When you specify a rotation for an object, you do something like this :
_earthNode.rotation = SCNVector4Make(1, 0, 0, M_PI/2);
What I am not getting is how to specify a specific rotation for each axis ? Because let's say that I wanted to rotate my node from PI on x, PI/2 on y, and PI/4 on z, how would I do that ? I thought that I could do something like this :
_earthNode.rotation = SCNVector4Make(1, 0.5, 0.25, M_PI);
But it doesn't change anything....
How does this property works ?
The rotation vector in Scene Kit is specified as the axis of rotation (first 3 components) follow by the angle (4th component), called axis-angle representation.
The format you are trying to specify (the different angles along each axis) is called Euler angles (unless I'm remembering wrong).
Translating between the two representations is just a bit of trigonometry. A quick online search for "Euler angles to axis angle" lead to this page which shows who to do it in Java.
SCNNode has an eulerAngles property that allows you to do just that
Related
I've got robotic arm with 6 DoF. I make constrain that x, z carteasian coordinate and orientation is exactly specified. I would like to get joint coordinates which are at cartesian position [x, y_max, z], where y_max is the maximum y cartesian coordinate which is reachable by the end-effector of the robotic arm.
For example:
I set x to be 0.5, z to by 1.0 and I want to find joint coordinates that satisfy after forward kinematics that robot's end-effector is at cartesian coordinates [0.5, maximum reachable coordinate, 1.0].
I know that if I know cartesian position and orientation I can find joint coordinates by inverse kinematics and check if the end-effector is at desired coordinateds by forward kinematics, but what if I don't know one of the axis in cartesian and it depends on robot how far it is possible to move? As far as I know, inverse kinematics is possible to solve analyticaly or numericaly, but to solve it I need to know the whole frame of the finish coordinate.
Moreover I would like to have orientation dependent on y coordinate. (for example I would like to guarantee that end-effector is always looking at coordinates [0.5, 0, 0]).
You could use a numerical task-based inverse kinematics with a task such as:
Orientation: the orientation you have specified
Position in (x, z): the coordinates you have specified
Position in y: something very far away
The behavior of a task-based approach (with proper damping) when a target is not feasible is to "stretch" the robot as far as it can without violating its constraints. Here is an example with a humanoid robot and three tasks:
(for example I would like to guarantee that end-effector is always looking at coordinates [0.5, 0, 0])
This should be possible with a proper task as well. For example, in C++ the mc_rtc framework has a LookAtTask to keep a frame looking at a desired point.
Recently I'm struggling with a pose estimation problem with a single camera. I have some 3D points and the corresponding 2D points on the image. Then I use solvePnP to get the rotation and translation vectors. The problem is, how can I determine whether the vectors are right results?
Now I use an indirect way to do this:
I use the rotation matrix, the translation vector and the world 3D coordinates of a certain point to obtain the coordinates of that point in Camera system. Then all I have to do is to determine whether the coordinates are reasonable. I think I know the directions of x, y and z axes of Camera system.
Is Camera center the origin of the Camera system?
Now consider the x component of that point. Is x equavalent to the distance of the camera and the point in the world space in Camera's x-axis direction (the sign can then be determined by the point is placed on which side of the camera)?
The figure below is in world space, while the axes depicted are in Camera system.
========How Camera and the point be placed in the world space=============
|
|
Camera--------------------------> Z axis
| |} Xw?
| P(Xw, Yw, Zw)
|
v x-axis
My rvec and tvec results seems right and wrong. For a specified point, the z value seems reasonable, I mean, if this point is about one meter away from the camera in the z direction, then the z value is about 1. But for x and y, according to the location of the point I think x and y should be positive but they are negative. What's more, the pattern detected in the original image is like this:
But using the points coordinates calculated in Camera system and the camera intrinsic parameters, I get an image like this:
The target keeps its pattern. But it moved from bottom right to top left. I cannot understand why.
Yes, the camera center is the origin of the camera coordinate system, which seems to be right following to this post.
In case of camera pose estimation, value seems reasonable can be named as backprojection error. That's a measure of how well your resulting rotation and translation map the 3D points to the 2D pixels. Unfortunately, solvePnP does not return a residual error measure. Therefore one has to compute it:
cv::solvePnP(worldPoints, pixelPoints, camIntrinsics, camDistortion, rVec, tVec);
// Use computed solution to project 3D pattern to image
cv::Mat projectedPattern;
cv::projectPoints(worldPoints, rVec, tVec, camIntrinsics, camDistortion, projectedPattern);
// Compute error of each 2D-3D correspondence.
std::vector<float> errors;
for( int i=0; i < corners.size(); ++i)
{
float dx = pixelPoints.at(i).x - projectedPattern.at<float>(i, 0);
float dy = pixelPoints.at(i).y - projectedPattern.at<float>(i, 1);
// Euclidean distance between projected and real measured pixel
float err = sqrt(dx*dx + dy*dy);
errors.push_back(err);
}
// Here, compute max or average of your "errors"
An average backprojection error of a calibrated camera might be in the range of 0 - 2 pixel. According to your two pictures, this would be way more. To me, it looks like a scaling problem. If I am right, you compute the projection yourself. Maybe you can try once cv::projectPoints() and compare.
