Re: [help-3dldf] How to z-sort the polygons of a cuboid using with_focus

[Laurence Finston]

I hope it's alright with you that I've "cc"'ed this to the mailing list.  
I'd like your comment on the focus and my answer to be in the archive.  
Your graphic isn't included in this reply.  

> Thank you!
> 
> I am very happy with the results! (See the attached pdf)
> 

You're welcome.  Thank you for sending me the graphic.  This is the first 
time I've ever seen a non-trivial graphic made using the package that I 
didn't make myself.  (And I haven't seen many trivial ones, either.)

You may know this already, but one way of making a border around the 
graphic is to use a `frame' picture and output it using the `parallel_x_y' 
projection.  I use this for animations, in order to keep consecutive 
images aligned.


> Just so you know, I think there is a bug in the camera projection calculation.
> If I use
> 
> focus f;
> set f with_position (10, 3, -2) with_direction (0, 0, 4) with_distance 30;
> 
> the image will be upside down, and has to be rotated 180 degrees with
> 
> ... with_angle 180;
> 
> When the camera is moved around the image will flip to 45 degrees, and
> sometimes be correct. 

Well, it may be a bug, but I don't think so.  The orientation of the 
camera, i.e., the "up" direction, is found by using the transformation 
that would place the line `position' -- `direction' such that it comes to 
lie on a main axis  (usually the z-axis), with the distance of `position' 
to the x-y plane equal to `distance'.  To the best of my knowledge, 
it's not obvious what `up' direction would "feel right" to a person, when 
the the line `position' -- `direction' isn't parallel to the "ground 
plane", usually the x-z plane.  In most perspective constructions that one 
sees, this is the case.

If you want a particular "up" direction, one way of doing this is to draw 
points for the `position' and `direction' of the focus you want, a 
line through them, a perpendicular, and a perpendicular planar figure, 
say, a circle or a rectangle, coplanar with the perpendicular line.  Then, 
project this image using a different focus, or transform it so that the 
planar figure lies in a major plane and use parallel projection.  Then, 
you can adjust the `up' direction using `with_angle'.  You can even use 
labels for the angles, to see what looks best.

There are a number of features I'd like to implement for foci, such as the 
affine transformations, but I simply haven't had time.  Currently, one has 
to use assignment to change them.  I hope someday I'll be able to work 
more on the package.

> Sometimes the projection even gets inverted so
> that closer objects appear further away.

I don't quite understand this.  This would happen if the focus was 
transformed such that it lay in front of the objects.  In principle, I 
suppose it could happen, but I've never run into this effect.  Trying to 
project a point that lies in the containing `position' and perpendicular 
to the line `position -- direction' would cause an error because of 
division by 0.  I believe points satisfying this condition are culled, but 
I'm not sure what would happen if a non-point object intersected this 
plane.

Laurence