Bias tape cut on the straight grain like you propose to do will not have any stretch. It won't go around the corners smoothly, or even lie flat and smooth all the way around.

What you are doing when you make continuous Is just as the name suggests, cutting the material on the bias. Welting should be done either in the same fabric as the cushion or a solid color matching fabric. Pick out the predominent color if you are going with a solid color. It seems you said you were doing this with striped material. I would go with the solid color. You would have less trouble and I think it would look better. That's my opinion but the choice is yours

The reason for making your tube out of triangles is so your bias strips are cut on the bias. A rectangular tube would have them on the straight of the fabric and therefore not as flexible and forgiving when you encase the cord. You'll find that the cording will be easier to sew around corners if it's bias cut. Putting the triangular sections together allows you to cut your strips in a constant circle around the tube with very little waste and no piecing short bias strips together.

I found it, doesn't show the tube and cutting but I'll try it using a sheet of paper tomorrow. This is still cutting on the bias, just using a rectangle to start with (still cutting a triangle off and sewing it back on other side) conserves a little fabric. And since the seam joining the triangle to what's left of the rectangle isn't exactly in the middle like it is using the square method, maybe there will be some longer strips without seams?

Here is a link that might be useful: Bias strips using rectangle of fabric

Hello, Remember these chairs I posted on the decorating forum? I used yards of piping cut on the bias, but I was running out of fabric. :0) Non of the strips were longer than 24", some only 6".....it doesn't show, it blends in. :0)The eye is tricked....and I don't care as long as I have enough fabric. :0) Sometimes you can over think "things".

So what, you just cut on a 45 degree angle across your fabric, made multiple strips and sewed them together? Seems like more work than sewing a couple of seams and cutting continuous strips. Then again, I only need a continuous 9ft strip for longest (settee cushion) and I can get that from a 5ft x 54" piece, *if* I can use the lightweight cotton I have. If I need heavier upholstery-weight fabric, I really need to use a smaller piece.

Yes you can use cotton as long as it's a sturdy cotton, like good sheets are made from. You don't want to use anything flimsy. I have even used 1/2 inch double fold bias tape for small welting on pillows. I just ironed out the folds.

Yes, I used a "lot" of short pieces for my piping.....I was running out of fabric. :0) No one will ever know.....

Using light weight fabric is fine. Upholstery weight is generally not used for slip covers or outdoor cushions. Worst case scenario.....in 7 years you'll have to recover the cushions. :0)