Opengl 当θ=360时，沿z轴观察gluLookAt起作用，但当θ=0时不起作用

我在OpenGL中绘制三角形时遇到了一个有趣的问题。显然，当你沿着“向上”的方向看时，在我的例子中，这意味着Eye_z=Up_z（因为我是在球坐标系下工作的，这意味着θ=0），对象不会显示（请参阅的顶部答案以获得数学解释）。 但是，当我将角度设置为360度而不是0度时，对象将毫无问题地显示出来。有人知道为什么吗？我在这里附上了我的代码片段和屏幕截图：

三角形.cpp

void Triangle::render(Camera C){
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
        glEnable(GL_DEPTH_TEST);
        glLoadIdentity(); 
        float th = C.Getth();
        float ph = C.Getph();

        float Eye_x = r*sin(th*DEGtoRAD)*cos(ph*DEGtoRAD);
        float Eye_y = r*sin(th*DEGtoRAD)*sin(ph*DEGtoRAD);
        float Eye_z = r*cos(th*DEGtoRAD);

        float Up_z = (th>=180.0f && th<360.0f)?-1.0f:1.0f;

        gluLookAt(Eye_x,Eye_y,Eye_z,0.0,0.0,0.0,0.0,0.0,Up_z); 
        glRotatef(m_rotationAngle, 0.0f, 0.0f, 1.0f);

        // Draw Triangle
        glBegin(GL_TRIANGLES);
                glColor3f(1.0f,0.0f,0.0f);
                glVertex3f(-0.5f,-0.5f,0.0f);
                glColor3f(1.0f,1.0f,0.0f);
                glVertex3f(0.5f,-0.5f,0.0f);
                glColor3f(0.0f,0.0f,1.0f);
                glVertex3f(0.0f,0.5f,0.0f);
        glEnd();

        // Draw Axes
        glBegin(GL_LINES);
                glColor3f(1.0f,0.0f,0.0f);
                glVertex3f(0.0f,0.0f,0.0f);
                glVertex3f(1.0f,0.0f,0.0f);
                glColor3f(0.0f,1.0f,0.0f);
                glVertex3f(0.0f,0.0f,0.0f);
                glVertex3f(0.0f,1.0f,0.0f);
                glColor3f(0.0f,0.0f,1.0f);
                glVertex3f(0.0f,0.0f,0.0f);
                glVertex3f(0.0f,0.0f,1.0f);
        glEnd();
}

void三角形：：渲染（摄影机C）{
glClear（GL_颜色_缓冲_位| GL_深度_缓冲_位）；
glEnable（GLU深度试验）；
glLoadIdentity（）；
float th=C.Getth（）；
浮动ph=C.Getph（）；
浮眼x=r*sin（th*DEGtoRAD）*cos（ph*DEGtoRAD）；
浮眼y=r*sin（th*DEGtoRAD）*sin（ph*DEGtoRAD）；
浮眼_z=r*cos（th*DEGtoRAD）；
向上浮动（th>=180.0f和th360.0f）{
th-=360.0f；
}
打破
案例-1://-th
th-=移动金额；
如果（th=360.0f）{
ph-=360.0f；
}
打破
案例2://-ph
ph-=移动量；
如果（pH）你的
th
可能不是真正的“0”或“360”，而是接近。如果你得到一个“真”的“0”，你的眼睛到目标向量将与upI平行。我已经考虑了我的360*DEGtoRAD中的错误，但它必须有多大才能工作？（或者，换句话说，你需要多小的变化才能不与上方向向量平行？）我现在的代码有度到弧度的转换，精确到6位。
void Camera::Move(int dir){
        switch(dir){
                case 1: // +th
                        th += move_amt;
                        if(th>360.0f){
                                th-=360.0f;
                        }
                        break;
                case -1: // -th
                        th -= move_amt;
                        if(th<=0.0f){
                                th+=360.0f;
                        }
                        break;
                case 2: // ph
                        ph += move_amt;
                        if(ph>=360.0f){
                                ph-=360.0f;
                        }
                        break;
                case -2: // -ph
                        ph -= move_amt;
                        if(ph<=0.0f){
                                ph+=360.0f;
                        }

                        break;
                default:
                        break;
        }
}