Develop Reference

How to get a Vector3 rotation between two Quaternions

I'm writing a script which rotates a Rigidbody using a Configurable Joint. I've got the targetRotation figured out, but now I'm struggling with targetAngularVelocity, which should help me avoid wobbliness if set correctly.
targetAngularVelocity is defined like this in the documantation: "This is a Vector3. It defines the desired angular velocity that the joint should rotate into". The problem is that I don't know how to get this Vector3 based on two Quaternions - current rotation of the object and the target rotation.
Am I not understanding it correctly? Is there a function that returns a rotation vector based on two Quaternions?

So mathematically a Quaternion represents the orientation of a rigid body. Consider the forward problem first, and see how the orientation q_1 transforms to another orientation q_2 after a rotational velocity ω is applied for t time.
Mathematically the rotation vector has a magnitude ω and a direction k such that ω = ω* k
This is done with quaternion multiplication as
q_2 = q_ω * q_1
Where q_ω represents a rotation about the axis of k of an angle θ=ω*t.
In reverse, you need to find q_ω with
var q_ω = q_2 * Quaternion.Inverse(q_1);
and extract the rotation axis and angle
q_ω.ToAngleAxis(out float angle, out Vector3 axis);
and compose the rotational velocity vector, that corresponds to this transformation in time seconds.
var ω = (angle/time)*axis;

Unity rotate object depending on other objects angle

I have two Gameobjects. The basic Question:
"When I spin circle 1, I want to spin circle 2 in the same way manipulated by factor x"
How do I sync the rotation around each of their local axis of circle 2 with the interactable rotation of circle one and scale that rotation by factor x? Setting the transform.right equal doesnt work, there are still to many degrees of freedom.
(Local Axis, because I want one or both gameobjects to be also tilted, but unrelated to one another.)
Trying math with rotational matrices didnt really work out based on the fact of them being evaluated every frame and thereby spinning Object 2 for eternity.
Thanks so much!

Assuming you rotate only around one single axis (as shown in the images) you can get the rotation difference in degrees of circle2 using e.g. Quaternion.Angle every frame
private Quaternion lastCircle2Rot;
//...
float rotDelta = Quaternion.Angle(lastCircle2Rot, circle2.transform.rotation);
lastCircle2Rot = circle2.transform.rotation;
than turn the circle1 accordignly using e.g. Transform.RotateAround
public float multiplier;
// e.g. rotate around local x = right
Vector3 YourAxis = circle1.transform.right;
circle1.transform.RotateAround(Vector3.zero, YourAxis, rotDelta * multiplier);
if using e.g. the right or another "clean" vector you could also simply use
circle1.transform.Rotate(Vector3.right, rotDelta * multiplier);
as it is done in local space by default.

Projectile Trajectory : Reaching specific coordinates

I am trying to implement a function in my game which will auto-lock a target and throw a projectile so that it lands perfectly on it.
I did the maths to calculate a parabola from Player 1 -> Target wherever their positions are but realised I wanted to use Unity's physics system rather than having the ball follow a path.
The throw velocity is constant, Player 1 and Target are moving objects but their positions will be registered once only to calculate the initial angle of the throw.
I believe this is the formula I need to use:
But how can I apply it for my Player and Target both having 3D coordinates?
Here is the pseudo-code of what I tried to write in Unity to make more easily readable.
float velocity = 100f;
float g = Physics.gravity;
Transform x = Target.position.x - Player.position.x;
Transform y = Target.position.z - Player.position.z;
double theta;
theta = **big formula using the values above**
And after that I do not know how to use this value to add force to the projectile.
I wanted to use AddForce(x,y,z, ForceMode.Impulse); but I clearly cannot use an initial angle here, only an x and y value.
Using RigidBody.velocity = Vector3(vx, vy, vz); gives me the same problem.
I believe I am missing something trivial but I really am stuck on this. Would anyone be able to help?

Transform kinect v2 coordinate to another coordinate

I actually measured (x,y) joint position that related to a human skeleton in the sagittal plan using Kinect v2 camera. Now, I want to create the angle between Kinect v2 and skeleton direction of motion( like in this figure: http://www.mediafire.com/file/7wf8890ngnmi1d4/kinect.pdf ).
How can I measure the joint position relative to a coordinate fixed on certain join on the skeleton like SpineBase position using MATLAB??
what is the transformation required to do that?

I have no kinect available right now, but here is the theory how I would tackle this:
First of you seem to already be able access the different joint coordinates, so you have sth like this:
if (body.IsTracked)
{
Joint spineMid = body.Joints[JointType.SpineMid];
float x = spineMid.Position.X;
float y = spineMid.Position.Y;
float z = spineMid.Position.Z;
}
This gives us a spineMid point with x,y,z. Each frame we compare that spineMid point to the spinMid point from last frame (and save it afterwards for the comparison in the next frame). Lets call these points P_new and P_old. To get the direction Vector we just subtract the two like so:
p_dir = P_new - P_old
now we have to get the angle between this direction vector and the vector "out" of the kinect which is <0,0,1> with the kinect coordinate system. But given your drawing we need to use z_dir = <0,0,-1>.
By using the unit vector of p_dir, lets call it p_dir_unit, we can use the dot product to get the angle between z_dir and p_dir_unit.
theta = acos(z_dir * p_dir_unit)
If you only need the direction in the x,z plane, you can just set the y value for p_dir to 0 and get the unit vector from that vector. From the absolute length of p_dir you can also get information on how quick the body is moving.
Hope that helps.

2 vectors difference to rotation

I've been hanging my head around this issue for some time now and I'm at the top of my head not figuring this out.
The issue:
Currently trying to do a fake "swing" moment. Where I have the player object becoming a child to an object you can latch onto during a keypush.
With this in mind, I need to get the correct rotation on the grappleobject, making the velocity of the player becoming the correct rotation on the grappleobject.
This is not meant to be 2D, but 3D. Which causes this headache.
http://img843.imageshack.us/img843/7434/rotations.jpg
I figured that if I could get the vector of position, and the vector of the direction where the player is going towards, as in velocity of the character motor, to get an unique Vector, and this vector info should be able to rotate the grappleobject correctly.
However, that's what I thought was easy, but I've been hacking at this for hours to get that vector difference to do the rotation as it was thought out to be.
tl:dr
2 Vectors, the difference of these two to one vector, this vector controls the rotation of grappleobject to "fake" a swing motion with the proper velocity.
Thank you in advance if there'll be an answer.
Added Info:
Current testings has been these.
///
Parent Orb is the grappleobjects which updates its transform depending on trigger events.
CurDirection is where the player is heading within the vector in world.
CurPos is where the player is at that point in time within the world.
CurDirection = (transform.position-ParentOrb.position);
CurDirection.Normalize();
motor.movement.velocity = (CurDirection);
CurPos = transform.position;
////
Also tried out to get the angle from the grappleobject to the player.
///
otherDirection = The direction of velocity in space.
OtherDirectionPre = Current position in space.
Vector3 targetDir = otherDirection;
Vector3 forward = otherDirectionPre;
angle = Vector3.Angle(targetDir, forward);
///
I assume these may not be helpful, but better to show where I have gotten so far.

I think you know the radius between the hit point and the center, let's call it r. With the velocity v of the player and the angular velocity ω (=omega) of the axis the player should be connected to you have the vector equation:
v = ω × r
Assuming all 3 vectors are perpendicular to each other you have ω = v / r.
EDIT: You get the radius r from the position of the center and the point of contact of your collision:
Vector3 r = collision.contacts[0].point - center;
float radius = r.magnitude;
float angularSpeed = rigidbody.veloctiy.magnitude / radius;