If we wanted to animate a transition between the initial state and A_0 instead, would we still need to decompose A_0 into rotation and scaling or would taking the linear combination of A_0 and the identity matrix work?

YutianW

If we just ignore X(t) in the transformation, how can we guarantee the composite transformation of Q(t) and P(t) together will generate a valid interpolation? Why can we just drop X(t) in this case?

Midoriya

If we drop X(t), wouldn't this result in wrong endpoints? Q(0) is not always equal to Q_0, and Q(t) is not always equal to Q_1.

mangopi

What exactly does x(t) represent and is it still the same rotation as (1-t)Q_0 + tQ_1?

ScreenTime

How did the shading on the cow change?

blahaj

why can we throw away x?

birb

How do people come up with more realistic ways of interpolating transformations? I'm probably lacking a lot of intuition but I don't understand how they decided to use a decomposition. Also, are there different ways of interpolating transformations used depending on the object being transformed?

If we wanted to animate a transition between the initial state and A_0 instead, would we still need to decompose A_0 into rotation and scaling or would taking the linear combination of A_0 and the identity matrix work?

If we just ignore X(t) in the transformation, how can we guarantee the composite transformation of Q(t) and P(t) together will generate a valid interpolation? Why can we just drop X(t) in this case?

If we drop X(t), wouldn't this result in wrong endpoints? Q(0) is not always equal to Q_0, and Q(t) is not always equal to Q_1.

What exactly does x(t) represent and is it still the same rotation as (1-t)Q_0 + tQ_1?

How did the shading on the cow change?

why can we throw away x?

How do people come up with more realistic ways of interpolating transformations? I'm probably lacking a lot of intuition but I don't understand how they decided to use a decomposition. Also, are there different ways of interpolating transformations used depending on the object being transformed?