_POINTS);”.Then the case will be followed by 5 kinds of function.
1. glTranslatef(x,y,z);
This function will translate the vertex(x’,y’,z’) to vertex(x+x’,y+y’,z+z’).
2. glRotatef(angle,x,y,z);
This function will turn angle radians counterclockwise around the axis (0,0,0)->(x,y,z).
3. glScalef(x,y,z);
This function wiil translate the vertex(x’,y’,z’) to vertex(x*x’,y*y’,z*z’).
4. glVertex3f(x,y,z);
This function will draw an initial vertex at the position(x,y,z). It will only appear once in one case just before “glEnd();”. In openGL, the transformation matrices are right multiplied by vertex matrix. So you should do the transformations in the reverse order.
5. glEnd();
This function tells you the end of the case.
In this problem angle,x,y,z are real numbers and range from -50.0 to 50.0. And the number of functions in each case will not exceed 100.

Output
For each case, please output the position of the vertex after several transformations x,y,z in one line rounded to 1 digits after the decimal point , separated with a single space. We guarantee that x,y,z are not very large.

Sample Input
1
glBegin(GL_POINTS);
glScalef(2.0,0.5,3.0);
glTranslatef(0.0,1.0,0.0);
glVertex3f(1.0,1.0,1.0);
glEnd();

Sample Output
2.0 1.0 3.0
Hint
In this sample, we first let the vertex do “glTranslatef(x,y,z);” this function, then do “glScalef(x,y,z)”.

      （1）编程思路。

      题目的意思是：给出三维空间一个点的坐标，对它进行多种变换（平移、缩放、绕过原点的任意轴旋转），输出它的最终坐标。需要注意的是它给出各变换的操作顺序是反过来的（见题目Hint）。

      根据输入构造好三维坐标点的平移、缩放和旋转转换矩阵，用矩阵乘法乘起来就是最终坐标。

      （2）源程序。