What's the math behind CMatrix4::transformVect(vector3df)

[fabietto]

Dear all,

first of all let me apologise if I'm not posting on the proper forum section (obviously, in case feel free to move my post).

As a poor computer scientist lacking a serious background in math/geometry, I'm wondering what's the math behind the transformVect function. Whenever I've experienced the need of moving an object across a 3D space I've always relied on code similar to the one posted below:

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vel = vector3df(0.0f, 0.0f, distance);
m.setRotationDegrees(currentRotation);	
m.transformVect(vel);
coordinates += vel;

But what sort of operations the m.transformVect(vel) instruction applies on the vel matrix? I looked across the Irrlicht sources, but couldn't find where that function is implemented. Furthermore, as far as you know there is a simple way to express in a mathematical way these operations (I'm writing a paper right now and I'd like to express in mathematically correct terms what happen when I use a function such the one posted above)?

Thanks all for your attention!

[CuteAlien]

The implementation is in matrix4.h

[fabietto]

The implementation is in matrix4.h

Me idiot. Looking at the documentation I obviously noticed that the function was defined in matrix4.h, but I thought only the prototype was there. So I spent minutes looking for a matrix4.cpp or similar (without any luck as you can guess... ).

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template <class T>
	inline void CMatrix4<T>::transformVect( vector3df& vect) const
	{
		f32 vector[3];

		vector[0] = vect.X*M[0] + vect.Y*M[4] + vect.Z*M[8] + M[12];
		vector[1] = vect.X*M[1] + vect.Y*M[5] + vect.Z*M[9] + M[13];
		vector[2] = vect.X*M[2] + vect.Y*M[6] + vect.Z*M[10] + M[14];

		vect.X = vector[0];
		vect.Y = vector[1];
		vect.Z = vector[2];
	}

I guess M is the current matrix (which in my case is the result of m.setRotationDegrees(currentRotation)), right?

[CuteAlien]

I guess M is the current matrix (which in my case is the result of m.setRotationDegrees(currentRotation)), right?

Hehe - check that matrix4.h file some more, M is even explained in there ;-) ("//! Matrix data, stored in row-major order")

[fabietto]

Hehe - check that matrix4.h file some more, M is even explained in there ("//! Matrix data, stored in row-major order")

Thanks, dude, I think I finally obtained what I was looking for...

Just to summarise my thoughts, let consider again the code I posted above (assuming currentRotation and coordinates two vector3df objects respectively containing the rotation of a 3D body around the three axis and its coordinates; m a CMatrix4; distance a float variable):

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vel = vector3df(0.0f, 0.0f, distance); 
m.setRotationDegrees(currentRotation);    
m.transformVect(vel); 
coordinates += vel;

m.setRotationDegrees(currentRotation) calls in turn setRotationRadians and assigns values to m[0], m[1], m[2], m[4], m[5], m[6], m[8], m[9], m[10] (I believe m[3], m[7], m[11+] are = 0, am I right?).

m.transformVect(vel) transforms vel in the following way (in my scenario m[12], m[13] and m[14] are equal to 0, as well as vel.X and vel.Y, thus I've removed all of these factors from the formulas below):

vel.X = vel.Z * m[8]
vel.Y = vel.Z * m[9]
vel.Z = vel.Z * m[10]

The new coordinates are then calculated simply as coordinates + vel.

In other terms (if my above considerations are correct) I might conclude that:

coordinates(t+1) = coordinates(t) + distance * (vel.Z * m[8], vel.Z * m[9], vel.Z * m[10]).

Hope I haven't written too much bullshit...

[fabietto]

And, in more technical terms, the result should be something like the following (couldn't copy/paste from LaTeX, sorry - I also just noticed there is a "both" too much within the text, while a "a" is missing):



I can't pretend anything, of course, but if anyone might want to give a look to it that would be ENORMOUSLY appreciated!