Construct a rotation matrix out of another rotation matrix

Click For Summary
To adjust a rotation matrix from one coordinate point A to another point B, it's essential to understand that the rotation about line AB remains consistent. The discussion highlights the need to modify the rotation and translation matrices to reflect the new center of rotation at B. Participants suggest using mathematical relationships involving the axes perpendicular to AB to facilitate this adjustment. Clarification is sought on specific terms used in the explanation, indicating a need for further elaboration on the concepts involved. Ultimately, the focus is on accurately recalibrating the matrices to ensure correct landmark positioning after the rotation around point B.
TravelGirl
Messages
9
Reaction score
0
The following is my problem: I have a rotation and rotation matrix, based on rotations around coordinate A(x1,y1,z1). But actually, the rotation found place around coordinate B(x2,y2,z2).

How can I adjust my rotation and translation matrix, so that it is adjusted for the rotations around coordinate B?
 
Mathematics news on Phys.org
Hi TravelGirl! :smile:

A rotation along AB is the same for both representations.

For rotations about axes AK and BK' perpendicular to AB, use σk'σk = … ? :wink:
 
Maybe I explained my problem incorrectly, I am sorry for that.

Based on the rotations around point A, I received landmarks of the object I rotated and also got a rotation and translation matrix.
Though, actually I should rotate around B, and correct the positions of my landmarks for this.

So how do I correct my matrices for rotating around B in stead of A.
(and what does 'K' mean in your explanation? )
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB How can I calculate the union of two rotated rectangles using an algorithm?
  • · Replies 8 ·
Replies
8
Views
5K
High School The mathematics of transforming images in Adobe Premiere - Part 1
  • · Replies 2 ·
Replies
2
Views
2K
High School Help Me Understand Rotation from an Arbitrary basis
  • · Replies 11 ·
Replies
11
Views
2K
High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
2K
High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
Understanding Rotation Matrices: A Journey of Mistakes and Lessons Learned
  • · Replies 12 ·
Replies
12
Views
3K
MHB Rotate Point p: How to Rotate by 75° Counterclockwise
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Elliptic Function Rotation Problem
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Finding vertex of a 3D Triangle on a Plane
  • · Replies 3 ·
Replies
3
Views
2K
Rotation matrix about an arbitrary axis
  • · Replies 2 ·
Replies
2
Views
3K