macOS core animation CATransform3D is a 4x4 matrix ?

[MrFusion]

Hello

I am messing around with core animation. The documentation says that CATransform3D is a 4x4 matrix, but doesn't really go into detail. Why is Apple using a 4x4 matrix, instead of a 3x3? I assume that Apple is not applying general relativity (Minkowski space is 4x4, with the fourth dimension time).

What is the 4th dimension here?

Thanks.

 

[chown33]

Hello

I am messing around with core animation. The documentation says that CATransform3D is a 4x4 matrix, but doesn't really go into detail. Why is Apple using a 4x4 matrix, instead of a 3x3? I assume that Apple is not applying general relativity (Minkowski space is 4x4, with the fourth dimension time).

What is the 4th dimension here?

Thanks.

There isn't a 4th dimension, at least not in the Minkowski sense. A 3x3 matrix is needed for 2D graphics transforms, so a 4x4 matrix is needed for 3D transforms.

The key terms are "affine transformation" and "homogeneous coordinates".

http://en.wikipedia.org/wiki/Transformation_matrix#Affine_transformations

If you want to understand the math, consult any comprehensive computer graphics textbook, e.g, Foley & van Dam.

 

[MrFusion]

The key terms are "affine transformation" and "homogeneous coordinates".

http://en.wikipedia.org/wiki/Transformation_matrix#Affine_transformations

If you want to understand the math, consult any comprehensive computer graphics textbook, e.g, Foley & van Dam.

Ok, thanks. That rings a bell from a distant past.