lemniscate of Bernoulli [closed]

Question

I am trying to learn and teach myself openGL and I wanted to draw a figure 8 in a 3D setting but I'm having a problem. Please forgive me, I am very new at this but I'll attempt to explain what I have done so far

I understand that I can use the Lemniscate of Bernoulli to draw a nice figure 8, so I've have adopted that idea into my code. I just want to draw it along the x and z plane. My code looks like this

#define PI 3.1415926535f
#define MAX_STEPS 100.0f
//...
Vector3 PointOnCurve1(Vector3 p1, float t)
{
    Vector3 tempPoint = {0.0f, 0.0f, 0.0f}; 
    float scaler = 2/ (3- cos(2*t));

    varX = scaler * cos(t);
    varZ = scaler * sin(2*t) / 2

    tempPoint.x = varX+p1.x;
    tempPoint.y += p1.y;
    tempPoint.z =varX+p1.z;

    return tempPoint;
}

Vector3 g_Point    = {-4,  0,  0};
glBegin(GL_LINE_STRIP);                              
    for(float t = -PI; t <= PI; t += PI / MAX_STEPS)
    {
        vPoint = PointOnCurve1(g_Point, t);
        glVertex3f(vPoint.x, vPoint.y, vPoint.z);
    }

glEnd();

All I'm getting is one straight green line instead of a figure 8. any ideas? Am I missing something here? I'm basing this equation from this gamedev article

How can I move an object in an "infinity" or "figure 8" trajectory?

Answer 1

Looks like a simple typo - you are updating tempPoint.z using varX, not varZ, so your coordinates move in unison and the shape collapses to a line. This is a common sort of mistake when writing componentwise math and you should learn to recognize the symptom.

Avoiding this mistake can be helped by using vector operations where possible, like p1 + var where var is a vector instead of varX and varZ.

Answer 2

You're viewing the figure 8 from the side, so it just looks like a line. Try building it on the XY plane instead of the XZ plane.