In a vain attempt to forstall flames, I'm posting here rather than in the
'books' newsgroup because I'm not looking for a book about Povray, per se,
I'm looking for books about 3D Computer Graphics and the mathematics behind
them, and it seems to me that the advanced users are the ones most likely
to do their own advanced math.

My fundamental problem is that I'm spending an inordinate amount of time
looking at the trigonometry review in my Calculus book (I don't have a trig
book - I took it in high school, and they took the books back at the end of
the semester. Of course, in college, the books were a horrible expense, but
worth it -now-! ;)), and of course my linear algebra book. Basically, I
enjoy modelling with mathematics and programming techniques, not to mention
fooling around with OpenGL programming, but I'm not sufficiently good at
mathematics to derive everything I need to know from the relevant
information at hand (two chapters of linear algebra are relevant, the trig
section of calculus, the math explanations in the back of the OpenGL
Programming Guide...). I could just beg for help here, but I want to really
learn this stuff so that I can solve -many- problems, not just get through
my current scene or object!

So far, I've identified '3D Computer Graphics' by Alan Watt and 'Mathematics
for 3D Game Programming and Computer Graphics' by Eric Lengyel as likely
candidates. This is, however, a fair chunk of coin... I've seen several
references to the first in the newsgroups and I think in the PovRay
documentation, so I'm fairly certain it's a good choice, and the amazon
reviews point me towards the second.
Still and all, I'm reluctant to spend a fortune on books for this, so if the
first $100 doesn't get what I'm looking for, I'm going to be pretty
unhappy. What do people here think? Are these what I should be looking at?
Am I missing some 'definitive text' in the field? Am I going to be in deep
trouble by lacking the more basic math texts, or will the appendices in my
calculus text suffice?

There's also the possibility that I'm simply insane and should give in and
use modelling software, but honestly, I don't find that very interesting
and the beauty of turning a textual scene description into a stunning image
is what got me into povray in the first place. ;)

Advise, discuss, set heat to low before flaming... ;)

--Chris

Post a reply to this message

I've bought "3D Computer Graphics" by Alan Watt
a couple of months ago. I've got to admit it has a lot
of nifty information, but it does focus more on
triangle-based rendering, rather than raytracing.
As for algebra, it covers the fundamental stuff very
nicely, and even some advanced stuff is explained.

Still, it's only an overview over what exists and
is possible today, if you want to create new stuff,
you still got to do your own work.

I'm not really sure what you're after though, but
IMHO: I'm using an algebra book which is filled
with formulae, and look up almost anything I don't
know, or search the web. Sure, it only gets you
through one problem at a time, but you learn more
and more as you go along.

-- 
Tim Nikias v2.0
Homepage: http://www.digitaltwilight.de/no_lights
Email: Tim### [at] gmxde

> In a vain attempt to forstall flames, I'm posting here rather than in the
> 'books' newsgroup because I'm not looking for a book about Povray, per se,
> I'm looking for books about 3D Computer Graphics and the mathematics
behind
> them, and it seems to me that the advanced users are the ones most likely
> to do their own advanced math.
>
> My fundamental problem is that I'm spending an inordinate amount of time
> looking at the trigonometry review in my Calculus book (I don't have a
trig
> book - I took it in high school, and they took the books back at the end
of
> the semester. Of course, in college, the books were a horrible expense,
but
> worth it -now-! ;)), and of course my linear algebra book. Basically, I
> enjoy modelling with mathematics and programming techniques, not to
mention
> fooling around with OpenGL programming, but I'm not sufficiently good at
> mathematics to derive everything I need to know from the relevant
> information at hand (two chapters of linear algebra are relevant, the trig
> section of calculus, the math explanations in the back of the OpenGL
> Programming Guide...). I could just beg for help here, but I want to
really
> learn this stuff so that I can solve -many- problems, not just get through
> my current scene or object!
>
> So far, I've identified '3D Computer Graphics' by Alan Watt and
'Mathematics
> for 3D Game Programming and Computer Graphics' by Eric Lengyel as likely
> candidates. This is, however, a fair chunk of coin... I've seen several
> references to the first in the newsgroups and I think in the PovRay
> documentation, so I'm fairly certain it's a good choice, and the amazon
> reviews point me towards the second.
> Still and all, I'm reluctant to spend a fortune on books for this, so if
the
> first $100 doesn't get what I'm looking for, I'm going to be pretty
> unhappy. What do people here think? Are these what I should be looking at?
> Am I missing some 'definitive text' in the field? Am I going to be in deep
> trouble by lacking the more basic math texts, or will the appendices in my
> calculus text suffice?
>
> There's also the possibility that I'm simply insane and should give in and
> use modelling software, but honestly, I don't find that very interesting
> and the beauty of turning a textual scene description into a stunning
image
> is what got me into povray in the first place. ;)
>
> Advise, discuss, set heat to low before flaming... ;)
>
> --Chris
>
>

