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 | 1 | initial version |
The best way to determine which transformation to inverse when confused is to draw the system. Here the transformations T1 and T2 are defined to a Origin/world frame. Now we want the transformation from T1 to T2 (the blue line). From the figure you can see that moving from T1 to Origin and from Origin to T2 will provide the same transformation. So we need to inverse T1. Therefore:
T12 = Inverse[T1] * T2
Transformation is like traveling a path and the difference reflect which direction you move. If we want the transformation from T2 to T1 it would be:
T21 = Inverse[T2] * T1
| | 2 | No.2 Revision |
The best way to determine which transformation to inverse when confused is to draw the system. Here the transformations T1 and T2 are defined to a Origin/world frame. Now we want the transformation from T1 to T2 (the blue line). From the figure you can see that moving from T1 to Origin and from Origin to T2 will provide the same transformation. So we need to inverse T1. Therefore:
T12 = Inverse[T1] * T2
Transformation is like traveling a path and the difference reflect which direction you move. If we want the transformation from T2 to T1 it would be:
T21 = Inverse[T2] * T1
Ps. regarding your question about the rotation the easiest way to calculate is by using the 3x3 rotation matrix and combine it with the 3x1 translation into a homogenous transformation matrix. With these matrixes you can calculate transformation with normal matrix operations. This link:paper looks like a good introduction into the concept
| | 3 | No.3 Revision |
The best way to determine which transformation to inverse when confused is to draw the system. Here the transformations T1 and T2 are defined to a Origin/world frame. Now we want the transformation from T1 to T2 (the blue line). From the figure you can see that moving from T1 to Origin and from Origin to T2 will provide the same transformation. So we need to inverse T1. Therefore:
T12 = Inverse[T1] * T2
Transformation is like traveling a path and the difference reflect which direction you move. If we want the transformation from T2 to T1 it would be:
T21 = Inverse[T2] * T1
Ps. regarding your question about the rotation the easiest way to calculate is by using the 3x3 rotation matrix and combine it with the 3x1 translation into a homogenous transformation matrix. With these matrixes you can calculate transformation with normal matrix operations. This link:paper looks like a good introduction into the concept
| | 4 | No.4 Revision |
The best way to determine which transformation to inverse when confused is to draw the system. Here the transformations T1 and T2 are defined to a Origin/world frame. Now we want the transformation from T1 to T2 (the blue line). From the figure you can see that moving from T1 to Origin and from Origin to T2 will provide the same transformation. So we need to inverse T1. Therefore:
T12 = Inverse[T1] * T2
Transformation is like traveling a path and the difference reflect which direction you move. If we want the transformation from T2 to T1 it would be:
T21 = Inverse[T2] * T1
Of cause you will only have to inverse when the transformation have the opposit direction of the one you want to move.
Ps. regarding your question about the rotation the easiest way to calculate is by using the 3x3 rotation matrix and combine it with the 3x1 translation into a homogenous transformation matrix. With these matrixes you can calculate transformation with normal matrix operations. This paper looks like a good introduction into the concept
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