9 Replies Latest reply on Nov 10, 2010 9:34 AM by Charles Culp

    Fit Spline with a closed Circle

    Charles Culp

      Is it me, or does fit spline not work on a closed circle?

       

      Step 1: Draw a full circle.

       

      Step 2: ???

       

      Step 3: Fit Spline.

        • Re: Fit Spline with a closed Circle
          Deepak Gupta

          Fit spline will not work on a closed circle because it's (circle) already a spline

           

          But if remove a small portion of arc from it, Fit spline works

          • Re: Fit Spline with a closed Circle
            Scott McFadden

            Charles,

            Isn't one of the purposes of  fit spline to create a continuous

            shape with no end?

             

            That is what I always used it for.  Mainly when creating lofts when you have sketches

            with differenet number of sides.

             

            So, it makes sense why it wouldn't work with circles, because it is only one entity.

            • Re: Fit Spline with a closed Circle
              Charles Culp

              It looks like a workaround is to use the Split tool, one of the sketching tools that isn't available by default. If you use it twice on a circle it creates two arcs (that form a circle), and that can then be "fit splined".

                • Re: Fit Spline with a closed Circle
                  Jerry Steiger

                  Charles,

                   

                  Inquiring minds want to know; why do you want to fit a spline on a closed circle?

                   

                  Jerry Steiger

                    • Re: Fit Spline with a closed Circle
                      Charles Culp

                      I am currently working on a project where I have a very contoured surface:

                      WhatIsCharlesWorkingOnToday.png

                      Note that these curves often end at flat circles. I create the flat circle, then create surfaces up to meet with that final circle (not tangent, just coincedent).

                       

                      To create this transition, I create a split line on the base part. At first, I just took the circle, and offset a larger circle, and used that for the split. Later, I wanted to tweak it a little bit. So instead of being a circle, I wanted a circle with a small bump. The easiest way to do this is to create a fit spline, then simplify spline, and then move one of the control points. Could I just sketch a spline with 8 control points around the circle? Sure, but fit spline should work, too.

                    • Re: Fit Spline with a closed Circle
                      Jerry Steiger

                      Charles,

                       

                      This got me thinking about how well splines fit an arc. I did a really simple experiment. I created a  100mm diameter construction circle. I created a couple of tangent construction lines at the top and bottom of the circle. Then I made a two point spline between the top and bottom points and made it tangent to the construction lines. The default spline is a really poor match to the circle. Setting the tangency to 200 seems to get the closest match at the point horizontal from the center, but the spline falls outside the arc everywhere else and the curvature comb doesn't look that uniform.

                       

                      Then I put in a 3 point spline, with the middle point coincident with the quadrant point of the circle. Setting the ends tangent to the construction lines, the default is fairly close to the arc, but falls inside the arc everywhere except at the 3 defining points. Setting the tangency at the ends to 90 seems to match the arc pretty well. The curvature comb may be slightly off. You can also get a nice match by playing with the middle point tangency. Bringing that handle up changes the control polygon from three points to four points. It also seems to be harder to deal with this handle, with more chances to overdefine the sketch.

                       

                      Changing the diameter of the circle changes the required values of the tangencies; the required value seems to be directly proportional to the size of the diameter.

                       

                      Jerry Steiger

                        • Re: Fit Spline with a closed Circle
                          Charles Culp

                          Jerry,

                           

                          Here is some reading on approximating a circle with NURBS/Bezier curves:

                           

                          http://en.wikipedia.org/wiki/NURBS#Example:_a_circle

                           

                          Check out page 57.5 of this PDF:

                           

                          http://www.tinaja.com/glib/ellipse4.pdf

                           

                          The BEST 2-spline magic number is 1.333333. Worst
                          case normalized error deviation is 0.0196725. The
                          average deviation is 0.00869406.
                          The BEST 3-spline magic number is 0. 0.7698112. Worst
                          case normalized error deviation is 0.00150716. The
                          average deviation is 0.000705631.
                          The BEST 4-spline magic number is 0.551784. Worst
                          case normalized error deviation is 0.000265718. The
                          average deviation is 0.00012482
                          The BEST 5-spline magic number is 0.433072. Worst
                          case normalized error deviation is 6.78897e-05. The
                          average deviation is 3.22829e-05.

                           

                          I have also seen it written that to get a good circle you need an 8-point spline; so that is what I always use when I create one by hand. I assume that is equivalent to the 0.000265718 worst case deviation shown above. I can live with two tenths per inch. Most of the parts I create are investment cast aluminum, with .008 in/in casting tolerance. For every 45° of curvature I have one spline point.