Post a reply to this message

Some things I'm doing are a spaceship in CSG ... mostly because I wanted
rounded corners, so it's cylinders & slabs (box or prism, depending)... I
need a fair bit
of 3D trig to get the slabs into the right places, of course. (Well, I could
have
made the spaceship a cube, but I think that one is trademarked... ;))

I'm working on a fountain, implemented as a parabolic distribution of
sphere-elements in a big glob, apply water parameters. The parabola is
simple
enough, of course, this one has been mostly trial and error to get a jet
that
is nice and noisy but not so noisy that it becomes pure static. I'm thinking
that
the water that the jets are in might be best modeled as an isosurface. I'm
going
to try some experiments with surfaces that look like,
sin(pow(x - fountain_x[i],2) + pow(y - fountain_y[i],2)) * (1/(abs(pow(x -
fountain_x[i],2) + pow(y - fountain_y[i],2))

I think that's it... of course, I haven't tried it yet, and the formula
needs a ripple-point for each jets source and splashdown point... by the
time I'm done
the object will probably take a couple days to render. It takes about six
hours to render anti-aliased with just the jets and a cylinder of water
(though if the
'granite' fountain & plane weren't also reflective that might help...)

Sorry, got sidetracked there. Hrm.

Things I -don't- know how to do include rotating about an arbitrary line
(though it seems like I should be able to derive -a- formula, if not an
-efficient- formula, from what math I have at this point.

Maybe I should find a 2D formula for rotation about an arbitrary point and
work from that...) and...
hrm. I'm sure there are lots of things. I know the latter parts of the
isosurface tutorial page started making me dizzy. ;)

Future projects are movements for a car, some constraints that approximate
cloth... oh, I got a recursive fractal tree macro working today, so I need
to
naturalize that... mmm....

Of course, sooner or later I've got to figure out a modeller, because I'm
unlikely to find a simple isosurface formula for Marilyn Monroe's body, or
such... ;) Of course there -is- one, but the best way to find it is
probably to  model and do a curve fitting. With a bit of work, I could
probably model most of a human figure without leaving the text editor (I've
defined M-x povray-current-buffer ... ;)) but the human face is a very
particular thing. I think I could CSG or hand-mesh up a reasonable
'cartoon' head, but the real thing requires a lot of detail -just so- ...
okay, I don't -have- to touch a modeller, but if I don't my scenes will
suffer for it. If I ever complete a scene. Mostly I get distracted by
another project after making an object and never really compose a 'scene'
as such.

Hrm. Oh, and I don't -have- a good algebra book, or a good trig book... I do
have a good calculus book, at least, but I think that will only help with
animations (a vector integral should, if I can still do them and I set it up
properly, give me the correct location and direction for an object
following a mathematically defined path. Not that I've done a vector
integral since it was homework some years back, but...)

Oh, I also don't know how to do anything but the simplest polynomial curve
fitting, and I should probably learn (I know, in many cases pov can do it
for me, but... pov can rotate a point about the axis for me too, but I
don't think
the result of that operation is returned anywhere I can use it... anyway,
there
will be cases where I need to be able to do for myself what pov can do...)

I suspect this post of reading like late night babble, which it probably is,
but it might give a better idea why I think I need more math texts, or at
least what I've done with the math that I have... it probably won't
engender much more advice, but it might encourage people to be a little
more sympathetic when I post a scraggly tree or a simple fountain to
images... ;)

And tempting as isosurfaces are to experiment with, I think I'm for bed.
'night povers!

--Chris

Post a reply to this message

Hi,

I think much of the functions you need are already implemented in POV's 
scene-description-language or in macros shipped with POV-Ray.

