Except that ellipses have curves with more than 1 radius similar to
sections of a sine wave.
Which is why I indicated an arc will fit more closely fit or follow the
shape of a bottle than an ellipse. An arc is a section of a circle. An
ellipse is a circle illustrated in isometric or 3d format.
| However, the question remains--what if I wanted a curve with a
| different amplitude or wavelength? This template idea crossed my
| mind, but how to generate such a curve? Can Autocad do it?
This is the easiest part of all. Draw a sinusoid (a sine or cosine
curve) with any amplitude or wavelength, then stretch (or squash) to
the amplitude and wavelength you want. Copy and paste as many cycles
as you want.
DeSoto, Iowa USA
On 18 Feb 2006 06:59:47 -0800, email@example.com wrote:
For future reference, if you want a real sine curve, and not an
approximation [within the bounds of the tools and shaky hands] use a
math program like Graphmatica, then copy/paste into a word processor
or image editor for printing to the scale you want/need.
Graphmatica is shareware, but free for those who can't afford it [so
just use it if you can't.] PhotoFiltre , or "The Gimp" are freeware
image editors. OpenOffice is a great free office suite with a
wordprocessor and spreadsheet and much more.
If you do it intelligently, you can do it to suit your project scale.
One hint: in Graphmatica type in y = sin(x) for the unit sine curve,
and you might want to change the default colours to black and white.
You can change the equation if you want varied results; something like
y = 3sin(x) or y = sin(3x) or whatever. You likely don't need that
Or, any basic trig text shows how to draw it from the unit circle.
What's the chances of someone throwing his wine rack up on comparator and
measuring the frequency and amplitude of it. The man said he had AutoCAD.
Those curves can be drawn in about a minute. Close enough for a wine rack.
That's what I was going to suggest. It's easy, and you can easily
scale the sine curve as large or small as you like by choosing an
appropriately-sized circle. Since all that's required is a compass
and straightedge you don't even have to leave the shop.
Guess who (in firstname.lastname@example.org) said:
| Graphmatica is shareware, but free for those who can't afford it [so
| just use it if you can't.] PhotoFiltre , or "The Gimp" are freeware
| image editors. OpenOffice is a great free office suite with a
| wordprocessor and spreadsheet and much more.
Wow! I downloaded Graphmatica and _really_ like it. Wish I'd had
something like this when I was in school...
DeSoto, Iowa USA
Perhaps your kids can use it ..or theirs?
It's mostly math, but anyone doing wood modelling can find a use. A
parabolic arch is the best support [to do with the focus], so would
make a good support for benches, tables, and so on. CAD will draw the
circle and ellipse, but I don't know of one that will draw a parabolic
curve. There are always layout methods, which were likely used in the
past [e.g. by the Romans] since the computer wasn't available way back
then. Layout is still generally the best if not too tedious, and I'm
not sure yet on the best way to get a printout to scale for a large
project. I'll work on that, or offer something about the layout
procedure. ...in time; too busy right now.
enter co-ordinates of one point (x,y) and press enter, repeat for all
select all then points you made
To make sure your cursor knows how to find these co-ord points you created.
(They will appear as dots), go to
Object Snap settings,
select nearest, under running object snap settings.
I always go to
Object Snap settings,
and check endpoint and intersection. In combination with the pick box
size it tells the software what to do. Actually just to make changes. Many
things like this can be saved.
if it takes up the whole page, but in the wrong direction, change the
rotation 90. Thats for scaled to fit. origin is if it is offset, integral
with the other print settings required = to center it, for instance
In the days before computers and fancy stuff, we used nails, sheet metal
or thin wood. Layout the points of the peaks and valleys (or wave points
if you prefer) and spot a 4d nail at the point. Take the sheet metal (
1" wide x 20 - 24 ga. ) and weave it through the nails. Trace the
pattern and now you know the rest of the story.
You've had all sorts of answers for how to do this with various computer
programs (or a pocket calculator), but here's another way that doesn't
involve anything but a compass, straightedge and protractor, and you can
lay it out directly on the board:
1.) Draw a horizontal line down the middle of where you want to put the
sine curve, with the ends aligned with where you want the ends of the
curve to go. Call this the "center line"
2.) Make marks (call them "section marks") to divide this line into
equally-spaced sections, one section for each up-and-down-and-back-up of
the sine curve that you want. Mark off divisions of each of the
sections into 16ths.
3.) Set the compass to draw circles with a diameter equal to the height
of the sine curve that you want to draw. Draw a half-circle centered at
each end of the center line, so it looks sort of like a C at the right
end and a reverse-C at the left end, and the center line goes from the
center of one half-circle to the center of the other.
4.) With the protractor, mark off angles on each half circle, at every
45-degree point, and every 22.5-degree point between these.
5.) Draw lines parallel to the center line by connecting the tops and
bottoms of the half-circles, and each corresponding pair of angle-marks.
6.) Go back to the marks you made in step 2. Starting at the left-hand
end of the center line, draw a line perpendicular to the center line
that goes all the way up to the top line. Put a dot where it crosses
the top line. (You don't actually need to draw the perpendicular line;
just draw the dot. But it's easier to explain if I say to draw the line.)
7.) Go to the right along the center line. For the next mark, draw
another perpendicular line and dot, but put the dot where it crosses the
second line from the top. For the next one, draw the dot on the third
line, then the fourth, and so on. When you get to the bottom, start
going back up. If you've counted right, you should get back to the top
line when you get to the first section-mark. Keep going until you get
to the other end.
8.) Connect the dots. If you're not good at sketching smooth lines, use
a french curve or something.
Obviously, the division into 16ths and the angles I picked are somewhat
arbitrary -- just so long as you divide the sections on the center-line
into twice as many divisions as you divide the half-circles into, it
will work out. If you're using drafting triangles instead of a
protractor, 12ths and marks at 30-degrees and 60-degrees will work well.
Or, if you're good at sketching with only a few dots (I'm not), just
make marks at 45 degrees and divide it into 8ths.
Is that clear enough, or should I do up some sketches and post them?
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