Ellipse Through Points?

[stressedgirl]

I am drawing the intersection of a plane and an oblique cylinder and I have all the points of intersection. Now I need to join the points with an ellipse.

I used a couple splines but there must be a better way. Any suggestions?

StressedGirl

PS I am a tutor for an introductory drafting course and I just want to give the students a good method of drawing in AutoCAD.

 

[JStephen]

I have run into this before. You can draw an ellipse of any proportions, but you have to have the major and minor axis intersections to do it. If the points you have located do not fall on these axes, you're up a creek as far as I can tell.

One problem is that any three points can define a circle, but you can have four points on an ellipse and still not have the ellipse defined. Example: Any number of ellipses can be drawn through the corners of a rectangle.

In some cases, you can construct the ellipse in various ways, but it's hard to be more specific without knowing your exact geometry. For example, "isocircles" are isometric ellipses, if you're doing an isometric drawing.

 

[stressedgirl]

Thanks for the response JStephen

I don't have the major and minor axis. I know that the points on the major axis should fall on the outside edges of the cylinder but I don't know exactly where.

Here is what the drawing looks like. I have used a spline and fudged the ellipse in the top drawing a bit.

http://freehost13.websamba.com/mech211/files/Tutorial9_Page1.dwg

StressedGirl

 

[hogetyler]

StressedGirl,
-extrude a circle of the correct diameter
-slice the resulting cylinder using your three points
-erase the unused cylinder piece
-explode the remainder
-the resulting region defines your ellipse
Hoge

 

[JStephen]

Sorry, can't open that- I'm using AutoCAD 2002, and it says that's an "incompatible format".

 

[stressedgirl]

JStephen,
Sorry here is the file in AutoCAD 2000 format. The original file was in 2004.

http://freehost13.websamba.com/mech211/files/Tutorial9_Page1_2000.dwg

Hoge,
I guess that your method would work but I shouldn't have to draw in 3D to get a 2D drawing.

StressedGirl

 

[chicopee]

if your drawing is in 2D you can use polyline to make the ellipse; then PEDIT and FIT option to get that smooth elliptical arc.
If you do the drawing in 3D you will have no choice in determining the major and minor axis to drawe the ellipse. You can use the 3D polyline but then you must use the SPLINE option to make that smooth elliptical arc.

 

[btrueblood]

stressedgirl,

There is a way to find the right ellipse using old-fashioned 2D paper-and-pencil techniques. Try looking up an old mechanical drawing textbook. Basically, you create an end view, and project the circle dimensions across the side view of the cut and into the view perpendicular to the cut. That description probably helps you about as much as the period at the end of this sentence, but I'm not sure how to go about getting you a .dwg/dxf file of the process.

I'll take a look at your file and post back here again later today.

BT

 

[JStephen]

trueblood, that's basically what she did. That gives her points on the ellipse (which is all you need for hand drafting). But that procedure doesn't locate the major/ minor axes because things are skewed around. So she can't just drawing the ellipse using the ellipse command. Look at the file, and you'll see, I think.

She has an ellipse drawn, so cosmetically, it looks okay, but there ought to be some way to put in a true ellipse of exactly the right size.

 

[btrueblood]

Ummm. Ok, I see the problem. But, you never create a true "projected end view" of the cylinder, so you can't easily define the plane or angle at which the major axis of the ellipse would lie along, which would then allow laying in an exact ellipse in the form that Acad would allow. Of course, doing so requires drawing in (I think) at least two more views to get that projection, and my brain is already sore just thinking about it.

It is a PITA that autocad doesn't have an ellipse fitting function for this purpose.

 

[JStephen]

I've run into a similar situation doing fairly straightforward drafting- specifically looking at a 45 degree ell which is then rotated about a horizontal axis so that it is 15 degrees out of the horizontal plane. It's not too hard to locate points on the ellipse, but you still wind up eyeballing an ellipse to go in there.

As best I can figure, fitting an ellipse to a an arbitrary set of points requires 5 points, and the solution of 5 non-linear equations with 5 unknowns. The center of the ellipse is two of the unknowns, which in a lot of cases like this, is easy to find.

 

[stressedgirl]

Thanks a lot everyone for you responses.

I posted here because I thought there was a trick in AutoCAD that I was missing. Apparently not.

For one last try in the top view I assumed that the points closest to the sides of cylinder are the closest to the ends of the major axis. Call them A and B on one side and C and D on the other. Then I joined A with B and C with D. Then I joined the midpoints of AB and CD and extended the line to meet the cylinder. This final line I took as the major axis in the ellipse command and picked the minor axis at some distance that looked right.

This gave a smoother curve than the spline but it misses some points by a little. At least it hits the sides of the cylinder exactly.

I guess this is why 3D modeling is popular. You can let the computer draw the strange geometry for you when you pick views for ploting.

Thanks again
StressedGirl