Ask Your Question

MageSean's profile - activity

2021-02-04 04:22:59 +0100 received badge  Famous Question (source)
2018-03-19 16:57:29 +0100 received badge  Notable Question (source)
2015-07-31 03:47:05 +0100 received badge  Popular Question (source)
2011-10-29 16:17:57 +0100 received badge  Editor (source)
2011-10-29 16:06:15 +0100 answered a question Affine transformations & Affine spaces

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

2011-10-29 14:26:46 +0100 asked a question Affine transformations & Affine spaces

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