Slerp vector code unity to specific algle

So instead of a divide operation we multiply by the inverse. Need to be able to distinguish between q1*q2 -1 and q2 -1*q1. Notation for division, since quaternion multiplication is not commutative we This operation will be coded in the sfrotation class ( seeДЄlternatively, if we want to use scalar and vector notation for quaternions, as defined on this page then multiplication is:.Other quaternion multiplication issues.So back to the general case of multiplying any two quaternions, we can just expand out the terms and group as follows: (a + i b + j c + k d)*(e + i f + j g + k h) Notice that squaring any linear combination of imaginary terms will give a negative real number because the leading diagonal is negative and the other terms cancel out because they anticommute. We can compare it with, say, geometric algebra. This table summarises the character of quaternions. The following table summarises these issues, it shows the type and sign for each permutation of parts of the multiplying quaternions. In other words, to reverse the order, take the conjugate of each part and then take the conjugate of the whole thing. If the quaternion is unit length (normalised) as when used to represent rotations: Useful to introduce the concept of the conjugate explained here. In order to understand more about the effect of reversing the operands it is In the general case quaternions containing all these parts would be neither commutative nor anti-commutative.

This apples when different imaginary quantities, as can be seen from the list above, so for example: Other subsets of quaternions anti-commute, in other words reversing the order multiplies the result by -1.

same imaginary part: i b * i f = i f * i b ( = -b*f ).real times imaginary: a * i f = i f * a.In mathematical terms quaternion rotation is not necessarily commutative, some subsets of quaternions may commute, for example:

Get a different result than if you rotate about the y-axis then the x-axis. Rotate 90 degrees about the x-axis and then 90 degrees about the y-axis you Note that the order of multiplication is significant, in other words q1 * q2 is not necessarily equal to q2 * q1, we might expect this because quaternions can be used to represent rotations and the order of rotations is significant, for example, if you When we are multiplying the imaginary operators we use the following rules: We just put each quaternion in brackets and multiply out all the terms: (a + i b + j c + k d)*(e + i f + j g + k h). The multiplication rules for the imaginary operators are the same as for other numbers. (a + i b + j c + k d)-(e + i f + j g + k h) = (a-e) + i ( b-f) + j ( c-g) +ДЄlternatively, if we want to use scalar and vector notation for quaternions, as defined on this page then subtraction is: Just subtract the real and imaginary components independently as follows: This operation will be coded in the sfrotation class ( seeДЄlternatively, if we want to use scalar and vector notation for quaternions, as defined on this page then addition is: Just add the real and imaginary components independently as follows:

Slerp vector code unity to specific algle