Selective Join
Normally, when a new control point is added to the end of a spline, it tries to “join”, continuing the smooth arc. To prevent this, and cause the new spline to “attach” instead, keep the <Shift> key on the keyboard pressed when you click. An attach will not terminate the Add.
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In the above example a new spline is added first by not depressing the <Shift> key while attaching to the existing spline, and second by pressing the <Shift> key while attaching to the existing spline.