Attached is the CMC8.js node file, and the CMC8_01.nod program, for creating symmetric half of an Undulary curve, and a Nodary curve.
Also attached is the NodoidUnduloidRadii08.3dm file which demonstrates that the formulas for the two Radii "R" and "r" correspond to the parameters "a", "b", and "c" for the parent roulette curves Ellipse for the Undulary curve, and Hyperbola for the Nodary curve, as described in the Word file Parameters for Undulary and Nodary curves.
In particular, an unwrap of half of the perimeter of the ellipse corresponds to 5 decimal places with the x_length of the undulary, which is equivalent to rolling the ellipse. The ellipse is drawn with MoI ellipse command.
Also an unwrap of half of the hyperbola, and Line/Line orient of the tangent at the "end" of the hyperbola segment, with attached Focus1 and Focus2, demonstrates that after "rolling" the hyperbola, that the new location of the two foci is (nearly) on the red nodary curve. (It is not perfect, but pretty close. There must be some calculation tolerances...). In addition, the y height of the vertical tangent to the nodary curve agreed within 6 decimal points of the calculated value of parameter "b". Once the parameters are calculated and points plotted, Michael's hyperbola script draws the hyperbola.
Also, moving the mu slider to zero will generate a quarter circle, (mirror and revolves Sphere), and setting mu equal to 1/(4*lambda) generates
a line, (revolves to a cylinder). Both with the proper radius R. (But there are better ways to make spheres and cylinders.)
(Roulette of parabola to a catenary, (revolve to a catenoid), uses other equations.)
This finishes up the CMC project, except for finding a formula for the widths of the nodary curve segments.
- Brian
ps The new Dimension commands were great for labeling the .3dm drawing. Someone should do a video. I've almost stopped hitting enter after adding
text. The detailed view is helpful for screen align, and altering distance for text. It might be nice to be able to have both distance and text in the horizontal and vertical dims.
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