How can I invert? a coordinate space?
Here's a problem that's been wrecking my brain for a while.
Given:
I have two coordinate spaces:
the global space G, and
a local space A, and
I know the position and rotation of A relative to G.
Question:
How can I programmatically calculate the position and rotation of G relative to A?
On graph paper, I can calculate this by hand:
- if A relative to G is (4, 1) 90deg, then G relative to A is (-1, -4) -90deg
- if A relative to G is (5, 0) 0deg, then G relative to A is (-5, 0) 0deg
... but I'm having trouble transferring this calculation to software.
geometry 2d coordinates
asked Nov 24 '18 at 13:41
David MDavid M
314
add a comment |
Here's a problem that's been wrecking my brain for a while.
Given:
I have two coordinate spaces:
the global space G, and
a local space A, and
I know the position and rotation of A relative to G.
Question:
How can I programmatically calculate the position and rotation of G relative to A?
On graph paper, I can calculate this by hand:
- if A relative to G is (4, 1) 90deg, then G relative to A is (-1, -4) -90deg
- if A relative to G is (5, 0) 0deg, then G relative to A is (-5, 0) 0deg
... but I'm having trouble transferring this calculation to software.
geometry 2d coordinates
asked Nov 24 '18 at 13:41
David MDavid M
314
en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05
add a comment |
Here's a problem that's been wrecking my brain for a while.
Given:
I have two coordinate spaces:
the global space G, and
a local space A, and
I know the position and rotation of A relative to G.
Question:
How can I programmatically calculate the position and rotation of G relative to A?
On graph paper, I can calculate this by hand:
- if A relative to G is (4, 1) 90deg, then G relative to A is (-1, -4) -90deg
- if A relative to G is (5, 0) 0deg, then G relative to A is (-5, 0) 0deg
... but I'm having trouble transferring this calculation to software.
geometry 2d coordinates
asked Nov 24 '18 at 13:41
David MDavid M
314
Here's a problem that's been wrecking my brain for a while.
Given:
I have two coordinate spaces:
the global space G, and
a local space A, and
I know the position and rotation of A relative to G.
Question:
How can I programmatically calculate the position and rotation of G relative to A?
On graph paper, I can calculate this by hand:
- if A relative to G is (4, 1) 90deg, then G relative to A is (-1, -4) -90deg
- if A relative to G is (5, 0) 0deg, then G relative to A is (-5, 0) 0deg
... but I'm having trouble transferring this calculation to software.
geometry 2d coordinates
geometry 2d coordinates
asked Nov 24 '18 at 13:41
David MDavid M
314
asked Nov 24 '18 at 13:41
David MDavid M
314
asked Nov 24 '18 at 13:41
David MDavid M
314
asked Nov 24 '18 at 13:41
David MDavid M
314
asked Nov 24 '18 at 13:41
David MDavid M
314
314
en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05
add a comment |
en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05
en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05
add a comment |
1 Answer
1
active
oldest
votes
In matrix form,
y = R x + t
where R is the rotation matrix and t the translation of the origin.
The reverse way,
x = R' (y - t) = R' y + (- R' t)
where R' is the inverse of R, and also its transpose.
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
In matrix form,
y = R x + t
where R is the rotation matrix and t the translation of the origin.
The reverse way,
x = R' (y - t) = R' y + (- R' t)
where R' is the inverse of R, and also its transpose.
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
add a comment |
In matrix form,
y = R x + t
where R is the rotation matrix and t the translation of the origin.
The reverse way,
x = R' (y - t) = R' y + (- R' t)
where R' is the inverse of R, and also its transpose.
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
add a comment |
In matrix form,
y = R x + t
where R is the rotation matrix and t the translation of the origin.
The reverse way,
x = R' (y - t) = R' y + (- R' t)
where R' is the inverse of R, and also its transpose.
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
In matrix form,
y = R x + t
where R is the rotation matrix and t the translation of the origin.
The reverse way,
x = R' (y - t) = R' y + (- R' t)
where R' is the inverse of R, and also its transpose.
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
answered Nov 24 '18 at 19:53
Yves DaoustYves Daoust
37.1k72559
37.1k72559
add a comment |
add a comment |
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en.wikipedia.org/wiki/Rotation_of_axes
– Ripi2
Nov 24 '18 at 13:54
construct 4x4 homogenous matrix representing the transform from G to A and just invert it ....see Understanding 4x4 homogenous transform matrices
– Spektre
Nov 25 '18 at 9:05