Rotation matrix from vectors to cone

In summary, a rotation matrix from vectors to cone is a mathematical tool used to represent the transformation of a vector from one coordinate system to another. It is calculated using a combination of trigonometric functions and vector operations, and has properties such as being square, orthogonal, and preserving distances and angles between vectors. In computer graphics, it is used to rotate objects in 3D space and cannot be used for non-linear transformations.
  • #1
barcerlona
2
0
I have a set of given vectors, I want to find a rotation matrix to convert them to vectors belong to surface of a cone with vertex is origin(vectors with the same slant angle but different tilt angles). Is there anybody know what is the solution?
Thanks
 
Last edited:
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  • #2
doesn't seem possible by a rotation. take (1,0), (0,1), (1,1).
 
  • #3
mathwonk said:
doesn't seem possible by a rotation. take (1,0), (0,1), (1,1).

Sorry, I don't understand. What do you mean?
 

1. What is a rotation matrix from vectors to cone?

A rotation matrix from vectors to cone is a mathematical tool used to represent the transformation of a vector from one coordinate system to another. It is commonly used in computer graphics and robotics to rotate objects in 3D space.

2. How is a rotation matrix from vectors to cone calculated?

A rotation matrix from vectors to cone is calculated using a combination of trigonometric functions and vector operations. The specific formula depends on the angle and axis of rotation.

3. What are the properties of a rotation matrix from vectors to cone?

A rotation matrix from vectors to cone is a square matrix with an equal number of rows and columns. It is orthogonal, meaning its inverse is equal to its transpose. It also preserves distances and angles between vectors.

4. How is a rotation matrix from vectors to cone used in computer graphics?

In computer graphics, a rotation matrix from vectors to cone is used to rotate objects in 3D space. It is used to manipulate the position, orientation, and size of objects to create realistic 3D animations and simulations.

5. Can a rotation matrix from vectors to cone be used for non-linear transformations?

No, a rotation matrix from vectors to cone is only used for linear transformations, meaning it can only rotate objects in a straight line. Non-linear transformations, such as scaling or shearing, require different mathematical tools.

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