GLUT GL 3/4球体出了点问题

Question

我的图形课程有任务要做。我必须仅使用GL_TRIANGLE_STRIP构建3/4。我已经完成了，但是有一个我无法接受的重大错误。

GLfloat radius = 3, alpha, beta, PI = 3.14314159;


//lHorizontal and lVertical im changing using keyboard it says how many 
 sphere divisions are 

for (alpha = 0.0; alpha < PI; alpha += PI / lVertical)
{

    glBegin(GL_TRIANGLE_STRIP);


    for (beta = 0.0; beta < 1.5075*PI; beta += PI / lHorizontal)
    {

        glColor3f(1, 1, 0);
        x = radius * cos(beta)*sin(alpha);
        y = radius * sin(beta)*sin(alpha);
        z = radius * cos(alpha);

        glNormal3f(x, y, z);
        glVertex3f(x, y, z);

        glColor3f(0, 1, 1);
        x = radius * cos(beta)*sin(alpha + PI / lVertical);
        y = radius * sin(beta)*sin(alpha + PI / lVertical);
        z = radius * cos(alpha + PI / lVertical);

        glNormal3f(x, y, z);
        glVertex3f(x, y, z);



    }
    glEnd();
}


glColor3f(1, 1, 0);
glBegin(GL_TRIANGLE_STRIP);

for (alpha = PI; alpha < 2.01*PI; alpha += PI / lVertical) {
    x = -radius * sin(alpha);
    y = 0;
    z = radius * cos(alpha);
    glNormal3f(x, y, z);
    glVertex3f(x, y, z);
    glNormal3f(0, 0, 0);
    glVertex3f(0, 0, 0);
}
glEnd();


glBegin(GL_TRIANGLE_STRIP);

for (alpha = PI; alpha < 2.01*PI; alpha += PI / lVertical) {
    x = 0;
    y = radius * sin(alpha);
    z = -radius * cos(alpha);
    glNormal3f(x, y, z);
    glVertex3f(x, y, z);
    glNormal3f(0, 0, 0);
    glVertex3f(0, 0, 0);
}
glEnd();

这段代码的结果是：

随着Im的变化，lHorizo​​ntal出现了不该出现的部分（请参见图片）。我可以在代码中进行哪些更改以避免出现此问题？

Answer 1

PI的值是错误的：

..., PI = 3.14314159; // 3.14159... ?

---

更正此错误后，让我们在外循环中测试alpha的{​​{1}}的值：

lVertical = 8

输出：

int lVertical = 8;
GLfloat radius = 3, alpha, beta, PI = 3.141592654;

for (alpha = 0.0; alpha < PI; alpha += PI / lVertical)
{
    printf("%f, %f\n", alpha, alpha + PI / lVertical);
}

0.000000, 0.392699 0.392699, 0.785398 0.785398, 1.178097 1.178097, 1.570796 1.570796, 1.963495 1.963495, 2.356194 2.356194, 2.748893 2.748893, 3.141593 3.141593, 3.534292 << 大于3.534292，这意味着它是PI的无效值。效果是最后一个多边形环“折叠”起来，产生了不应该存在的部分。

最好直接从整数索引计算角度：

alpha