How to predict the shape of the circle from any point of view

In summary, there is a theory to apply this example. It is based on the light source theory and the idea of shadows.
  • #1
OFF_Smog
3
0
As we know a circle view at an angle appears as an ellipse ,
as you see in the picture, the center of the camera aim to the center of the circle ,
the angle between the circle axis and the camera is ө,
the azimuth between mojor axis(a) and the camera is ∞,
the rotation of the camera is €,

1. How to predict an orientation of major and minor axis and the ratio of its axes(b/a) ,if we only know these ө,∞,€ angle, regardless of size of ellipses

2. Is there any theory to apply this example?

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  • #2
consider the simpler problem of a circle on a hinge along its horizontal diameter. The circle is oriented so that initially its plane is vertical. Let phi be the angle the plane of the circle makes with the vertical axis as we rotate it around the hinge.

now suppose we have a light source (at infinity) and look at the shadow cast by the circle on a nearby vertical plane. Initially (phi=0) the shadow is a circle of the same radius as the circle. As we rotate the circle on its hinge, the shadow changes to an ellipse in the same manner as the camera in your diagram viewing the circle from different angles.

The horizontal axis of the shadow corresponds to a in your diagram. It is constant and always equal to the radius of the circle. The height of the shadow (b) changes with phi and a simple diagram will show you that its value is

[tex]b=a\cos\phi[/tex]

I will leave you to relate phi back to the angles in your diagram.
 
Last edited:
  • #3
Hi,

We can apply the light source(at infinity) theory in case a camera rotating,
Thus the shadow of ellipses will rotate the same as the camera rotation(€) right?

One thing that i concern is how to find formula to apply this circumstance?


Thank you very much
 

1. How do you predict the shape of a circle from any point of view?

The shape of a circle can be predicted by understanding its defining characteristics. A circle is a two-dimensional shape with all points on its circumference equidistant from its center. Therefore, no matter the point of view, the circle will appear as a symmetrical, round shape.

2. Can the shape of a circle change depending on the point of view?

No, the shape of a circle remains the same regardless of the point of view. This is because the defining characteristics of a circle, such as its symmetry and constant radius, do not change with perspective.

3. How can a circle appear differently from different angles?

While the shape of a circle remains constant, its appearance can change depending on the angle from which it is viewed. For example, if a circle is viewed from above, it will appear as a perfect circle. However, if viewed from the side, it may appear as an elongated oval shape.

4. Is there a mathematical formula for predicting the shape of a circle from any point of view?

Yes, the equation for a circle is x^2 + y^2 = r^2, where x and y represent the coordinates of any point on the circle's circumference and r represents the radius. This equation can be used to determine the shape of a circle from any point of view.

5. Can the shape of a circle be distorted from certain perspectives?

While the shape of a circle itself cannot be distorted, the way it appears from certain perspectives can give the illusion of distortion. For example, when viewed from an angle, a circle may appear as an ellipse or a distorted shape, but its defining characteristics remain the same.

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