Fun with Matrices

[Daniel Brassard]

Probiner on an other thread peek my curiosity and I made a bunch of transform matrices for fun.

His thread: http://www.si-community.com/community/v ... =15&t=4800

Here is the result.

[Daniel Brassard]

The classical SRT and Cross_product Matrix compounds.

Enjoy!

[Bullit]

What will be the best way to use this with several objects? is it possible?

[Daniel Brassard]

It depend on what you are trying to do with the objects, their relationship to each other and the parenting.

Say you have an object sitting on a table, if you increase the size of both objects without taking into account their relationship, then the second object will penetrate the first object.

During transformation, you will need to consider the hierarchy of the objects within your scene. But it is faisible or we would not be able to move complex objects natively.

[Bullit]

Sorry to no be clear, the propose is for motion graphic type of animation.

[probiner]

Hi Daniel
I see you sized your "test bed" up and put some bells and whistles on it Thanks for sharing!

What's the Cross Product Matrix used for?

Cheers

[Daniel Brassard]

There is multiple use of the cross product. The Cross Product (also called the vector product) involves taking two vectors and getting as a result another vector which is perpendicular to both vectors. With the cross product:

[*]you can calculate the normal of those two vector, very useful for shading calculation.
[*]helps define rotation about an arbitrary axis
[*]calculate angular velocity and rotation matrix time derivatives
[*]Help determine clockwise vs counterclockwise order (positive is CCW for right handed system)

ICE provide the cross product of vectors natively but not too many have seen the equivalent matrix representation. I just provided it as an extra and made it affine (accepting 4D vectors instead of 3D vectors) for alternate functionality. From there, it is easy to modify that matrix for 3D vectors use (just remove the last row and column of the matrix)

If you open the Classical_SRT matrix, you will have access to five small matrices for your own exploration (Scale, rotate, translate, shear and reflection matrices). Combine with the invert and transpose nodes, you will have all the tools you need for your own exploration of matrices.

Cheers!