Comments on: World, View and Projection Matrix Unveiled

By: sdg

sdg — Wed, 07 Jul 2010 08:31:52 +0000

Thank you. Really helpful.

By: Mitch

Mitch — Sat, 05 Jun 2010 22:19:11 +0000

I just happened upon your page while searching google for this this very subject, and I thank you for providing insight. I do, however partially agree with the post made by n0p: were the 1s of the identity matrix occupying the “rotation” subcategory of the homogeneous, 4×4 matrix to be changed to any other number, the corresponding component of the vertex’s position would scale in a directly proportional fashion. Yet, if only one of the elements of the “scale” subcategory [M(0,3) for example] is changed from zero, it could scale all the vertex’s components similarly and in an inversely proportional style. This is provided that the vertex is made into a 1×4 matrix with elements [x y z w] and the resulting 1×4 matrix is translated into a 3d point, such that P(x/w, y/x, z/w).

By: n0p

n0p — Wed, 07 Apr 2010 16:08:19 +0000

Please update your page.

An homogeneous matrix does have a scale part in the fourth column.
The scale part is mixed within the 3×3 rotation part.

By: RobertoK

RobertoK — Sun, 04 Apr 2010 20:06:31 +0000

I’ll see to update that part, ASAP! Thanks!

By: Vite Falcon

Vite Falcon — Thu, 11 Mar 2010 22:00:52 +0000

That didn’t turn out right…
the matrix format is:
R*Sx R R T R R*Sx R T R R R*Sz T 0 0 0 1

By: Vite Falcon

Vite Falcon — Thu, 11 Mar 2010 21:57:30 +0000

You got a good tutorial but I believe the ordering of the matrix elements are wrong. Ogre3D (even OpenGL and standard mathematics) matrices uses the format:

R*SxRRT

RR*SyRT

RRR*SzT

0001

And the standard order of multiplying is:
matrix3 x matrix2 x matrix1 x vector, where vector is treated to be a 3×1 matrix.

By: Dorset Software

Dorset Software — Wed, 10 Mar 2010 17:08:42 +0000

Thank you. This helped!
Particularly the 4×4 homogeneous matrix diagram.
I have seen this before in other places, but I couldn’t find it when I went looking for it.
I knew enough of this stuff already to be able to get by fine on most things – (including modifying shaders even!), but nice to have it all laid out so clearly and comprehensively.

By: Tharindu Dasun

Tharindu Dasun — Mon, 25 Jan 2010 14:55:04 +0000

Omg You Open My Eyes To 3D World.. !