Does preserving distance imply preserving orientation? (Oops, this was answered later in the lecture)

manchas

When we talk about the origin here we seem to be talking about the origin of the object. Do we always mean this, or does it sometimes refer to the origin of the space the object contains? In a translation this would make more sense it seems. Is it just based on context?

Zishen

Is there any situation that origin and distance are preserved but orientation are altered? Can this be achieved by change the order of all vertexs?

Coyote

What exactly does preserving orientation mean here, or rather what would not preserving orientation look like? I thought that rotations in 3D didn't always preserve orientation because the order of rotations matters (rotation about XYZ != rotation about ZYX).

Olivia

Is rotating something around a point other than the origin still a linear map?

Does preserving distance imply preserving orientation? (Oops, this was answered later in the lecture)

When we talk about the origin here we seem to be talking about the origin of the object. Do we always mean this, or does it sometimes refer to the origin of the space the object contains? In a translation this would make more sense it seems. Is it just based on context?

Is there any situation that origin and distance are preserved but orientation are altered? Can this be achieved by change the order of all vertexs?

What exactly does preserving orientation mean here, or rather what would not preserving orientation look like? I thought that rotations in 3D didn't always preserve orientation because the order of rotations matters (rotation about XYZ != rotation about ZYX).

Is rotating something around a point other than the origin still a linear map?