How do you convert a vector to a quaternion?

How do you convert a vector to a quaternion?

So take the cross product of your direction vector D and up vector U for the side vector S then cross D and S for a new Un. Then use D, Un, S as rows (or columns depending on how your calculation rule is set up) as a matrix. Matrix to quaternion is well known math.

How do you find direction vector from quaternion?

1 Answer

1. If you are talking about recovering the direction vector for the axis from a rotation quaternion, and q=a+bi+cj+dk, then axis of rotation is the same direction as.
2. bi+cj+dk, which would be the vector (b,c,d) in 3-space.

How do you calculate the rotation of a quaternion?

For rotation quaternions, the inverse equals the conjugate. So for rotation quaternions, q−1 = q* = ( q0, −q1, −q2, −q3 ). Inverting or conjugating a rotation quaternion has the effect of reversing the axis of rotation, which modifies it to rotate in the opposite direction from the original.

How do you find a quaternion?

Any quaternion can be written as q=cos(ϕ/2)+sin(ϕ/2)k, where k is a unit vector representing the axis of rotation and ϕ is the angle in radians.

What does quaternion Euler do?

Quaternion. Euler generates a Quaternion that represents the orientation or relative rotation specified by the Euler/Tait-Bryan angles you provide as inputs. Transform. Rotate rotates a transform by an incremental amount, specified by the Euler/Tait-Bryan angles you provide as inputs.

How do you convert a quaternion to a rotation matrix?

The cool thing about quaternions is they work just like complex numbers. In two dimensions, you can rotate a vector using complex number multiplication. You can do the same with quaternions. The math is more complicated with four terms instead of two, but the principle is the same.

What is a quaternion in math?

In mathematics, the quaternion number system extends the complex numbers. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative.

How do you use quaternion?

With quaternions, it’s as simple as multiplication. Typically you will take the orientation you have (as a quaternion) and just multiply by the rotation (another quaternion) you want to apply.

Are quaternions vectors?

A quaternion that equals its real part (that is, its vector part is zero) is called a scalar or real quaternion, and is identified with the corresponding real number. That is, the real numbers are embedded in the quaternions. A quaternion that equals its vector part is called a vector quaternion.

What is the difference between quaternion and Euler?

Euler angles are “degree angles” like 90, 180, 45, 30 degrees. Quaternions differ from Euler angles in that they represent a point on a Unit Sphere (the radius is 1 unit). Quaternions differ from Euler angles in that they use imaginary numbers to define a 3D rotation.