What is the difference between two quaternions?
Using quaternions¶ The difference rotation quaternion that represents the difference rotation is defined as r ≜ p q ∗ . The distance between rotations represented by unit quaternions p and q is the angle of the difference rotation represented by the unit quaternion r = p q ∗ .
How do quaternions compare?
If your two quaternions are q1 and q2 , they represent the same rotation if either of these two conditions hold:
- q1 is component wise approximately equal to q2 OR.
- q1 is component wise approximately equal to -q2.
How do you find the angle difference between two quaternions?
So, let us consider the two quaternions q1 and q2… the angle between them (ang) is given by the following relation: q1(inner)q2 = norm(q1)norm(q2)cos(ang). ang = acos{[q1(inner)q2] / [norm(q1)norm(q2)]}. Thank you Mr.
What are quaternions used for?
Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.
Can I subtract quaternions?
Quaternion subtraction is defined as the subtraction of the corresponding parts of each quaternion. Create two quaternions and perform subtraction.
What is the dot product of two quaternions?
The dot-product (inner product) of two quaternions is their usual vector dot-product: ˙p· ˙q = p0q0 + pxqx + pyqy + pzqz. a vector. A unit quaternion has squared length one.
How do you compare two rotations in a matrix?
Method
- Compute the rotation RAB between RA and RB as RAB=RTARB.
- Compute the axis-angle (ω, θ) representation of RAB using the following formula: Tr(RA)=1+2cos(θ)
- Use the angle θ as the rotation error.
Why are quaternions better?
A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo- metric meaning is also more obvious as the rotation axis and angle can be trivially recovered. This is because quaternion composition takes merely sixteen multiplications and twelve additions.
How do you invert quaternions?
The inverse of a quaternion refers to the multiplicative inverse (or 1/q) and can be computed by q-1=q’/(q*q’) for any non-zero quaternion.
What is quaternion product?
The quaternion product of two vectors (x, y, z) and (x´, y ´, z´) is the product of q = xi + yj + zk and q’ = x’i + y’j + z’k as quaternions. The quaternion product qq´ works out to be. – (xx´ + yy´ + zz´) + (yz´ – zy´)i +(zx´ – xz´)j + (xy´ – yx´)k.