How to draw a circle in oblique pictorial (45 degrees)

[Anonymous]

Hi, my assignment was to draw the projections below in oblique pictorial (45 degrees) but i am struggling on how to draw the circle.

  

 I would really appreciate it if someone could tell me how to draw the far right cirlce in Autocad. In isometric drawing (30 degrees) i can use Isodrafting and i will be able to draw on the left, top and right plane but it does not work for oblique pictorial. Any ideas?

The picture below is what i have so far

for further clarifications please ask and i've also attached the .dwg file incase you wana have a crack at it. Thanks. 

[ChicagoLooper]

That circle on the right is not a circle, it’s an ellipse (a circle is always represented by an ellipse in an oblique drawing). Look closely and you’ll see the major and minor axes are shown as 0.50 and 0.25 respectively. Don't forget to rotate the ellipse like it's shown in the source drawing. 

[j.palmeL29YX]

Activate the Isoplane Top (see image) and then use the Ellipse -> Isocircle command.

If my reply solves your problem, click the "accept as solution" button. This can help others find solutions faster

[j.palmeL29YX · Accepted solution]

What you want to draw is neither a circle nor an ellipse. But you can approximate it with a spline as shown in >>this video<<.

Assuming you want to draw an obliqued circle 50 diameter:

- draw a parallelogram, horizontal lines 50 long, 45° lines 25 long.

- draw a spline segment from midpoint to midpoint. For the Tangency at the Start- and Endpoint of the spline use the direction of the lines. You can increase the quality of the result using other values for the weight (I used always 1).

- draw the next spline segment

- rotate (and copy) both linesegments 180°.

[dbroad]

I hate to comment on other teacher's assignments but this assignment is a poor use of student time.  No one draws an oblique of a circle unless the circle lies in the undistorted plane of the oblique.  If you have circles in more than one orthogonal plane, then it is traditional to use an isometric view, not an oblique view.

AutoCAD has no built in ways BTW to do oblique projection of a 3d solid but it can do perspectives quite well.  If you can set the camera to look at a 3d solid perpendicular to the plane you want to view true shape, the other directions will be in perspective.  This would be a better alternative to obliques.

[j.palmeL29YX]

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@dbroad wrote:

 No one draws an oblique of a circle unless the circle lies in the undistorted plane of the oblique. 

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I agree with you. But this cavalier perspective is a valid and not uncommon method of drawing 3D objects in 2D. And if the (student?) task is to create exactly such a view? (Even if this is not very practice-oriented ...)

My first thought was also why no isometric projection is used. But then I decided (to try) to answer the specific question.

[Kent1Cooper]

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@j.palmeL29YX wrote:

What you want to draw is neither a circle nor an ellipse. ....

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Actually, it is  an ellipse, but the tricky [if possible in AutoCAD] part is to find the axis directions and axis ratio that puts it in the right place to tangentially hit the midpoints of the edges of the bounding axonometric representation of the rectangle.  See >this<, where the subject is discussed in more detail.  It's worth reading the rest of the thread up to that point, to get the fuller context.

[leeminardi]

Here’s my 2 cents.

I agree @dbroad  in that this not a good assignment.  The benefit of oblique projections are that they are easier to  make than a pictorial drawing than an isometric using manual drafting techniques for geometry that has circles on a principal  plane.  Whereas an isometric would require you to draw these circles as ellipses they are true circles in an oblique projection. The general oblique projection uses the same scale for dimensions in the third direction (the 45° slope in your example). A cabinet projection scales the third dimension by one half in an attempt to make a more realistic image.  Although oblique projections are a type of parallel projection (no perspective) they are not axonometric projections like isometric, dimetric, or trimetric projections.  As such, AutoCAD does not support the viewing of a 3D model as an oblique projection.

The curve required to create the circle that is not on the front plane is an ellipse but it is not an iso-ellipse.  The yellow curve in the image below is an iso-ellipse while the cyan curve is the ellipse required for the 45° oblique projection.  If the circle radius is 1.000 then the major axis for this oblique ellipse is 1.3066 and the minor axis is 0.5412.  Note that the major axis is greater than 1, the radius of the circle!  This is because of the lack of scaling in the third direction and why cabinet projections are preferred.

[dbroad]

I think @leeminardi  makes the point clearer.  Pictorials are best for visualization.  The method that represents the object most clearly with the least amount of effort is ideal.  In this case, this 45 degree cabinet oblique (1/2 scaled dept) contains two perpendicular planes that contain circles.  The orthogonal plane is easy and sensible to draw circles. The distorted cabinet face is ridiculously difficult unless a block is prepared for the task.

Whether the circle is an ellipse or a spline, I can't say but early treatises on drawing perspectives indicate that most views of a circle result in an ellipse. I followed your idea of using 4 tangent defined spline segments and then joined them.  I then reduced the length of the diagonals to 70.7% of their original (as for circles). Then I divided each part of the rhombus into 4 parts and dragged the control verticies to corresponding points.  Its still not perfect as the diagonals show (and is quite a waste of time IMO). The red version is without adjustment of control verticies.

[j.palmeL29YX]

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@Kent1Cooper wrote:

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Actually, it is  an ellipse,

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Yes, you're right. I stand corrected.