E.g:
 > Things I -don't- know how to do include rotating about an arbitrary
 > line (though it seems like I should be able to derive -a- formula, if
 > not an-efficient- formula, from what math I have at this point.

check out:
Axis_Rotate_Trans(Axis, Angle) or
Rotate_Around_Trans(Rotation, Point)

in the transforms.inc include file.

If you're looking for explainations about how vecotrs, matrices, etc. 
work and can be used for 3D computer graphics just do some searches on 
google - there is plenty of information out there...

 > I'm thinking that the water that the jets are in might be best modeled
 > as an isosurface.

Blobs or sphere sweeps would be an option too. Don't re-invent the 
wheel, check out

http://www.geocities.com/SiliconValley/Lakes/1434/spray.html

for example.

 > some constraints that approximate cloth...

Megapov - http://megapov.inetart.net/features.html
has the cloth simulation patch included.

 > Of course, sooner or later I've got to figure out a modeller, because
 > I'm unlikely to find a simple isosurface formula for Marilyn Monroe's
 > body

If you'd find it, it would render very slow and it would be hard to pose 
or animate it ;-)
If you're looking for a modeller for POV which let's you model faces, 
human bodies, animals, aliens, etc. check out one of those free tools:

sPatch - http://www.geocities.com/getspatch/
(Windows only)

hamapatch - http://www.geocities.com/hamapatch/program/index.html
(Windows only)

or

<advertisement :-)>

JPatch - http://jpatch.sourceforge.net
(Windows, Linux, Mac)

JPatch is my own project and work in progress. Right now it's a open 
source replacement for sPatch written in Java, but I'm working on more 
sophisticated features like morphing or bones for animation...

</advertisement :-)>

-sascha

Post a reply to this message

Well, the book by Alan Watt is more or less
concerned with the functions of raytracing,
radiosity etc, how the internal structure is
handled. More or less the parsing and rendering
process (on POV terms) rather than modelling.

For modelling, I've never found any book of
real use, they mostly rely on a certain program
and a certain version number. Same goes
for tutorials. Some techniques can be applied
universally (like connecting two splines via
triangles for a surface or such), but others are
just to specific.

For the math, as already mentioned, I've bought
an extensive math-book which has the formulae
for almost anything (Fourier Transformations,
Vector Arithmetics, Graphs, Functions etc), though
its only of use to move slowy and enhance things
step by step that you already know. The WWW
is the source I most often use, and the Newsgroups
are the best place to begin with. You've got a
whole bunch of nerds right there, all waiting for
some "newbie" (in a certain area) to ask a question,
and then they'll explode with knowledge you've
never dreamed of... I like it very much in these
groups! :-)


-- 
Tim Nikias v2.0
Homepage: http://www.digitaltwilight.de/no_lights
Email: Tim### [at] gmxde

