direct transform matrix definition..?

[coffeecup]

Hi all,

Using Sketch just since today I am pretty impressed by the
capabilities this offers. As many have stated already, it is a pretty
neat tool for parametric 3D work.

However, there is one part which made me wonder. Could anyone explain
what exactly the "direct matrix" (section 3.1.3.3 in the manual)
transforms and how the a_11, ... , a_44 operate on these objects?

Thanks for any clarification on this!

Regards,

Philip

[Gene]

On Sep 7, 6:15 pm, coffeecup <philip.eisenl...@gmail.com> wrote:
> Hi all,
>
> Using Sketch just since today I am pretty impressed by the
> capabilities this offers. As many have stated already, it is a pretty
> neat tool for parametric 3D work.
>
> However, there is one part which made me wonder. Could anyone explain
> what exactly the "direct matrix" (section 3.1.3.3 in the manual)
> transforms and how the a_11, ... , a_44 operate on these objects?
>

Thanks.

Sketch, as most 3d graphics systems, uses 4d homogeneous coordinates
internally. These are transformed with 4x4 matrix multiplications.
The built-in transformation constructors (rotation, scaling,
translation) are all translated internally to such 4x4 matrices. The
matrix literal feature of Sketch allows you to enter a matrix of your
own choice directly. There are not many cases where this is useful,
but if you do need it, you need it badly!

For more information on homogeneous transformations, see any good
computer graphics textbook. The Wikipedia article on this topic is
not bad, though most of the examples are in 2d (with 3x3 matrices)
rather than 3d (wirh 4x4). http://en.wikipedia.org/wiki/Transformation_matrix

[coffeecup]

Dear Gene,

Many thanks for the essential hint. This turns out to be exactly what
I did "need badly"...

Have you ever thought of giving this small extra information (i.e.,
first paragraph of your reply plus the wikipedia ref) also in the
Sketch manual? Might be useful to a broader audience, since it allows
for a quick way to do arbitrary transformations without the need for
polar decomposition and sequential scale(V) and rotate(..) operations.

Anyway, people should now be able to find this post on the web, since
it is likely to become the fourth result in a Google search on "direct
transform matrix definition" -- the other three refer to Sketch..!

Cheers
Philip

[Gene]

On Sep 8, 4:29 am, coffeecup <philip.eisenl...@gmail.com> wrote:
> Dear Gene,
>
> Many thanks for the essential hint. This turns out to be exactly what
> I did "need badly"...
>
> Have you ever thought of giving this small extra information (i.e.,
> first paragraph of your reply plus the wikipedia ref) also in the
> Sketch manual? Might be useful to a broader audience, since it allows
> for a quick way to do arbitrary transformations without the need for
> polar decomposition and sequential scale(V) and rotate(..) operations.
>

The manual has been updated as you suggest.
Thanks,
Gene