Yes and yes, to the Homogeneous coordinate being the first column or row. That way, you can have sparse vectors, or sparse matrices. It doesn't matter how man

Yes and yes, to the Homogeneous coordinate being the first column or row. That way, you can have sparse vectors, or sparse matrices. It doesn't matter how many dimensions are specified for your object, stored in memory. It gets transformed the same. Have a point at the origin? [1] Done. It doesn't matter if it's a 2D, 3D, 7D. Have a 0-vector? [0] Done. Have a 2D point? [1, x, y] Have a 3D point? [1, x, y, z] Have a 1D vector? [0, x] I honestly don't know why we don't all do it this way.