When it comes to transformations, I learned not to follow my imagination :) The first thing I Do with the returned rVec and tVec is usually creating a 4x4 rigid transformation matrix out of it (I posted once code here). This makes things even less intuitive, but instead it is compact and handy.
Now I know the answers.
Yes, the camera center is the origin of the camera coordinate system.
Consider that the coordinates in the camera system are calculated as (xc,yc,zc). Then xc should be the distance between the camera and
the point in real world in the x direction.
Next, how to determine whether the output matrices are right?
1. as #eidelen points out, backprojection error is one indicative measure.
2. Calculate the coordinates of the points according to their coordinates in the world coordinate system and the matrices.
So why did I get a wrong result(the pattern remained but moved to a different region of the image)?
Parameter cameraMatrix in solvePnP() is a matrix supplying the parameters of the camera's external parameters. In camera matrix, you should use width/2 and height/2 for cx and cy. While I use width and height of the image size. I think that caused the error. After I corrected that and re-calibrated the camera, everything seems fine.
I'm a libgdx NOOB - apologies if this is an obvious question..
Using libgdx I have set up a Perspective camera, looking at origin (camera near = 1f, far = 300f). Viewport extends across the entire screen.
Basically, I would like to know how to convert a 2D screen coordinate (x,y) to the 3D world coordinate (x, y, z) where the Z value is clamped to the camera's near plane.
I think I should use the camera.getPickRay method to get a picking ray for the screen coordinate. I should then get the intersection point of this ray and the camera's near plane to get the world coordinate of the point on the near plane.
I thought that the resulting Ray object's origin property was the near-plane intersection point I was after, but this doesn't seem to be the case.
Am I on the right track?
Camera#unproject() returns, depending on the z-value, the value between the near (z=0) and far plane (z=1), see the javadocs. Camera#getPickRay() sets the origin member to the unprojected value at z=0, thus on the near plane, see the code. If you don't need the ray (including the direction) then you don't have to calculate the pick ray, instead you can call the unproject method directly.
Vector3 pointOnNearPlane = camera.unproject(new Vector3(touchX, touchY, 0f));
Likewise, for the point on the far plane:
Vector3 pointOnFarPlane = camera.unproject(new Vector3(touchX, touchY, 1f));
camera.rotate.y pans left or right in a predictable manner.
camera.rotate.x looks up or down predictably when camera.rotate.y is at 180 degrees.
but when I change the value of camera.rotate.y to some new value, and then I change the value of camera.rotate.x, the horizon rotates.
I've looked for an algorithm to adjust for horizon rotation after camera.rotate.x is changed, but haven't found it.
In three.js, an object's orientation can be specified by its Euler rotation vector object.rotation. The three components of the rotation vector represent the rotation in radians around the object's internal x-axis, y-axis, and z-axis respectively.
The order in which the rotations are performed is specified by object.rotation.order. The default order is "XYZ" -- rotation around the x-axis occurs first, then the y-axis, then the z-axis.
Rotations are performed with respect to the object's internal coordinate system -- not the world coordinate system. This is important. So, for example, after the x-rotation occurs, the object's y- and z- axes will generally no longer be aligned with the world axes. Rotations specified in this way are not unique.
So, for example, if in code you specify,
camera.rotation.y = y_radians; // Y first
camera.rotation.x = x_radians; // X second
camera.rotation.z = 0;
the rotations are applied in the object's rotation.order, not in the order you specified them.
In your case, you may find it more intuitive to set rotation.order to "YXZ", which is equivalent to "heading, pitch, and roll".
For more information about Euler angles, see the Wikipedia article. Three.js follows the Tait–Bryan convention, as explained in the article.
three.js r.61
I've been looking for the same info for few days now, the trick is: use regular rotateX to look up/down, but use rotateOnWorldAxis(new THREE.Vector3(0.0, 1.0, 0.0), angle) for horiz turn (https://discourse.threejs.org/t/vertical-camera-rotation/15334).
I am building an augmented reality application and I have the yaw, pitch, and roll for the camera. I want to start placing objects in the 3D environment. I want to make it so that when the user clicks, a 3D point pops up right where the camera is pointed (center of the 2D screen) and when the user moves, the point moves accordingly in 3D space. The camera does not change position, only orientation. Is there a proper way to recover the 3D location of this point? We can assume that all points are equidistant from the camera location.
I am able to accomplish this independently for two axes (OpenGL default orientation). This works for changes in the vertical axis:
x = -sin(pitch)
y = cos(pitch)
z = 0
This also works for changes in the horizontal axis:
x = 0
y = -sin(yaw)
z = cos(yaw)
I was thinking that I should just make combine into:
x = -sin(pitch)
y = sin(yaw) * cos(pitch)
z = cos(yaw)
and that seems to be close, but not exactly correct. Any suggestions would be greatly appreciated!
It sounds like you just want to convert from a rotation vector (pitch,yaw,roll) to a rotation matrix. The conversion can bee seen on the Wikipedia article on rotation matrices. The idea is that once you have constructed your matrix, to transform any point simply.
final_pos = rot_mat*initial_pose
where final and initial pose are 3x1 vectors and rot_mat is a 3x3 matrix.