MageSean's profile - activity

Thanks Benjamin:

I am aware how it could be used in vector algebra. The source I use is Geometric Tools for Computer Graphics by Schneider & Eberly 2003.

There is a distinction unlike vector algebra between a vector and a point. *Add two vectors to get a third. *Multiply a vector by a scalar to get a vector. *Add a vector to a point to get another point. *Subtract two points to get vector. (edited) *etc.

In affine algebra, a point can be translated in a matrix multiplication where in vector algebra it cannot. I have to admit that vector algebra is used quite a lot in CG, for example, the affine matrix has a vector matrix embedded.

The elements of a point in affine space for example is [0, 1, 0, 1] for the vector [0, 1, 0] in vector space. The elements for a vector in affine space is [0, 1, 0, 0] for the vector [0, 1, 0] in vector space.

Please don't ask me to prove this. I do believe that sage developers can implement this as a subset to the module linear algebra. CG is a large and fast growing business.

I suppose the answer from Benjamin is NO. There is no affine algebra unless we define the vectors as points and the matrices as affine matrices....

Many Thanks

Can Sage do affine transformation in affine spaces - adding a vector to a point?