Normal spherical image of x

The normal image of a point is a point on a curve that is perpendicular to the tangent at that point. This can be proven using the fact that all functions and curves considered are at least C3 and by defining the tangent, normal, and binomial spherical images of x. The tangent spherical image may not always be regular, but the normal and binomial spherical images can be defined. Therefore, it can be concluded that the normal spherical image of x is never constant.
  • #1
drc4rd1n
6
0
Helo..i have a problem about geometry..
How to show that the normal spherical image of x is never constant?
 
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  • #2
what is normal image of a point??
please explain
 
  • #3
rahuliitkgp said:
what is normal image of a point??
please explain

all functions anda curves considered here are assumed to be of class at least C3.
If x(s) is a regular curve parametrized by arc length s, then t:(a,b)-> R3 defined a curve on S2..

this curve might not be regular and is called the tangent spherical image of x.
the normal spherical image n(s) and binomial spherical image b(s) of x can also be defined.

so, the question is how to proof that the normal spherical image of x is never constant?
 

1. What is a normal spherical image of x?

A normal spherical image of x is a representation of an object or subject that is captured on a spherical surface, such as a globe or a planet. It is commonly used in scientific research and mapping.

2. How is a normal spherical image of x created?

A normal spherical image of x is created using specialized equipment, such as a camera with a fisheye lens, that can capture a wide field of view. The images are then stitched together to create a seamless spherical image.

3. What are the applications of a normal spherical image of x?

A normal spherical image of x has various applications, including mapping, navigation, virtual reality, and scientific research. It can also be used for creating immersive experiences, such as 360-degree videos and photos.

4. How is a normal spherical image of x different from a traditional image?

A normal spherical image of x captures a much wider field of view compared to a traditional image. It also allows for a more immersive experience and can be viewed from different perspectives, unlike a traditional image which is limited to one perspective.

5. Can a normal spherical image of x be converted to a traditional image?

Yes, a normal spherical image of x can be converted to a traditional image by using specialized software. However, the converted image will lose the immersive and interactive qualities of the original spherical image.

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