I have an up vector , position vector of the camera and position vector of the object the camera needs to be looking at. Is it possible to compute the quaternion based on this information? How can I do that ?
I tried this -
I thought the camera (at A) is by default looking in direction given by up vector(U). From there it needs to turn towards the object(B). Therefore final direction will be B-A. So I compute the angle and axis of rotation from U to B-A. But that doesn't give the right answer.
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So, for anyone familiar with Google Maps, when you zoom, it does it around the cursor.
That is to say, the matrix transformation for such a zoom is as simple as:
TST^{-1}*x
Where T is the translation matrix representing the point of focus, S the scale matrix and x is any arbitrary point on the plane.
Now, I want to produce a similar effect with a spherical camera, think sketchfab.
When you zoom in and out, the camera needs to be translated so as to give a similar effect as the 2D zooming in Maps. To be more precise, given a fully composed MVP matrix, there exists a set of parallel planes that are parallel to the camera plane. Among those there exists a unique plane P that also contains the center of the current spherical camera.
Given that plane, there exists a point x, that is the unprojection of the current cursor position onto the camera plane.
If the center of the spherical camera is c then the direction from c to x is d = x - c.
And here's where my challenge comes. Zooming is implemented as just offsetting the camera radially from the center, given a change in zoom Delta, I need to find the translation vector u, colinear with d, that moves the center of the camera towards x, such that I get a similar visual effect as zooming in google maps.
Since I know this is a bit hard to parse I tried to make a diagram:
TL;DR
I want to offset a spherical camera towards the cursor when I zoom, how do i pick my translation vector?
I have two spheres on which panoramic image is mapped. I want to make smooth transition between 2 panoramas with fade effect. for both panorama I have initial camera direction set for best view.
Now the issue is if user is looking at some camera angle in first panorama and then he clicks on some button to switch panorama I want to give fade effect and directly land on initial camera angle of another pano.
But as both pano are sharing common camera, I cannot play with camera to achieve it so I devised following solution -
image depicting problem
rotate target sphere so that it looks at desired camera direction.
rotate target sphere so that it looks at existing camera direction.
fadeout source sphere.
camera look at new panos camera direction.
rotate back pano to initial orientation.
Here I am not able to find formula of rotating panorama to look at camera. (like camera is static and pano is rotated to achieve similar effect as if we are moving camera).
Can somebody please help in finding formula to rotate pano(sphere) relative to camera.
Matrix is a very powerful tool to solve rotation problem. I made a simple to explain.
At the beginning, the camera is in the center of the left sphere and face to initial viewpoint, then, the camera face to another point, now, the camera's rotation has changed, next, camera move to the center of the right sphere and keep its orientation. and we need to rotate the right sphere. If C is the point that we want to make the camera to face, first, we rotate A to B， second, we rotate some angle θ equal to C to A.
So, how to do like that? I used matrix, because A is an initial point, matrix in an identity matrix, and the rotation from A to C can be represented by a matrix, calculated by three.js function matrix4.lookAt(eye,center,up) which 'eye' is the camera position, 'center' is coordinate of C, and 'up' is camera up vector. Then, rotation matrix from C to A is the inverse matrix of the matrix from A to C. Because the camera is face to B now, so the camera's matrix equals to the rotation matrix from A to B.
Finally, we put it all together, the final rotation matrix can be written in:rotationMatrix = matrixAtoB.multiply(new THREE.Matrix4().getInverse(matrixAtoC));
jsfiddle example.
This way is a matrix way, you can also solve the problem with the spherical polar system.
Given are the vector of direction in which the SCNCamera looks and the up vector that points into the upside direction of the camera.
How can the rotation of the camera of each individual axis be calculated?
I would like to find a solution for taking a rotation represented as a matrix and then resetting one of it's components. Basically I want to be able to multiply a vector by this matrix and get a direction that is rotation around x and z axis and be constant along the y axis (up). I want to take object rotation and get the vector that represents gravity but in object local space and disregarding the yaw. So I want to reset the yaw.
I don't want to convert this to euler angles. I would prefer using a quaternion or doing some sequence of operations on the rotation matrix directly in order to avoid possible bugs with certain angles.
Ok, so I have the follwoing:
btTransform t;
mBody->getMotionState()->getWorldTransform(t);
btMatrix3x3 trans = t.getBasis().inverse();
btVector3 up = (trans * btVector3(0, 1, 0));
I realized that if I used quaternion then I got completely wrong results (why?). Now I'm getting a vector in object space that represents up vector in world space. BUT I want to rotate this vector so that it represents global up vector in object space WHEN MODEL HAS ZERO rotation around Y axis. So I have to somehow rotate this vector back. How?
You can use quaternion swing twist decomposition with passed "Y" axis. It will decompose quaternion to rotation around Y axis and rotation around axis that is perpendicular to Y.
It is described here, in my answer.
Component of a quaternion rotation around an axis
I have a rotation matrix calculated from the calibration of the PTZ camera mount.
Given the rotation matrix, how can I calculate the roll angle of the video image at the current Pan/Tilt position?
I think I figured it out.
If I cross the Up Vector, from my rotation matrix, with the Forward Vector, calculated from the camera current Pan/Tilt, I will get the Side Vector which I can use to calculate the Roll angle.
double roll = Math.atan(side.z / Math.sqrt(side.x * side.x + side.y * side.y));