Transforming a circle onto another plane

In summary, the conversation discusses the process of creating a new flue for a Pot Belly stove, with the flue passing through a sloped ceiling. It is suggested to cut a hole in a metal plate that will be fixed to the ceiling, with the shape of the hole being an ellipse with specific dimensions. The method involves generating a circle and transforming it into an ellipse, then using it as a template to cut the hole in the metal. The mathematical calculations for the dimensions of the ellipse are confirmed to be correct, and it is suggested to test the method with a cardboard cutout before cutting the metal.
  • #1
guyburns
32
7
I am putting in a new flue for a Pot Belly stove. The ceiling through which the flue goes slopes at 12.5º. I want to cut a hole in a metal plate that will be fixed to the ceiling, and through which the flue passes.

So, a vertical circular flue, radius R, passing through a ceiling sloped at 12.5º to the horizontal.

How do I get the shape of the hole? I assume it is going to be an ellipse with short axis A, long axis B, where:
A = R
B = R/Cos (12.5º)

My thinking is to:

1. Generate a circle of Radius R in Photoshop.
2. Transform (stretch) the circle horizontally by 1/Cos(12.5º). It becomes an ellipse.
3. Print the result, lay it on top of the sheet metal, punch a few holes as markers, then cut it out.

Is the mathematical part of the above correct?
 
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  • #2
That looks right to me.
 
  • #3
Thanks PeroK. I'm a bit long in the tooth to be sure of my maths anymore.

Next step: try it with a cardboard cutout.
 
  • Like
Likes PeroK

Related to Transforming a circle onto another plane

1. How do you transform a circle onto another plane?

To transform a circle onto another plane, you can use a mathematical technique called a similarity transformation. This involves using a scale factor and a rotation to map the points of the original circle onto the new plane.

2. What is a similarity transformation?

A similarity transformation is a mathematical process that preserves the shape and size of an object while moving it to a different location or orientation. It is often used in geometry and can be represented by a combination of scaling and rotation operations.

3. How does a scale factor affect the transformation of a circle?

The scale factor determines the amount by which the original circle will be enlarged or reduced when transformed onto the new plane. It is a ratio of the lengths of corresponding sides or radii on the two planes.

4. Can you transform a circle onto any plane?

No, a circle can only be transformed onto a plane if the plane is parallel to the original circle's plane. This is because a similarity transformation preserves the shape and size of the object, so the planes must be oriented in the same way.

5. Are there any other techniques for transforming a circle onto another plane?

Yes, there are other techniques such as affine transformations and projective transformations, which can also be used to transform a circle onto another plane. These techniques involve more complex mathematical operations and are often used in computer graphics and computer vision applications.

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