Homogeneous coordinates and frame change
0
$begingroup$
I have a transformation T described in a frame A by an homogeneous matrix (of size 4*4).
I would like to express T in another frame B. How can I do that ?
Thank you.
geometry projective-geometry
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
$endgroup$
add a comment |
0
$begingroup$
I have a transformation T described in a frame A by an homogeneous matrix (of size 4*4).
I would like to express T in another frame B. How can I do that ?
Thank you.
geometry projective-geometry
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
$endgroup$
$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
1
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56
add a comment |
0
0
0
$begingroup$
I have a transformation T described in a frame A by an homogeneous matrix (of size 4*4).
I would like to express T in another frame B. How can I do that ?
Thank you.
geometry projective-geometry
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
$endgroup$
I have a transformation T described in a frame A by an homogeneous matrix (of size 4*4).
I would like to express T in another frame B. How can I do that ?
Thank you.
geometry projective-geometry
geometry projective-geometry
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
asked Dec 17 '18 at 19:48
user1482030user1482030
1356
1356
$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
1
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56
add a comment |
$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
1
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56
$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
1
1
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56
add a comment |
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$begingroup$
$STS^{-1}$ where $S$ is the change of basis
$endgroup$
– Federico
Dec 17 '18 at 19:51
$begingroup$
Do you have a link to a demonstration ? I don't get why it's not just only ST
$endgroup$
– user1482030
Dec 17 '18 at 19:53
1
$begingroup$
Because you have to: 1) transform coordinates wrt $B$ to coordinates wrt $A$ with $S^{-1}$, 2) apply the transformation $T$, 3) transform coordinates wrt $A$ to coordinates wrt $B$ with $S$
$endgroup$
– Federico
Dec 17 '18 at 19:56