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It's completely unnecessary to understand what the individual components of quaternions represent. All that is necessary is to build an understanding of what th
by moron4hire 8y ago
It's completely unnecessary to understand what the individual components of quaternions represent. All that is necessary is to build an understanding of what the operations do for you. Do you need to understand Russell's proof that 1+1=2 to compute the tip on your bar bill, or do you just need to know what to expect when you apply the addition operation to two numbers? Treat quaternions as indivisible whole values as you would floating point numbers.
- vanderZwan 8y agoRussell's proof that 1+1=2 is more complicated than the existing intuition of adding up numbers. GA is less complicated and more intuitive than the maths of quaternions. So your comparison does not really hold up.
- yiyus 8y agoI will give you an example (from my recent work) where actually knowing what the components mean was useful. I had to calculate misorientations between many pairs of orientations. If I treated quaternions as a whole, I would find their quotient and then get the angle. But since I know what the components mean, and I know I can get the misorientation angle from just the cosine (the scalar component), and I know that I can get this value from a simple dot product, I can easily save a few operations to calculate every misorientation. And since I have to calculate many of them, this change supposed a big speedup. Black boxes are nice when learning or thinking at a high level, but if you frequently use a black box, knowing what is inside will probably become useful at some point.