Rotate a std::vector as a rigid transformation?
I have a few 3d points, stored in a std::vector<Eigen::Vector3d>. I need to rigidly rotate and translate these points, without changing their relationship to one another. As if moving the cloud as a whole.
Based on this question:
https://stackoverflow.com/questions/50507665/eigen-rotate-a-vector3d-with-a-quaternion
I have this code:
std::vector<Eigen::Vector3d> pts, ptsMoved;
Eigen::Quaterniond rotateBy = Eigen::Quaterniond(0.1,0.5,0.08,0.02);
Eigen::Vector3d translateBy(1, 2.5, 1.5);
for (int i = 0; i < pts.size(); i++)
{
//transform point
Vector3d rot = rotateBy * (pts[i] + translateBy);
ptsMoved.push_back(rot);
}
When i view the points and compare them to the original points, however, I get this: (White are the original, green are the transformed).
What i expect, is the cloud as a whole to look the same, just in a different position and orientation. What i get, is a moved and rotated and scaled cloud, that looks different to the original. What am i doing wrong?
EDIT:
If i apply the inverse transform to the adjusted points, using:
std::vector<Eigen::Vector3d> pntsBack;
for (int i = 0; i < ptsMoved.size(); i++)
{
//transform point
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] - translateBy);
pntsBack.push_back(rot);
}
It gives me an even worse result. (dark green = original points, white = transformed, light green = transformed inverse)
c++ eigen point-clouds
asked Nov 23 '18 at 12:36
antianti
9571231
|
show 7 more comments
I have a few 3d points, stored in a std::vector<Eigen::Vector3d>. I need to rigidly rotate and translate these points, without changing their relationship to one another. As if moving the cloud as a whole.
Based on this question:
https://stackoverflow.com/questions/50507665/eigen-rotate-a-vector3d-with-a-quaternion
I have this code:
std::vector<Eigen::Vector3d> pts, ptsMoved;
Eigen::Quaterniond rotateBy = Eigen::Quaterniond(0.1,0.5,0.08,0.02);
Eigen::Vector3d translateBy(1, 2.5, 1.5);
for (int i = 0; i < pts.size(); i++)
{
//transform point
Vector3d rot = rotateBy * (pts[i] + translateBy);
ptsMoved.push_back(rot);
}
When i view the points and compare them to the original points, however, I get this: (White are the original, green are the transformed).
What i expect, is the cloud as a whole to look the same, just in a different position and orientation. What i get, is a moved and rotated and scaled cloud, that looks different to the original. What am i doing wrong?
EDIT:
If i apply the inverse transform to the adjusted points, using:
std::vector<Eigen::Vector3d> pntsBack;
for (int i = 0; i < ptsMoved.size(); i++)
{
//transform point
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] - translateBy);
pntsBack.push_back(rot);
}
It gives me an even worse result. (dark green = original points, white = transformed, light green = transformed inverse)
c++ eigen point-clouds
asked Nov 23 '18 at 12:36
antianti
9571231
If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
thanks for your reply. usingVector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy);to apply the inverse, I get a very incorrect result.
– anti
Nov 23 '18 at 12:56
that isn't the opposite transformation. Iirc it would be(rotateBy.inverse() * ptsMoved[i]) - translateBy;
– Caleth
Nov 23 '18 at 12:57
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58
|
show 7 more comments
I have a few 3d points, stored in a std::vector<Eigen::Vector3d>. I need to rigidly rotate and translate these points, without changing their relationship to one another. As if moving the cloud as a whole.
Based on this question:
https://stackoverflow.com/questions/50507665/eigen-rotate-a-vector3d-with-a-quaternion
I have this code:
std::vector<Eigen::Vector3d> pts, ptsMoved;
Eigen::Quaterniond rotateBy = Eigen::Quaterniond(0.1,0.5,0.08,0.02);
Eigen::Vector3d translateBy(1, 2.5, 1.5);
for (int i = 0; i < pts.size(); i++)
{
//transform point
Vector3d rot = rotateBy * (pts[i] + translateBy);
ptsMoved.push_back(rot);
}
When i view the points and compare them to the original points, however, I get this: (White are the original, green are the transformed).
What i expect, is the cloud as a whole to look the same, just in a different position and orientation. What i get, is a moved and rotated and scaled cloud, that looks different to the original. What am i doing wrong?
