Can a 2D reflection be seen as a rotation in 3D when using homogeneous coordinates?

WhaleVomit

I guess if we are thinking of the 2d shapes as a bunch of scaled copies in the homogeneous coordinate system, then scaling x3 along with x1 and x2 would mean doing nothing. Each point would get translated along the line associated with it, but all the points on the line correspond to the same point in 2d. So if we scale x3 along with x1 and x2, that would be equivalent to doing nothing.

dshernan

scaling x3 could change the orientation? but I do agree with whalevomit

kpshah

are there transformations in 2D that are a different type of transformation in 3D in homogenous coordinates?

MrRockefeller

From this slide I finally understand why homogeneous coordinates are important--it allows you to write the transformation operation in only one matrix (for translation-->shear)

Can a 2D reflection be seen as a rotation in 3D when using homogeneous coordinates?

I guess if we are thinking of the 2d shapes as a bunch of scaled copies in the homogeneous coordinate system, then scaling x3 along with x1 and x2 would mean doing nothing. Each point would get translated along the line associated with it, but all the points on the line correspond to the same point in 2d. So if we scale x3 along with x1 and x2, that would be equivalent to doing nothing.

scaling x3 could change the orientation? but I do agree with whalevomit

are there transformations in 2D that are a different type of transformation in 3D in homogenous coordinates?

From this slide I finally understand why homogeneous coordinates are important--it allows you to write the transformation operation in only one matrix (for translation-->shear)