could someone pass a link to a paper from the times them scientist dudes

were making first steps toward 3d as we know it ?

i would like to see and understand how they synthesized the matrix not just

copy their values to 3x3 array.

thanks

could someone pass a link to a paper from the times them scientist dudes

were making first steps toward 3d as we know it ?

i would like to see and understand how they synthesized the matrix not just

copy their values to 3x3 array.

thanks

> could someone pass a link to a paper from the times them scientist dudes

> were making first steps toward 3d as we know it ?

Well, links to their Web sites are unfortunately dead. But - perhaps you

might think it over - there are some University libraries in this best of

worlds.

Jerzy Karczmarczuk

you probably mean how the 4x4 transformation

matrix we use in OpenGL and such was derived ?

well, there's this one book anyone must have read:

http://www.amazon.com/exec/obidos/tg/detail/-/0201848406/002-9460732-...

?vi=glance

they dont go into history ( much ) but youll get a good

feel on how things were derived.

J

--

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please tear the sticker off my eddress before use

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> > could someone pass a link to a paper from the times them scientist dudes

> > were making first steps toward 3d as we know it ?

> Oh, you mean people like Descartes, or a bit later Monge?

> Well, links to their Web sites are unfortunately dead. But - perhaps you

> might think it over - there are some University libraries in this best of

> worlds.

> Jerzy Karczmarczuk

I applaud your intent; but you seek an anachronism! Any such papersQuote:>could someone pass a link to a paper from the times them scientist dudes

>were making first steps toward 3d as we know it ?

>i would like to see and understand how they synthesized the matrix not just

>copy their values to 3x3 array.

predate the web, so are unlikely to be online. For modern computer

graphics probably the most important early paper is

Roberts, L.G., Homogeneous Matrix Representation and Manipulation of

N-dimensional Constructs. MIT Lincoln Laboratory, MS 1405, May 1965.

The idea of using a matrix had to wait for the matrix to be invented,

which did not happen until 1858.

<http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Matrices_and_dete...>

Yet the eventual entries of the matrices had been known for quite some

time, merely expressed in other forms.

Using mathematics you already understand, like cartesian coordinates,

trigonometry, and so on, you can probably recreate the matrix forms

for yourself. Start in 2D, which is much simpler.

> >could someone pass a link to a paper from the times them scientist dudes

> >were making first steps toward 3d as we know it ?

> >i would like to see and understand how they synthesized the matrix not

just

> >copy their values to 3x3 array.

> I applaud your intent; but you seek an anachronism! Any such papers

> predate the web, so are unlikely to be online. For modern computer

> graphics probably the most important early paper is

> Roberts, L.G., Homogeneous Matrix Representation and Manipulation of

> N-dimensional Constructs. MIT Lincoln Laboratory, MS 1405, May 1965.

> The idea of using a matrix had to wait for the matrix to be invented,

> which did not happen until 1858.

ts.html>

but what about projection matrix, that didn't? have any appliance in the 19Quote:> Yet the eventual entries of the matrices had been known for quite some

> time, merely expressed in other forms.

> Using mathematics you already understand, like cartesian coordinates,

> trigonometry, and so on, you can probably recreate the matrix forms

> for yourself. Start in 2D, which is much simpler.

century -did it?

> but what about projection matrix, that didn't? have any appliance in the 19

> century -did it?

18th century, beginning of 19th. Mind you, the descriptive geometry was and

still is, differently but is, used by architects.

I would - if you really want to learn some basic ideas - postpone matrices just

a little bit. *BEFORE* learning the rotation matrices try to understand well the

Rodrigues formula.

Try to grasp the geometric meaning of some objects, take into account that they

remain as they are, independently of the coordinate system used for their

analytic description, while matrices representing vectors and transforms

obviously change. Concrete mathematics is a wonderful tool, I would die without,

but I strongly believe that intuition should come first.

Jerzy Karczmarczuk

> >could someone pass a link to a paper from the times them scientist dudes

> >were making first steps toward 3d as we know it ?

> >i would like to see and understand how they synthesized the matrix not just

> >copy their values to 3x3 array.

> I applaud your intent; but you seek an anachronism! Any such papers

> predate the web, so are unlikely to be online.

Some key words for a Google search:

Filippo Brunelleschi discovered the geometrical laws of perspective

projections (1401 demonstrated on the market place in Firenze/Florence).

1855 or 1858: Cayley invented the matrices.

Best regards --Gernot Hoffmann

Again we must distinguish between forms. First artists began to paintQuote:>but what about projection matrix, that didn't? have any appliance in the 19

>century -did it?

perspective. Then mathematicians developed the theory of "projective

geometry". Later, homogeneous coordinates gave that theory an elegant

representation. And eventually matrices gave homogeneous transforms a

happy home. Only recently did computer graphics enter the picture. ;-)

<http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Art.html>

Consider Leonardo da Vinci's portrait of Mona Lisa (La Gioconda).

<http://www.ibiblio.org/wm/paint/auth/vinci/joconde/joconde.jpg>

<http://www.louvre.fr/anglais/visite/peint/grands/31n111.htm>

Behind the lady herself is some lovely scenery, small in the distance.

So even though the artist knew nothing of projection matrices, still

he could render perspective around the year 1504.

Computer graphics is so obsessed with coordinates it is easy to forget

that Euclid and most geometers worked without them, using figures,

axioms, and proofs. Also there is a subtle distinction between talking

about perspective in Euclidean geometry and formalizing self-contained

projective geometry.

<http://www.geometryalgorithms.com/history.htm>

"Just d' FAQs"

Thanks for the links and I like the this quote from that great math historyQuote:> Again we must distinguish between forms. First artists began to paint

> perspective. Then mathematicians developed the theory of "projective

> geometry".

site:

" Descriptive geometry originated with Drer in this work although it was

only put on a sound mathematical basis in later work of Monge. One of the

methods of overcoming the problems of projection, and describing the

movement of bodies in space, is descriptive geometry. Drer's remarkable

achievement was through applying mathematics to art, he developed such

fundamentally new and important ideas within mathematics itself."

> Thanks for the links and I like the this quote from that great math history

> site:

> " Descriptive geometry originated with Drer in this work although it was

> only put on a sound mathematical basis in later work of Monge. One of the

> methods of overcoming the problems of projection, and describing the

> movement of bodies in space, is descriptive geometry. Drer's remarkable

> achievement was through applying mathematics to art, he developed such

> fundamentally new and important ideas within mathematics itself."

Drer had never applied mathematics (in our understanding, or as Descartes

would have done it).

He had described four apparatus' for the construction of perspective

images from a real scenery. Not even his own inventions - import from

Italy (which was an achievement as well).

Nothing new about the geometry - applications of Brunelleschi's great

discovery: he placed the IMAGE PLANE between the eye point and the scene.

This step was misssing in Euclids knowledge, though he knew already the

principle of the center of projection.

Sorry, I cant follow further discussions - travelling for several weeks

to Web-free regions.

Best regards --Gernot Hoffmann

"Gernot Hoffmann"

Oh, my! How sad. I wonder what else this might be suspect on this site?Quote:> Before and after asking several experts I thought this might be wrong.

Thanks for saying pointing this out.

1. clipping matrix = projection matrix X modelview matrix ?

Hi!

Why do I have to multipli the modelview matrix and the projection matrix

to get the clipping matrix?

Aren't the clipping planes described in the projection matrix?

Thanks in advance!

/Michael Andersson

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