What mean the transformation matrix, rotation submatrix parameters? 2

[ZsZs]

Hi!

I have a C++ program.
I know to moving my components by this transformation matrix, but I like rotating too.

The Solidworks help wrote at the MathTransform Object:

"The SolidWorks transformation matrix is stored as a homogeneous matrix of 16 elements, ordered as shown. The first 9 (a to i) are elements of a 3x3 rotational sub-matrix, the next 3 (j,k,l) define a translation vector, the next 1 (m) is a scaling factor. The last 3 elements (n,o,p) are unused in this context.

The 3X3 rotational sub-matrix represents 3 axis sets: row 1 for x-axis components of rotation, row 2 for y-axis components of rotation, and row 3 for z-axis components of rotations."

Which (value) filling the rotation sub-matrix?
What mean the 3 axis parameter? What contain it?
It is coordinate? or any distance of origin? or...?

Thanks!

ZsZs.

 

[handleman]

See

http://en.wikipedia.org/wiki/Translation_matrix

 

[TheTick]

To understand the transformation matrix, you must first understand what a unit vector is. A unit vector has a scalar value of 1, thus the sum of the squares of the vector components equals one(i.e. x² + y² + z² = 1). Unit vectors are used to express direction.

The "translation vector" is a unit vector to express the direction of translation. The "scaling factor" is the scalar distance. Scaling factor multiplied by translation vector yield x, y, and z components of total translation.

For rotational submatrix, each row represents the unit vector (= direction) of the transformed x, y, and z axes. If a transformation involves pure translation and no rotation, the rotation vectors are as follows: x=(1, 0, 0); y=(0, 1, 0), z=(0, 0, 1).

Honesty may be the best policy, but insanity is a better defense.

http://www.EsoxRepublic.com

-SolidWorks API VB programming help

 

[ZsZs]

Thanks!
I beleive help me more a example:
If I have a component, and I moving the x=1, y=1, z=1 positions, then I set the transformation matrix 9-11. element = 1.
This is the translation vector. (I don't use the scaling factor.)
I put (move) the component this position (and it is working: the component move the position.)

But, if I want move the component x=1, y=1, z=1 positions AND I like my component rotate by 90 degree to right (center = y-axis)?
What I do?
How I use the rotation sub-matrix?
What is a center of rotation? the assembly file origin? or components origin? or my component center of body? What around rotating?

Sorry my stupid questions...

ZsZs.

 

[ZsZs]

I haven't idea how able to rotating a component... :-(

 

[tygerdawg]

this should be enough about transformational math to keep you busy for weeks

http://casgm3.anorg.chemie.uni-tuebingen.de/klaus/nmr/conventions/euler/euler.html

http://mathworld.wolfram.com/EulerAngles.html

http://mathworld.wolfram.com/EulerParameters.html

http://www.euclideanspace.com/maths/geometry/rotations/euler/

http://mathworld.wolfram.com/RotationMatrix.html

TygerDawg
Blue Technik LLC
Advanced Robotics & Automation Engineering

http://www.bluetechnik.com

 

[ZsZs]

Thanks!!!
This is very good!
I understand the rotation, and set my rotation matrix, and it work!

ZsZs.