[Blindmath] Understanding how to draw 3D objects

[Michael Whapples]

Now you point this out, I think I understand why its not strictly an elipse.

As my question mainly focuses on how one goes from an internal image of what 
they want to draw to actually putting it down in elements one can use in 
LaTeX (or may be other drawing systems), I start to think, is there standard 
ways of drawing a number of 3D shapes? As an example your description of how 
you drew the torus mathematically correctly might be the pattern for drawing 
a torus. If there are a set of patterns for drawing certain 3D shapes, is 
there somewhere hich lists this stuff?

This puts me in mind of design patterns in computer programming. Such a set 
of patterns for drawing might do what I set out to find out by asking the 
initial question.

Michael Whapples

-----Original Message----- 
From: Andrew Stacey
Sent: Thursday, March 22, 2012 7:04 PM
To: Blind Math list for those interested in mathematics
Subject: Re: [Blindmath] Understanding how to draw 3D objects

It's probably just going to muddy the waters to say that that isn't a true
rendering of a torus.  The outer boundary shouldn't be an ellipse.  I know
because I've spent ages working out the formula in order to draw a more
realistic version of a torus.

The first time that I drew a torus in LaTeX then I did it the mathematically
correct way: I drew a lot of circles and rotated them around a larger 
circle.
This produces a really nice looking torus, but takes a significant amount of
time to generate.  The second time then I did it by creating a mesh and
drawing the rectangles.  However, I still doubt that either of these would 
be
in any way accessible to someone who had no conception of what the picture 
was
meant to represent.

The pictures that I'm talking about are available on my webpage.  They are
probably not accessible in any shape or form.

The first torus is part of this picture:

http://www.math.ntnu.no/~stacey/documents/smooth.1-1.svg

The second is part of this picture:

http://www.math.ntnu.no/~stacey/documents/smooth_chern.3-1.svg

Andrew

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