Yusuf,
This is an awesome way of doing this in CA, I been making them in Sketchup using the following bellow formula and then importing model into CA, now you saved me a s^*t load of time doing this in CA, I just never tried manipulating stairs this way in CA. If you in NY, lunch is on me.
This is how I calculate when laying out the stairs in Sketchup I made a template as you using to start in CA, then I use basic guidelines to meet the building code to calculate the stairs. Usually I use rule of thumb and make a 70" diameter staircase, it makes it easier to walk on it. Knowing min tread should be 26" I make it 32"-34 when doing layout (of course depending on the room you have) .The center column and two treads make a total diameter of 70". That would be the 2 treads (2 x 32") and 6" support column you get 70" diameter. Next to find the circumference of the stairway which is diameter x 3.1416 so in this case 70" x 3.1416 = 220" (rounded to the nearest "). So with a 9' ceiling per say that's 14 steps+ landing and 220"÷14=15.7" that will give us the tread width, so with overlapping this and that a 16" wide tread makes a nice comfortable stairway and it will make one full 360-degree turn through its travel.