[Blindmath] Understanding how to draw 3D objects

[Andrew Stacey]

On Fri, Mar 23, 2012 at 09:13:37AM -0000, Michael Whapples wrote:
> Unfortunately that page is awful to read as there's so many
> meaningless heading structures and distracts from the reading with a
> screen reader.

Yes, I did try to warn you.  The SVGs were automatically generated from the
TeX source and can be a little ... verbose.  I have no idea how to make SVGs
accessible, sorry.

> However from what I was gathering it sort of is dealing with what I
> was on about. One thing I am not sure of is, the difference between
> computer 2D and 3D drawing libraries, and then how these relate to
> drawing in LaTeX for paper documents (if they apply at all to this
> type of drawing).

The LaTeX drawing system that I use, TikZ/PGF, is definitely a 2D system.  So
when I want to draw something that is really 3D I have to figure out the
necessary transformations myself.  The easy part is specifying coordinates
(TikZ has rudimentary support for that).  The hard part is figuring out
exactly what to draw, and what order to draw it to ensure that things in front
obscure things behind.

> After Andrew's message I think I can specify what I need a bit
> better. I am able to create the internal mental 2D image of the
> object, however this image is probably very visual, may be even to
> the standard of a photo. My difficulty is going from that internal
> image to what lines and other elements I need to specify in LaTeX to
> achieve my mental image, this may include what parts of my mental
> image can I simplify and still maintain the affect of the 3D object.

See above remark.  This is something that can be quite difficult for anyone to
do.

But this seems to be going the other way around to what I thought you were
asking for, which was how to work out that that LaTeX drawing was a torus.
After all, it is just lines on a page.  I would only know that it was meant to
be a torus because that is a picture with which I am extremely familiar so it
immediately suggests itself to my brain as a possible interpretation for what
the picture means.

> As an example, for a torus I probably would still use shading to
> show lighting sources to help show the 3D affect, however the torus
> in the wikibook does not use shading and Andrew didn't say he used
> any shading either, so may be I could get away without using shading
> (shading would have significantly complicated that wikibook drawing,
> not sure about Andrew's drawings).

My drawings use shading because I decompose the picture into pieces and draw
each piece with an appropriate colour depending on the angle it presents in
space.  However, in a mathematics seminar then I would hesitate at going to
such lengths simply because I would expect everyone there to know what a torus
looks like and so be able to add in the necessary details.

>                                    For some reason I seem to think
> shading for lighting is more important on curved surfaces as when
> drawn on paper you don't have any lines showing corners which may
> indicate a change of direction, IE. while simpler to shade
> correctly, I would see it less important to shade the side of a
> cube.

Agreed.  So I guess what I'm saying in my previous comment is that for me (and
for the mathematicians that I would be likely to be talking with) a torus is
one of those shapes with which we are so familiar that we don't need
complicated stuff like shading to see what it should be.  However, there are
other shapes for which we would so I agree with your point.

> I think its the decomposing an image into the element parts which is
> difficult, particularly as its more work for me to compare the final
> result with my internal image.

Moreover, the final image isn't necessarily the result of this decomposition.
Often with rendering 3D shapes it is enough to specify the edge (that's what
the wikibooks torus does).  This can actually be quite hard to work out
exactly (for example, the torus is more complicated than I expected it to be)
and not always worth the bother.  Drawing it "correctly" often takes second
place to drawing it simply and quickly.

Andrew