Question

Greetings all,

As seen in the image,

I have an object named O (set of linestripes).Its object-coordinate system is (x’,y’,z’).
I translate,rotate this object in my OpenGL scene using following code snippet:

glPushMatrix();
 glTranslatef(Oz, Oy,Oz);
 glRotatef(rotationX , 1.0, 0.0, 0.0);  
 glRotatef(rotationY, 0.0, 1.0, 0.0);
 glRotatef(rotationZ, 0.0, 0.0, 1.0); 
contour->render();
glPopMatrix()

;

I have a point called H ,which is translated to (hx,hy,hz) world coordinates using

glPushMatrix();
 glTranslatef(hx,hy,hz);
glPopMatrix();

If I am correct, (Oz,Oy,Oz) and (hx,hy,hz) are world coordinates.

Now,what I want todo is calculate the position of H (hx,hy,hz) relative to O’s object-coordinate system.(x’,y’,z’);
As I understood,I can do this by calculating inverse transformations of object O and apply them to point H.

Any tips on this? Does OpenGL gives any functions for inverse-matrix calculation ? If I somehow found inverse-matrices what the order of multiplying them ?

Note : I want to implement “hammer” like tool where at point H ,I draw a sphere with radius R.User can use this sphere to chop the object O like a hammer.I have implemented this in 2D ,so I can use the same algorithm if I can calculate the hammer position
relative to (x’,y’,z’)

Thanks in advance.

Answer 1

Inverting the matrix would be the general solution, but as far as I can see this isn’t actually a “general” problem. Rather than undoing an arbitrary transformation, you are trying to do the reverse of a known sequence of transformations, each of which can be inverted very simply. If your object-to-world transformation is:

glTranslatef(Ox, Oy, Oz);
glRotatef(rotationX , 1.0, 0.0, 0.0);
glRotatef(rotationY, 0.0, 1.0, 0.0);
glRotatef(rotationZ, 0.0, 0.0, 1.0);

Then the world-to-object inverse is just:

glRotatef(-rotationZ, 0.0, 0.0, 1.0);
glRotatef(-rotationY, 0.0, 1.0, 0.0);
glRotatef(-rotationX , 1.0, 0.0, 0.0);
glTranslatef(-Ox, -Oy, -Oz);

Basically, just back out each applied transformation in the opposite order originally applied.