Is My Transformation Matrix Correct?

In summary, The conversation is about transformations from one axis to another and the speaker is looking for clarification on the correct mapping of u,v,w to x,y,z. They also mention their calculations may be incorrect and ask for the final transformation matrix. They provide the angles between each axis and ask for help in finding the transformation matrix.
  • #1
kajalschopra
40
0
Hi,

I have attached a pdf which shows clearly how I have carried out my transformations from one axis into another.

However, I am not convinced that it is right and I have described why I feel so.

I shall be grateful if someone can help me

Kajal
 

Attachments

  • Mathcad - transformation_4.pdf
    176.9 KB · Views: 405
Mathematics news on Phys.org
  • #2
Can anyone please hekp? I am really struggling and will be extremely grateful
 
  • #3
Could you please clarify in your figure, which of u,v,w maps into which of x,y,z, i.e., is x the (rotated) image of u, y of v etc?
 
  • #4
u should map into the y axis
v should map into the z axis
w should map into the x axis

Thanks a lot, looking forward for the response

I think my calculation is wrong (in the pdf) because theta_v, theta_w and theta_t are final rotations (not intermediary rotations)

I need final transformation matrix

Angle between u and y-axis is (90 - theta_v) see the figure where theta_v is marked
Angle between v and z axis is theta_t (See figure theta_t is marked)
Angle between w and x-axis is (90 - theta_h). See figure where theta_h is marked

I need a transformation matrix
 

FAQ: Is My Transformation Matrix Correct?

What is a transformation matrix?

A transformation matrix is a mathematical tool used in computer graphics and geometry to transform and manipulate objects in a three-dimensional space. It is represented as a square matrix and contains values that specify translations, rotations, scaling, and shearing of an object.

How is a transformation matrix used?

A transformation matrix is used to apply various transformations to an object in a three-dimensional space. These transformations include translation, rotation, scaling, and shearing. By multiplying the transformation matrix with the coordinates of the object, the resulting coordinates are transformed accordingly.

What are the components of a transformation matrix?

A transformation matrix is a 4x4 matrix that contains values for translation, rotation, scaling, and shearing. The first three columns contain values for each transformation, and the last column contains the object's position in the three-dimensional space.

Can a transformation matrix be inverted?

Yes, a transformation matrix can be inverted. The inverse of a transformation matrix is used to reverse the transformation and restore the object's original position and orientation in the three-dimensional space.

How do I create a transformation matrix?

A transformation matrix can be created using a combination of translation, rotation, scaling, and shearing operations. Each transformation has its own matrix representation, and by multiplying these matrices in a specific order, a transformation matrix can be created. Alternatively, there are also tools and libraries available that can generate a transformation matrix for specific transformations.

Similar threads

I Get the time axis right in an inverse Fast Fourier Transform
Replies
2
Views
3K
Matrix and transformation problem
Replies
4
Views
1K
MHB Help Solving Linear Transformation Problem in R^2
Replies
1
Views
1K
Matrix transformations and effects on the unit square
Replies
4
Views
3K
I Want to understand how to express the derivative as a matrix
Replies
8
Views
2K
Transformations to both sides of a matrix equation
Replies
25
Views
1K
I Transform a 2x2 matrix into an anti-symmetric matrix
Replies
5
Views
1K
Finding the transformation of a matrix
Replies
31
Views
2K
MHB Matrix Methods for Difference Problems II
Replies
7
Views
2K
I Strange index notation for linear transformation matrix
Replies
4
Views
665

Hot Threads

Recent Insights

Back
Top