[Bf-committers] Proposal to Change Mathutils Vectors

[Andrew Hale]

By no modification of the w component, I meant no renormalising, just
compute the product as for regular matrix/vector multiplication.

On Wed, Dec 7, 2011 at 9:33 PM, Andrew Hale <trumanblending at gmail.com>wrote:

> Hi Paul,
>
> Correct me if I'm wrong, but do you propose to have 3D vectors with matrix
> multiplication just work (i.e. making assumptions about the w coordinate
> and renormalising if necessary) but retain 4D vectors which compute the
> product without modification of the w component? This sounds quite logical,
> however, these transformations deal with points so I'm not sure I
> understand what you mean by differentiating between vectors and normals.
>
> Thanks again,
> Andrew
>
>
> On Wed, Dec 7, 2011 at 9:15 PM, Andrew Hale <trumanblending at gmail.com>wrote:
>
>> 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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>>>
>>
>>
>