I am adapting a simple, 2D, boids-like flocking simulation to 3D, and I have been trying to figure out how to recreate the 'tails' of the boids. The tail is basically an array of spring objects, attached to the next one in the chain. To draw the tail I calculated two points to both sides of the location of the spring object, and drew simple quads.
For the 3D version, I am trying to define a ring of points around the spring object, and render each triangle based on the points of its ring, and the rings of the adjacent spring objects on the chain. I have been able to calculate the points, but only oriented in the direction of the screen.

float interval_ang = radians(360 / render_detail);
for (int i = 0; i < render_detail; i ++) {      
     float x = (sin(interval_ang*i)*radius);
     float y = (cos(interval_ang*i)*radius);
     float z = 0;
     ring[i] = new PVector(x,y,z); // ring locations are stored based on spring object location
   }

My trig skills extend only to basic 2D. How do I incorporate z, and rotate the entire array based on the heading of the spring object?

Thanks, I now understand how to get the coordinate system. How would I  generate the points for a circle perpendicular to the main direction vector?

I would then use those points as 'ribs' along the length of the tail.

That would mean the tail is visualized as a tube, not as a series of planes.