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# RE: Transforms, Transformations, Matrices confusion

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After re-reading and re-reading I have put myself into a state of confusion over the meanings of Transforms, Trasnformations and Matrices and how they all work together. Just wondering if someone could let me know if I have the definition of them correct. Matrices are used to create and store Transformations, matrices are also the plural of a matrix. The three main Transformations are the World, View and Projection transformations. These control the object position, camera position and the lens details. The methods for actual Transformations made to the afore mentioned Transformations are Translation, scaling and rotation Transformations. A Transformation means when an object is altered say scaled. Transformations is the plural of transform(s). As you can probably see I am bit confused by this, I understand the concept behind the World,View and Projection transformations but what I don''t get is why these are called transformations and also the scaling, rotation etc.. are also called transformations. If anyone can put me straight or let me know if what I have just written is basically it I would appreciate it. Thanks, Paul Kirkbride.

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Matrices are used to create and store Transformations, matrices are also the plural of a matrix.

Correct. Matrices can also be thought of as a set of vectors describing various things such as coordinate systems.

Matrices are used to create and store Transformations, matrices are also the plural of a matrix.

Matrices can be used to store transformations. Yep, one=matrix, many=matrices.

The three main Transformations are the World, View and Projection transformations. These control the object position, camera position and the lens details.

Yep. Those are the three main Transformations for a 3D viewing system - there are plenty of other transformations in the world.

IMO a better way to think of a transformation matrix is "it transforms from one coordinate system/space to another".

The World matrix transforms from object (aka model or local) space to world space.

The View matrix transforms from world space into view (aka camera) space.

The Projection matrix transforms from view space into clip space (in D3D terms, projection transforms in other 3D APIs sometimes transform into different spaces.)

The methods for actual Transformations made to the afore mentioned Transformations are Translation, scaling and rotation Transformations. A Transformation means when an object is altered say scaled. Transformations is the plural of transform(s).

Scaling, Translation, Rotation (amongst other things) are all types of transformation. A transformation matrix can be composed from a combination of a number of these individual transformations.

The process of combining multiple transformations into a single transformation matrix is known as "concatenation"

To transform an object is to apply a matrix containing those transformations. You could even have an identity transformation matrix which would do nothing to the object.

A book I''d definately suggest you get hold of is "Mathematics for Computer Graphics Applications" by Michael E. Mortenson. It introduces the maths concepts behind this stuff in a very non-intimidating way (i.e. with only a GCSE in maths you should still be able to understand most of what it''s talking about).

--
Simon O''Connor
Creative Asylum Ltd
www.creative-asylum.com

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I need to do a final project in 2 years for school. The theme has to do with math and computer science..

I''m going to explain matrices and vectors (and some other things). I write it in dutch but I could translate it to english...

I think a good site to read is:

http://www.andypike.com/tutorials/directx8/005.asp

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Hey,

Thanks a lot for the help guys!!

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