[Bf-committers] Proposal to Change Mathutils Vectors

[Andrew Hale]

Hi Paul,

You make an excellent point (no pun intended!), this is correct and I made
the mistake of not considering points vs vectors here. Would it be suitable
then just to assume those using 4D vectors are aware of the pitfalls/issues?

Thanks,
Andrew

On Wed, Dec 7, 2011 at 9:03 PM, Paul Melis <paul.melis at sara.nl> wrote:

> Hi Andrew,
>
> On 12/02/2011 12:47 PM, Andrew Hale wrote:
> > I've written a proposal to change the current handling of transfomations
> of
> > vectors and remove the use cases for 4D vectors. The proposal can be
> found
> > here:
> >
> http://wiki.blender.org/index.php/User:TrumanBlending#Proposal:_Four_Dimensional_Mathutils_Vectors
>
> A few comments on your proposal:
>
> (x1, y1, z1, 1) + (x2, y2, z2, 1) = (x1+x2, y1+y2, z1+z2, 2)
>
> This addition doesn't make much sense. You're adding two 3D points here,
> i.e. 3D coordinates, for which there is no sensable geometric
> interpretation. Addition of two 3D *vectors*, i.e. 3D directions, does
> make sense, but in that case the w component should be 0. E.g.
>
> (x1, y1, z1, 0) + (x2, y2, z2, 0) = (x1+x2, y1+y2, z1+z2, 0)
>
> The value of w is also the major difference between representations of
> points and vectors in homogenous coordinates. When sticking to w=0 for
> vectors and w=1 for points things like subtraction actually make sense:
>
> (4, 4, 4, 1) - (1, 1, 1, 1) = (3, 3, 3, 0)
>
> That is, subtracting two 3D points results in a vector that points from
> the second point to the first. Subtraction of vectors also just works:
>
> (0, 1, 0, 0) - (1, 0, 0, 0) = (-1, 1, 0, 0)
>
> Adding a vector to a point gets you a new point:
>
> (1, 2, 3, 1) + (4, 4, 4, 0) = (5, 6, 7, 1)
>
> The point being that in these cases you don't need to explicitly worry
> about the w component, as for the sensible operations the results are
> correct. It's only with applying transformation matrices that you need
> to normalize the result by dividing by the w-component of the result
> (but only if it is non-zero).
>
>
> In general I would say, just like Stephen Swaney did somewhere in this
> thread, that there's two kinds of users:
>
> 1. The first type of user doesn't need/want to know about the underlying
> complexities of 3D math. He/she just wants to do simple manual
> transformations on 3D geometry. The easiest interface would be to
> provide methods in the Matrix class for transforming points, vectors and
> normals specified as 3-tuples (e.g. transformPoint(Vector3),
> transformVector(Vector3), transformNormal(Vector3)). These methods can
> then hide the underlying assumptions about the value of the w component
> and the different method needed for transforming vectors versus normals.
> The results from these methods would be 3-tuples as well. By using
> multiplication of transformation matrices you can simply compose
> transformations from separate steps. I think that's about all the
> operations this group of users wants to do (but correct me if I'm wrong).
>
> 2. The second type of user knowns his 3D math and just wants to work
> with general 4x4 transformation matrices and the operations on length-4
> tuples. They will worry themselves about homogenous coordinates and
> such. These users also know that v*M and M*v produce different results
> and ignore the fact that v plays the role of column-vector versus
> row-vector here, etc.
>
> I consider myself to be in the second category and completely removing
> vectors with homogenous coordinates from the Blender API makes me
> nervous. I don't think the two types of usage conflict, it's more about
> providing different APIs for accomplishing the same thing and educating
> users in the first category what methods to use, providing good example
> scripts, etc.
>
> Just my 2 euro-cents,
> Paul
>
>
>
>
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