Johannes Dahlstrom <sad### [at] tkukoulufi> wrote:
> Oh well, so I misinterpreted the drawings. Anyway, IMHO that particular 
> kind of transformation does imply a perspective; it provides an important 
> visual cue, as is seen in various illusions, such as here:

  I don't follow you. Which transformation are you talking about? Why
do you keep talking about perspective when there's no perspective involved
anywhere in the drawings?

  The problem is simple: Take a four-sided polygon which is not
rectangular (but eg. trapezoidal as in the illustration), apply
UV-coordinates to the vertices of this polygon so that they map a
rectangle on the texture, and feed this to the OpenGL API.
  What OpenGL does is to divide the polygon into two triangles. Then the
3D hardware draws these two triangles independently, causing the deformation
of the texture depicted in the illustration.

  There's no perspective anywhere. There are no transformations anywhere.

> And, although it is of course possible to map a texture like that, I'm not 
> sure how common or useful it is. 

  You seem to misunderstand the problem completely.
  Of course it's very common to build a surface using quadrilaterals
(ie. polygons of four sides). For example if you build a torus with
quadrilaterals, you'll get the depicted problem with the texturing
(at the top and bottom of the torus).

> Well, a triangle texture mapper without perspective correction interpolates 
> linearly both in screen space and in texture space, and produces the 
> artifact.

  What is "the artifact"?
  Yes, it produces *an* artifact, which is completely different from what
is depicted in my illustration.
  In fact, even if that polygon was _rectangular_ and drawn in perspective
and even if it was made _without_ perspective correction, there would be
no visible artifact due to the texture in question. There would be a visible
artifact if the texture had horizontal lines (in which case they would be
mapped at equal distances throughout the polygon instead of decreasing
distance due to perspective).

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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Warp wrote:
>   What in the image makes you (and 90% of other people as well) think
> that that image has something to do with perspective? I can't understand
> it.

I'am guilty, too.

>   There's no perspective nowhere in the drawings. It's purely 2D.

Now I get it!
Never thought of this problem before...

Sebastian H.

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Warp wrote:

>   I don't follow you. Which transformation are you talking about? Why
> do you keep talking about perspective when there's no perspective involved
> anywhere in the drawings?

Sorry, bad choice of word from my part, "mapping" would have been more 
adequate. What I meant was that there are two ways to interpret your 
drawing: Either

A) there is a tilted rectangular quad, or

B) there is a non-tilted trapezoidal quad. 

It is simply impossible to know which is the correct way to interpret it 
from the drawing only, without some depth information. The converging 
lines, however, give a visual cue which would suggest the case A. Human 
brains simply are wired that way, and this phenomenom is utilized in the 
illusion I posted a link to in my previous message.


>   The problem is simple: Take a four-sided polygon which is not
> rectangular (but eg. trapezoidal as in the illustration), apply
> UV-coordinates to the vertices of this polygon so that they map a
> rectangle on the texture, and feed this to the OpenGL API.
>   What OpenGL does is to divide the polygon into two triangles. Then the
> 3D hardware draws these two triangles independently, causing the
> deformation of the texture depicted in the illustration.
> 
>   There's no perspective anywhere. There are no transformations anywhere.

But my point was that it is impossible to see it from the drawing. I did 
some experiments with OpenGL, and the results are here:

http://koti.mbnet.fi/~sharlin/with_pc.png 
http://koti.mbnet.fi/~sharlin/without_pc.png

Without perspective correction (the second image) and without resorting to 
the texts, can you tell case A from case B? I don't think so. The texture 
mapper doesn't make a difference between them, because it isn't conserned 
about depth information if it doesn't do perspective correction.


>   Of course it's very common to build a surface using quadrilaterals
> (ie. polygons of four sides). For example if you build a torus with
> quadrilaterals, you'll get the depicted problem with the texturing
> (at the top and bottom of the torus).

OK, I see that with such round shapes it can be a problem. My bad.


>   What is "the artifact"?
>   Yes, it produces *an* artifact, which is completely different from what
> is depicted in my illustration.

Erm, no. As you can see from the aforementioned images, without perspective 
correction the two cases have the exactly same artifact, caused by exactly 
same thing: linear interpolation in texture space. Perspective correction 
does what it's meant to do: renders the perspective correctly. If it 
wouldn't, most 3D games would look very very ugly.

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Johannes Dahlstrom <sad### [at] tkukoulufi> wrote:
> What I meant was that there are two ways to interpret your 
> drawing: Either

> A) there is a tilted rectangular quad, or

> B) there is a non-tilted trapezoidal quad. 

  I see.

  Do you have any idea how that drawing should be done so that it doesn't
cause confusion?

> Erm, no. As you can see from the aforementioned images, without perspective 
> correction the two cases have the exactly same artifact, caused by exactly 
> same thing: linear interpolation in texture space. Perspective correction 
> does what it's meant to do: renders the perspective correctly. If it 
> wouldn't, most 3D games would look very very ugly.

  But the artifact which I'm talking about has nothing to do with perspective
correction, and using perspective correction does not affect the artifact
in question: It will still be there regardless of PC.

  There actually exists an algorithm to handle this problem, but I have never
heard that any 3D hardware supports this algorithm. The principle of the
algorithm is to perform a more complicated texture mapping.

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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Warp wrote:
> 
> Johannes Dahlstrom <sad### [at] tkukoulufi> wrote:
> > What I meant was that there are two ways to interpret your
> > drawing: Either
> 
> > A) there is a tilted rectangular quad, or
> 
> > B) there is a non-tilted trapezoidal quad.
> 
>   I see.
> 
>   Do you have any idea how that drawing should be done so that it doesn't
> cause confusion?

I can think of at least three -

1. Title it as a trapezoid.
2. Make the top length a bit shorter.
3. Draw a thick lined rectangle around the illustration.

-- 
Ken Tyler

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Shouldn't the distance between the coordinates of the texture be in
proportion to the coordinates in the polygon?

"Warp" <war### [at] tagpovrayorg> wrote in message
news:3e0f4330@news.povray.org...
> Johannes Dahlstrom <sad### [at] tkukoulufi> wrote:
> > What I meant was that there are two ways to interpret your
> > drawing: Either
>
> > A) there is a tilted rectangular quad, or
>
> > B) there is a non-tilted trapezoidal quad.
>
>   I see.
>
>   Do you have any idea how that drawing should be done so that it doesn't
> cause confusion?
>

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Mike White <mik### [at] mindspringcom> wrote:
> Shouldn't the distance between the coordinates of the texture be in
> proportion to the coordinates in the polygon?

  Why should it?

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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"Warp" <war### [at] tagpovrayorg> wrote in message
news:3e104469@news.povray.org...
> Mike White <mik### [at] mindspringcom> wrote:
> > Shouldn't the distance between the coordinates of the texture be in
> > proportion to the coordinates in the polygon?
>
>   Why should it?
>

Isn't the idea to just lay a bitmap across a face?

What you're asking OpenGL to do is reshape the bitmap, something I doubt it
was designed for.

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Mike White <mik### [at] mindspringcom> wrote:
> What you're asking OpenGL to do is reshape the bitmap, something I doubt it
> was designed for.

  Well, if you do it with a triangle, it works flawlessly. The texture
will be stretched correctly.

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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Warp wrote:

>   Do you have any idea how that drawing should be done so that it doesn't
> cause confusion?

You could put some evenly-spaced horizontal lines to the texture - they 
would make a difference between the two cases: In the case B the mapping 
wouldn't change their mutual distances, whereas in the case A it obviously 
would (the lines "farther away" would be closer to each other).

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