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programering

I don't understand!

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I don't understand the articles about texture mapping. And why one uses homogeneous coordinates. In a matrix vertex: [ Px ] [ Py ] [ Pz ] [ 1 ] <-- is this a homogeneous coordinate x = x * matrix[row 0][col 0] + y * matrix[row 0][col 1] + z * matrix[row 0][col 3] + matrix[row 0][col 4]; <-- this add on? A * x + B * y + C * z + D = 0 is D the homogeneous coordinate? I don't quite understand the equation can someone explain how it works? I might need an illustration maybe.

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Quote:
Original post by programering
A * x + B * y + C * z + D = 0


This is the equation of a plane. A, B, C and D are the parameters of the plane. Any point P = (x, y, z) that makes this equation true is in the plane. If D == 0, then the point (0, 0, 0) will also be in your plane, your plane is goin through the origin.


Homogeneous coordinates:
If you have a point P1 = (x, y, z, w) in homogeneous coordinate space, then you can transform it into a 'normal' 3D coordinate space point P2 = (x/w, y/w, z/w).

You can see that many points in homogeneous space represent the same point in 3D space. If w is zero, you actually specify a direction.

Homogeneous coordinates are useful when doing transformations in 3D space. With a 3x3 matrix you can calculate rotations and you may scale objects, but you cannot translate them to another position. But if you use 4D homogeneous coordinates and set w to one, this allows to specify the translation as part of your transformation matrix (4th column).

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First off, don't multiple post pointlessness.
If someone feels like answering, they will.
All the spamming does is piss people off.


We use homogeneous coordinates so that we can do matrix multiplications for translations. We like matrix muls because they neatly represent rotations and scalings as well.
So we simply work with a system that lets us do everything by matrix muls.
Look up the difference between affine and linear transforms, and then work through rotation and translation with 3x3 and 4x4 matrices and see which ones are affine and which ones are linear.

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I have no experience about this, I need to learn.
Sorry for the spamming.
But I want to understand this logical on how it works.
And I can't really find anything that helped me understand this with google.com
And you've rote me down for wanting help, witch makes me a bit sad.
next you'll maybe rate me to zero, close my/this thread and ban me.
you experience me as irritating, but what shall I do when I what to understand this so badly.
How the equation A * x + B * y + C * z + D can be equal to zero.

[Edited by - programering on August 25, 2004 8:02:43 AM]

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