Calculating sphere orientation

In summary: Basically, my idea is to use a different coordinate system for the sphere rotation than the one that is used to generate the original image. So, when I rotate the sphere, I would use a different coordinate system than the one used to generate the image. This would allow me to keep track of the sphere orientation even when it is rotated.
  • #1
_Seven_
3
0
Hi everyone.

I have been around a problem that I cannot figure out a solution (if there is one) which is related with sphere orientations and rotations. I already searched in many places, including here in this forum but without success.

Let me introduce my problem. Given a black sphere (binary image so black sphere and white background) I need to define a orthogonal 3D axis on it. At a first glance seems easy, we can define the 3D axis in the middle of the sphere because it is a well known point. The problem rises when I need to rotate the sphere, because the previous 3D axis must rotate accordingly with the rotation of the sphere. So basically, I'm trying to find the sphere (shape) orientation along rotation movements. In the book that I'm reading, Volumetric Image Analysis, this problem is called orientation ambiguities and it is a section in the middle of Moments chapter, but unfortunately the book goes just till the ellipsoids, resolving problems of 2 ambiguities. The sphere case has 3 ambiguities because the shape of it cannot define any of the axis implicitly.

I thought in the following: with the point in the middle of the sphere, I make a plan that contains that point and with this plan, I can have the normal vector. With this normal vector I can project it on the plane giving another vector orthogonal with the previous one. To find the 3rd vector I just need to calculate the product between these vectors. But when the sphere is rotated I don't know how to define again the plane to give the same vectors.

Could you please help me?
 
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  • #2
Can't you choose the origin of your coordinate system to be some point other than the center of the sphere so that when it is rotated you don't get the same image?
 
  • #3
Hi.

Yes I can, I have total freedom to make it work. The only thing that is important is that I can perform it correctly. I just proposed an idea that is based on that plane but if you can propose another one I thank you for that.

Could you explain better your idea?

Thank you very much.
 

Related to Calculating sphere orientation

1. What is the difference between calculating sphere orientation and calculating sphere rotation?

The terms "orientation" and "rotation" are often used interchangeably, but there is a subtle difference. Calculating sphere orientation refers to determining the direction in which the sphere is facing, while calculating sphere rotation involves determining the angle and direction of the sphere's movement around a fixed point.

2. How is the orientation of a sphere represented in mathematical terms?

The orientation of a sphere is typically represented using three angles: pitch, roll, and yaw. Pitch refers to the angle of rotation around the x-axis, roll refers to the angle of rotation around the y-axis, and yaw refers to the angle of rotation around the z-axis.

3. What factors affect the orientation of a sphere?

The orientation of a sphere is affected by its initial starting position, the forces acting upon it, and any external influences such as gravity or collisions with other objects. Additionally, the shape and mass distribution of the sphere can also impact its orientation.

4. Can the orientation of a sphere be changed without physically moving it?

Yes, the orientation of a sphere can be changed using mathematical equations and algorithms. This is often done in computer graphics and animation, where spheres and other objects are simulated and given specific orientations based on the desired movements and interactions.

5. How can I calculate the orientation of a sphere in a specific coordinate system?

The orientation of a sphere can be calculated using various mathematical formulas and algorithms, depending on the desired coordinate system. Some common methods include using quaternion representations, Euler angles, or rotation matrices. It is important to properly understand the mathematical concepts and equations involved in order to accurately calculate the orientation.

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