In >>this video<<  we can see (at the beginning) an ellipse that fills a parallelogram. The main axis of the ellipse are exact hor./vert.

This looks good for me, but is doesn't look as shown in the image above. Now we can rotate the ellipse. But which angle is the correct one?

(To create this dwg I used parametric constraints)

[ChicagoLooper]

For the ellipse, the length of the axes, major and minor, are given in the opening post. The orientatin of those axes can be determined by examing the images in the opening post.

<<Hint: look at all three images, the first two with white bachground and the third image with black--don't just look at the black background image, all three must be condsidered simultaneously.>>

Right or wrong, theoretical discussion notwithstanding, it's an ellipse and all you need to draw an ellipse in Plain Vanilla AutoCAD is the major and minor axes.

Don;'t put too much into it just so you can debate who has the better theory.It's an ellipse and its orientation can be determined by any imtermediate AutoCad user.

[Kent1Cooper]

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@ChicagoLooper wrote:

For the ellipse, the length of the axes, major and minor, are given in the opening post. The orientatin of those axes can be determined by examing the images in the opening post....

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Those dimensions in Message 1 are not  the major and minor axes of the drawn Ellipse in oblique projection.  They are the dimensions of the bounding oblique representation of the square in which the circle represented by the drawn Ellipse sits, one of them cut in half for "cabinet projection" as described in Message 8.

If we use those sizes as Ellipse axes, we get this, with the right side being the two together:

No amount of rotation is going to get that Ellipse to sit right in that quadrilateral.

I eye-balled a result close to what would be required, with a narrower Ellipse axis ratio, the minor axis being less  than 0.25 and the major axis more  than 0.50.  You can see that the other reason it's not as simple as it may appear is that the axis directions of the drawn Ellipse do not align  with either the mid-lines or the diagonals of the bounding quadrilateral.

They look  sort of like they could be along bisector angles between those, but while pretty close, they're not.

[ChicagoLooper]

OK understood, they are NOT exact. 

So just to be clear, if you were the fabricator, you wouldn't be able to fabricate the object using all three images. The third image would so offending to you, and overpowrt your thought process that you'd ignore the the first two images and declare they hold no value especially when combined with the oblique and you'd be incapable of exercising AutoCAD judgement and unable produce the part. Is that correct?

Wow! you make good argument, the OP should simply tell his instructor it can't be done due to your logic.

[dbroad]

@ChicagoLooper 

You're missing the point.  The assignment must be done but it is a bad assignment, because it is an inappropriate use of obliques which are intended to make drawing pictorials easy. No one in industry would deliberately choose such a difficult form of pictorial.  The distorted face can't be dimensioned and isn't of any use to a fabricator other than to visualize.

[ChicagoLooper]

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@dbroad wrote:

<<can't be dimensioned and isn't of any use to a fabricator other than to visualize.>>

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Which is why you have the other two images to go along with the third. If the dimensions cause you and the fabricator such a problem in the third image, then don't dimension the that hole in third image. The hole  can still be accurately determined using the other two images. 

 Your idea to consider that third image with black background as a stand-a-alone document that supercedes all other drawings is clouding your judgement.

[dbroad]

The whole point of an oblique is to be able to copy the front elevation and to fake the depths and be done with it.  To add the complexity of approximating an ellipse is insane when the choice of doing an isometric is easier. The only reason to do it is to satisfy the instructor due to lack of assignment flexibility.

[Kent1Cooper]

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@ChicagoLooper wrote:
.... the fabricator ....

It's not about fabrication, but about a drafting assignment [see the third word in the entire Topic].

Let's go back to the last sentence in Message 11.  With a Forum rank of 10, surely you're far more advanced than an intermediate AutoCAD user -- show us how you would determine its orientation.

[ChicagoLooper]

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@dbroad wrote:

...... to fake the depths and be done with it. .....

.......approximating an ellipse is.....

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Well how is faking the depths  different from approximating?

The moment you say an oblique is fake is the same moment you say 'the measurements are not real' and that the oblique is for visualization only. Yes, they are fake and should be considered as fake. Which is why the dimensions in the oblique shouldn't have to be treated as accurate, it's already understood. That's why you, as an instructor, have the obligation to tell your students it's distorted. Transferring that blame to AutoCAD is a cop-out, it's irresponsible.

When cartographers draw maps of cities and continents they are distorted, always distorted. Why? Because our monitors are not shaped like 3D crystal balls and we don't print on spherical paper mache balls. Any intermediate AutoCAD user should know this and any advanced user will know this.

You can't say I'm 'faking the depths' in the oblique and in the same breath say 'you must treat the measurements as accurate.' 

[j.palmeL29YX]

In my video above (Post # 10) I have shown that we can draw an ellips which fills the bounding frame, only the rotation angle of the ellipse is "free". If we give the ellipse a dimension of the circle diameter along their main axis then the ellipse gets a definititely position and is easy to reproduce.  This would make sense for me ...

(But I have not yet found a way to solve this problem by drawing. I have left this work to AutoCAD (using parametric constraints and dimensions).

[R_Tweed]

Here is another option...  Use lines to transfer the shape using the align command with the scale option from a true circle to the oblique one. You could also do the same thing using basic commands copy, rotate and scale (reference).  Once you have done this for all quadrants you can then use the spline command to draw your shape.