[Bf-committers] Proposal to Change Mathutils Vectors

[Andrew Hale]

Let me see if I can summarise the current thinking from this thread:

   1. Retain 4D vectors.
   2. Permit 4x4 matrix mulitplication of 3D vectors by assuming w=1 and
   renormalising if necessary.
   3. Compute 4x4 matrix multiplication of 4D vectors as per normal
   matrix/vector math, relying on the user to ensure correct use of the w
   coordinate if they wish to translate back to a 3D point.
   4. Write docs to explain to users that unless they have specific need to
   expose homogeneous coordinates, 3D vectors will calculate all
   transformations correctly.

Please let me know if you do not feel this adequately sums up the
discussion so far.

Thanks,
Andrew

On Wed, Dec 7, 2011 at 9:35 PM, Andrew Hale <trumanblending at gmail.com>wrote:

> 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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>>>>
>>>
>>>
>>
>