EDIT:
If i apply the inverse transform to the adjusted points, using:
std::vector<Eigen::Vector3d> pntsBack;
for (int i = 0; i < ptsMoved.size(); i++)
{
//transform point
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] - translateBy);
pntsBack.push_back(rot);
}
It gives me an even worse result. (dark green = original points, white = transformed, light green = transformed inverse)
c++ eigen point-clouds
asked Nov 23 '18 at 12:36
antianti
9571231
I have a few 3d points, stored in a std::vector<Eigen::Vector3d>. I need to rigidly rotate and translate these points, without changing their relationship to one another. As if moving the cloud as a whole.
Based on this question:
https://stackoverflow.com/questions/50507665/eigen-rotate-a-vector3d-with-a-quaternion
I have this code:
std::vector<Eigen::Vector3d> pts, ptsMoved;
Eigen::Quaterniond rotateBy = Eigen::Quaterniond(0.1,0.5,0.08,0.02);
Eigen::Vector3d translateBy(1, 2.5, 1.5);
for (int i = 0; i < pts.size(); i++)
{
//transform point
Vector3d rot = rotateBy * (pts[i] + translateBy);
ptsMoved.push_back(rot);
}
When i view the points and compare them to the original points, however, I get this: (White are the original, green are the transformed).
What i expect, is the cloud as a whole to look the same, just in a different position and orientation. What i get, is a moved and rotated and scaled cloud, that looks different to the original. What am i doing wrong?
EDIT:
If i apply the inverse transform to the adjusted points, using:
std::vector<Eigen::Vector3d> pntsBack;
for (int i = 0; i < ptsMoved.size(); i++)
{
//transform point
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] - translateBy);
pntsBack.push_back(rot);
}
It gives me an even worse result. (dark green = original points, white = transformed, light green = transformed inverse)
c++ eigen point-clouds
c++ eigen point-clouds
asked Nov 23 '18 at 12:36
antianti
9571231
asked Nov 23 '18 at 12:36
antianti
9571231
edited Nov 23 '18 at 13:01
anti
asked Nov 23 '18 at 12:36
antianti
9571231
asked Nov 23 '18 at 12:36
antianti
9571231
asked Nov 23 '18 at 12:36
antianti
9571231
9571231
If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
thanks for your reply. usingVector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy);to apply the inverse, I get a very incorrect result.
– anti
Nov 23 '18 at 12:56
that isn't the opposite transformation. Iirc it would be(rotateBy.inverse() * ptsMoved[i]) - translateBy;
– Caleth
Nov 23 '18 at 12:57
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58
|
show 7 more comments
If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
thanks for your reply. usingVector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy);to apply the inverse, I get a very incorrect result.
– anti
Nov 23 '18 at 12:56
that isn't the opposite transformation. Iirc it would be(rotateBy.inverse() * ptsMoved[i]) - translateBy;
– Caleth
Nov 23 '18 at 12:57
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58
If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
thanks for your reply. using
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy); to apply the inverse, I get a very incorrect result.– anti
Nov 23 '18 at 12:56
thanks for your reply. using
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy); to apply the inverse, I get a very incorrect result.– anti
Nov 23 '18 at 12:56
that isn't the opposite transformation. Iirc it would be
(rotateBy.inverse() * ptsMoved[i]) - translateBy;– Caleth
Nov 23 '18 at 12:57
that isn't the opposite transformation. Iirc it would be
(rotateBy.inverse() * ptsMoved[i]) - translateBy;– Caleth
Nov 23 '18 at 12:57
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58
|
show 7 more comments
1 Answer
1
active
oldest
votes
Your Quaternion is not a unit-Quaternion, therefore you will get unspecified results.
If you are not sure your quaternion is normalized, just write
rotateBy.normalize();
before using it. Additionally, if you want to rotate more than one vector it is more efficient to convert the Quaternion to a rotation matrix:
Eigen::Matrix3d rotMat = rotateBy.toRotationMatrix();
// ...
// inside for loop:
Vector3d rot = rotMat * (ptsMoved[i] - translateBy);
Also, instead of .inverse() you can use .conjugate() for unit quaternions and .adjoint() or .transpose() for orthogonal Matrices.
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, usingVector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy);The rotation looks correct, but the translation is off in one axis.
– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy;thank you again for your help!
– anti
Nov 23 '18 at 14:19
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
votes
active
oldest
votes
Your Quaternion is not a unit-Quaternion, therefore you will get unspecified results.