> Some things I'm doing are a spaceship in CSG ... mostly because I wanted
> rounded corners, so it's cylinders & slabs (box or prism, depending)... I
> need a fair bit
> of 3D trig to get the slabs into the right places, of course. (Well, I
could
> have
> made the spaceship a cube, but I think that one is trademarked... ;))
>
> I'm working on a fountain, implemented as a parabolic distribution of
> sphere-elements in a big glob, apply water parameters. The parabola is
> simple
> enough, of course, this one has been mostly trial and error to get a jet
> that
> is nice and noisy but not so noisy that it becomes pure static. I'm
thinking
> that
> the water that the jets are in might be best modeled as an isosurface. I'm
> going
> to try some experiments with surfaces that look like,
> sin(pow(x - fountain_x[i],2) + pow(y - fountain_y[i],2)) * (1/(abs(pow(x -
> fountain_x[i],2) + pow(y - fountain_y[i],2))
>
> I think that's it... of course, I haven't tried it yet, and the formula
> needs a ripple-point for each jets source and splashdown point... by the
> time I'm done
> the object will probably take a couple days to render. It takes about six
> hours to render anti-aliased with just the jets and a cylinder of water
> (though if the
> 'granite' fountain & plane weren't also reflective that might help...)
>
> Sorry, got sidetracked there. Hrm.
>
> Things I -don't- know how to do include rotating about an arbitrary line
> (though it seems like I should be able to derive -a- formula, if not an
> -efficient- formula, from what math I have at this point.
>
> Maybe I should find a 2D formula for rotation about an arbitrary point and
> work from that...) and...
> hrm. I'm sure there are lots of things. I know the latter parts of the
> isosurface tutorial page started making me dizzy. ;)
>
> Future projects are movements for a car, some constraints that approximate
> cloth... oh, I got a recursive fractal tree macro working today, so I need
> to
> naturalize that... mmm....
>
> Of course, sooner or later I've got to figure out a modeller, because I'm
> unlikely to find a simple isosurface formula for Marilyn Monroe's body, or
> such... ;) Of course there -is- one, but the best way to find it is
> probably to  model and do a curve fitting. With a bit of work, I could
> probably model most of a human figure without leaving the text editor
(I've
> defined M-x povray-current-buffer ... ;)) but the human face is a very
> particular thing. I think I could CSG or hand-mesh up a reasonable
> 'cartoon' head, but the real thing requires a lot of detail -just so- ...
> okay, I don't -have- to touch a modeller, but if I don't my scenes will
> suffer for it. If I ever complete a scene. Mostly I get distracted by
> another project after making an object and never really compose a 'scene'
> as such.
>
> Hrm. Oh, and I don't -have- a good algebra book, or a good trig book... I
do
> have a good calculus book, at least, but I think that will only help with
> animations (a vector integral should, if I can still do them and I set it
up
> properly, give me the correct location and direction for an object
> following a mathematically defined path. Not that I've done a vector
> integral since it was homework some years back, but...)
>
> Oh, I also don't know how to do anything but the simplest polynomial curve
> fitting, and I should probably learn (I know, in many cases pov can do it
> for me, but... pov can rotate a point about the axis for me too, but I
> don't think
> the result of that operation is returned anywhere I can use it... anyway,
> there
> will be cases where I need to be able to do for myself what pov can do...)
>
> I suspect this post of reading like late night babble, which it probably
is,
> but it might give a better idea why I think I need more math texts, or at
> least what I've done with the math that I have... it probably won't
> engender much more advice, but it might encourage people to be a little
> more sympathetic when I post a scraggly tree or a simple fountain to
> images... ;)
>
> And tempting as isosurfaces are to experiment with, I think I'm for bed.
> 'night povers!
>
> --Chris
>
>

Post a reply to this message

sascha wrote:
>Hi,
>
>I think much of the functions you need are already implemented in POV's
>scene-description-language or in macros shipped with POV-Ray.
>
>E.g:
> > Things I -don't- know how to do include rotating about an arbitrary
> > line (though it seems like I should be able to derive -a- formula, if
> > not an-efficient- formula, from what math I have at this point.
>
>check out:
>Axis_Rotate_Trans(Axis, Angle) or
>Rotate_Around_Trans(Rotation, Point)
>
I'll have to look at these and through the function library then...


>Blobs or sphere sweeps would be an option too. Don't re-invent the
>wheel, check out
<clip>
Yes, I've heard of these, but there are merits to making your own
implementation. There's a reason that undergraduates are asked to re-write
quicksort even though there are implementations available on every
platform...
if my experiments now are repeating some work that's been done, that's fine.
Sooner or later I'm going to get to the point where I'm doing things that
haven't been done - I hope - but if I skip the 'hard parts' and rely on
other
people's include files for my effects, the only skills I'm going to be
building are layout skills.

(which isn't to say that I won't use Axis_Rotate_Trans, or even spray.inc,
just
that I feel a need to do it by hand at least once; there are definite merits
to
letting the computer grind through tedious repeat calculations for something
you can already do, of course.)

In a production environment, of course, these arguments break down, since an
employer's interest is primarily in producing, and improvement of the
employee
is only a secondary (or tertiary or ...) consideration, but I'm not -in- a
production environment, and it's definitely in my first best interest to
improve myself. Erm. That sounds a little... preachy or something... but
maybe
it gets some of the idea across. (also to consider, for me, is that if I
end up with 3D programming employment one day, I won't be able to just stick
'sprays.inc' into a system that isn't povray...)


>If you'd find it, it would render very slow and it would be hard to pose
>or animate it ;-)
>If you're looking for a modeller for POV which let's you model faces,
>human bodies, animals, aliens, etc. check out one of those free tools:
>
I've got blender installed, but I've accomplished nothing useful with it;
I don't use windows, but I will check out
>JPatch - http://jpatch.sourceforge.net
>(Windows, Linux, Mac)
even if it is a shameless advertisement. ;) Java implementations of free
software rock. ;) (*cough* *quickly hides 'advocate' hat under the chair*)


--Chris

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