Thank you very much Michael.
Your Hyperbola script works perfectly.
- Brian
I think I will try to roulette it along a vertex line, with tangents and cplanes, and trace focus,
but will not be able to get all the way to infinity :-)
With var pt = cplane.evaluate( x, y, z ); (Or some such) And unwrap curve...
Post # 1766 has updated CMC6 node. CMC4 is gone. Only one person downloaded it.
Curve output added. Comments modified. Rotated curves to align with screen.
Still puzzling on several issues. Nodary and Undulary look nice, but the Sphere and Cylinder need to have the y coordinates divided by 2,
to get the proper quarter arc or line, with correct radius. So maybe Nodary and Undulary curves need the same???
For the Nodary and Undulary, the revolve axis needs to be determined. The revolve axis is the same as the roulette line, which passes through the upper
vertex of the generating hyperbola for the Nodary, and through a vertex of the ellipse for the undulary.
The relation of rmin and rmax to the hyperbola a, b, and c parameters is not complete.
"a" may be equal to (rmax - rmin). Or not?
One fact is that the point on the side of the Nodary with vertical tangent is at the distance "b" from the roulette axis, because at infinity,
the asymptote of the hyperbola is horizontal. A general property of the hyperbola is that the Focus of the hyperbola is at perpendicular
distance "b" from the asymptote.
One mystery is solved. Need to divide by 2 turned out to be lack of parenthesis.
Correct factor of 1/sqrt2 became *sqrt2. (1/sqrt2 = sqrt2/2).
Second mystery, the modulus needs to be k*k. (now certain:-)
Also got rid of my negative sign. Learned a long time ago that if the professor's equations seem wrong, they are not, my thinking is wrong.
Now the undulary and nodoid line up with each other, at proper R and r, and the x-axis is the roll and revolve axis line.
Values of R and r corresponding to parameters a, b, and c for ellipse and hyperbola also solved.
Will post CMC8 later tonight, and word doc, and example node.
Still need to check if sample roulettes match the profiles.
A formula for the widths of the nodary would be nice...
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.
Hi Brian, I'm glad the dims are useful! You can have both the distance and additional text show in a dimension by going to the "Details..." object properties dialog and under Annotation properties > Text put in the text you want and also include a <> (less-than and greater-than characters with no space between them). The <> will be substituted with the numeric value.
So for example if you set the dimension's text value to be "Distance = <>", it will display like this:
A quick Tip.
For a screen capture of a Dark theme screen, the Color (in particular black & white), can be reversed, for easier printing, with the Snagit screen capture editor.
In the editor, click on image> effects> filter> invertcolors.
>I have seen this incredible thing by nkallen ! I believe that is in WIp but...very promising! (Pilou)
Elephant knot editor to automatically create knots when modeling. It would be really very useful for modeling, learning to master MoI, the node editor, etc.
This video walks you through how to install it on Windows. I'm encouraging people for now to use git rather than downloading zip files etc. I'll make another video for Mac users tomorrow.
Hyperbola.zip