I have code that draws a parabola given two end points and a value for droop/sag to simulate a wire. I'm currently using a GL_LINE_STRIP to draw it, but it's limited to pixel thicknesses, and I need world coordinate thickness. So what I need to do is pass in a radius for thickness and draw a cylinder with it's segments at each point on this parabola. In this coordinate system +Y is up. Here's my code:

const double pPrecision = 50;
double wx1, wy1, wz1, wx2, wy2, wz2, wx3, wy3, wz3;
double wa = gWires[i].Sag;
WorldToLocal(gWires[i].Lat1, gWires[i].Lon1, (gWires[i].El1 * FtToMtrs), &wx1, &wy1, &wz1);
WorldToLocal(gWires[i].Lat2, gWires[i].Lon2, (gWires[i].El2 * FtToMtrs), &wx3, &wy3, &wz3);

double mXZ = (wz3-wz1)/(wx3-wx1);
double mXY = (wy3-wy1)/(wx3-wx1);

wx2 = wx1 + ((wx3 - wx1) / 2.0);
wy2 = (mXY * (wx2 - wx1) + wy1) - wa;
wz2 = (mXZ * (wx2 - wx1) + wz1);

double denom = (wx1 - wx2) * (wx1 - wx3) * (wx2 - wx3);
double A = (wx3 * (wy2 - wy1) + wx2 * (wy1 - wy3) + wx1 * (wy3 - wy2)) / denom;
double B = (wx3*wx3 * (wy1 - wy2) + wx2*wx2 * (wy3 - wy1) + wx1*wx1 * (wy2 - wy3)) / denom;
double C = (wx2 * wx3 * (wx2 - wx3) * wy1 + wx3 * wx1 * (wx3 - wx1) * wy2 + wx1 * wx2 * (wx1 - wx2) * wy3) / denom;

double px = wx1;

glLineWidth(gWires[i].Thickness);

glColor4f(gWires[i].R, gWires[i].G, gWires[i].B, 1.0f);
glBegin( GL_LINE_STRIP );
    for ( int p = 0; p <= pPrecision; ++p) {
        double thisZ = (mXZ * (px - wx1) + wz1);
        double thisY = (A * (px*px)) + (B * px) + C;
        glVertex3f(px, thisY, thisZ);
        px = px + ((wx3 - wx1) / pPrecision);
    }
glEnd();

gWires.Thickness on line 21 will be used as a radius once this is converted. This code is in a loop of gWires with i being the current wire being drawn...each wire is a parabola with two fixed end points.

As you can see, I have a WorldToLocal that converts Lat/Long/El to local opengl coordinates...wx1, wy1, wz1 is one end point while wx3, wy3, wz3 is the other end point.

Assume a cylinder precision of say 6 vertices per segment...I'm thinking due to the GL_TRIANGLE_STRIP plot method, I'll need to add these parabola points to an array and use them in some form of lofted draw method like a parallel transport frame. I've seen a bunch of code that calculated parallel transport frames, but nothing that draws them. I'm limited to immediate mode, so I can't create a VAO or anything, it has to be done in a loop of sorts.

Where do I begin? I know I need to start by adding the points created on the glVertex3f on line 28 to an array and then calling a whole new set of routines to draw the cylinder but as for the math/drawing, I've no clue.