How can translation be expressed as a linear map if translation doesn't keep the origin fixed?
motoole2
By using homogeneous coordinates! We will cover this in a future class. In short, you can turn translation into a linear map by working with 4D vectors to represent 3D points.
Here's an example. Let's say we want to translate a 3D point (x,y,z) to (x+2,y+3,z+5). We can do this by increasing the dimensionality of our vectors by 1: (x,y,z,1). Then, there exists a linear map that produces the vector (x+2,y+3,z+5,1).
How can translation be expressed as a linear map if translation doesn't keep the origin fixed?
By using homogeneous coordinates! We will cover this in a future class. In short, you can turn translation into a linear map by working with 4D vectors to represent 3D points.
Here's an example. Let's say we want to translate a 3D point
(x,y,z)to(x+2,y+3,z+5). We can do this by increasing the dimensionality of our vectors by 1:(x,y,z,1). Then, there exists a linear map that produces the vector(x+2,y+3,z+5,1).