If you are not sure your quaternion is normalized, just write
rotateBy.normalize();
before using it. Additionally, if you want to rotate more than one vector it is more efficient to convert the Quaternion to a rotation matrix:
Eigen::Matrix3d rotMat = rotateBy.toRotationMatrix();
// ...
// inside for loop:
Vector3d rot = rotMat * (ptsMoved[i] - translateBy);
Also, instead of .inverse() you can use .conjugate() for unit quaternions and .adjoint() or .transpose() for orthogonal Matrices.
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, usingVector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy);The rotation looks correct, but the translation is off in one axis.
– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy;thank you again for your help!
– anti
Nov 23 '18 at 14:19
add a comment |
Your Quaternion is not a unit-Quaternion, therefore you will get unspecified results.
If you are not sure your quaternion is normalized, just write
rotateBy.normalize();
before using it. Additionally, if you want to rotate more than one vector it is more efficient to convert the Quaternion to a rotation matrix:
Eigen::Matrix3d rotMat = rotateBy.toRotationMatrix();
// ...
// inside for loop:
Vector3d rot = rotMat * (ptsMoved[i] - translateBy);
Also, instead of .inverse() you can use .conjugate() for unit quaternions and .adjoint() or .transpose() for orthogonal Matrices.
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, usingVector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy);The rotation looks correct, but the translation is off in one axis.
– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy;thank you again for your help!
– anti
Nov 23 '18 at 14:19
add a comment |
Your Quaternion is not a unit-Quaternion, therefore you will get unspecified results.
If you are not sure your quaternion is normalized, just write
rotateBy.normalize();
before using it. Additionally, if you want to rotate more than one vector it is more efficient to convert the Quaternion to a rotation matrix:
Eigen::Matrix3d rotMat = rotateBy.toRotationMatrix();
// ...
// inside for loop:
Vector3d rot = rotMat * (ptsMoved[i] - translateBy);
Also, instead of .inverse() you can use .conjugate() for unit quaternions and .adjoint() or .transpose() for orthogonal Matrices.
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
Your Quaternion is not a unit-Quaternion, therefore you will get unspecified results.
If you are not sure your quaternion is normalized, just write
rotateBy.normalize();
before using it. Additionally, if you want to rotate more than one vector it is more efficient to convert the Quaternion to a rotation matrix:
Eigen::Matrix3d rotMat = rotateBy.toRotationMatrix();
// ...
// inside for loop:
Vector3d rot = rotMat * (ptsMoved[i] - translateBy);
Also, instead of .inverse() you can use .conjugate() for unit quaternions and .adjoint() or .transpose() for orthogonal Matrices.
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
answered Nov 23 '18 at 13:49
chtzchtz
6,96811232
6,96811232
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, usingVector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy);The rotation looks correct, but the translation is off in one axis.
– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy;thank you again for your help!
– anti
Nov 23 '18 at 14:19
add a comment |
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, usingVector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy);The rotation looks correct, but the translation is off in one axis.
– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy;thank you again for your help!
– anti
Nov 23 '18 at 14:19
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, using
Vector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy); The rotation looks correct, but the translation is off in one axis.– anti
Nov 23 '18 at 13:55
Thank you! This has indeed fixed my issue. However, when I try to get the points back to where they started, using
Vector3d rot = rotateBy.conjugate() * (ptsMoved[i] - translateBy); The rotation looks correct, but the translation is off in one axis.– anti
Nov 23 '18 at 13:55
Adjusting teh order of operations has fixed this last part.
Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy; thank you again for your help!– anti
Nov 23 '18 at 14:19
Adjusting teh order of operations has fixed this last part.
Vector3d rot = rotateBy.conjugate() * (ptsMoved[i]); rot = rot - translateBy; thank you again for your help!– anti
Nov 23 '18 at 14:19
add a comment |
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If you apply the inverse transform to the transformed points, do you get back to where you started?
– Caleth
Nov 23 '18 at 12:49
Or even better, apply the inverse transform to the camera, and compare those pictures
– Caleth
Nov 23 '18 at 12:55
thanks for your reply. using
Vector3d rot = rotateBy.inverse() * (ptsMoved[i] -translateBy);to apply the inverse, I get a very incorrect result.– anti
Nov 23 '18 at 12:56
that isn't the opposite transformation. Iirc it would be
(rotateBy.inverse() * ptsMoved[i]) - translateBy;– Caleth
Nov 23 '18 at 12:57
To me, the differences look like parallax
– Caleth
Nov 23 '18 at 12:58