Movement of a surgical robot's arm OpenGL

Question

I have a question concerning surgical robot arm's movements in OpenGL.

Our arm consists of 7 pieces that suppose to be the arm's joints and they are responsible for bending and twisting the arm. We draw the arm this way: first we create the element which is responsible for moving the shoulder like "up and down" and then we "move" using Translatef to the point in which we draw the next element, responsible for twisting the shoulder (we control the movement using Rotatef) and so on with the next joints (elbow, wrist).

The point is to create an arm that can make human-like movements. Our mechanism works, but now our tutor wants us to draw a line strip with the end of the arm. We put the code responsible for drawing and moving an arm between push and pop matrix, so it works like in real, I mean when we move the soulder, any other elements in arm also moves.

There is a lot of elements moving, rotating, we have a couple of rotate matrices that are attached to different elements which we can control and now we have no idea how to precisely find a new location of the end of an arm in space to be able to add a new point to a line strip. Anyone can help?

    glGetFloatv(GL_MODELVIEW_MATRIX,mvm2);

     x=mvm2[12];
     y=mvm2[13];
     z=mvm2[14];

     glPointSize(5.0f);
     glColor3f(1.0f, 0.0f, 0.0f);

     glBegin(GL_POINTS);
     glVertex3f(x,y,z);
     glEnd();

When I checked using watch what are the x,y,z values, I got (0,-1.16-12e,17.222222), what can't be true, as my arm has length about 9.0 (on z-axis). I think only the last column of modelview matrix is important and I don't have to muliply it by local coordinates of the vertex, as the they are (0,0,0) since I finish my drawning here.

Answer 1

If you're supposed to use glGetFloatv, then this refers to calling it with the GL_MODELVIEW_MATRIX argument, which returns the current model view matrix. You can then use this matrix to transform a point from the coordinate system of the hand to the world space CS.

However, calling glGetFloatv is bad practice, as it will probably result in reduced rendering performance. I think you should talk to your tutor about teaching outdated and even deprecated functionality, maybe he can get the prof to update the materials.

Edit: Your code for retrieving the translation is correct. However, you can't draw the point with the same model view matrix applied. Before drawing it, you have to reset the model view matrix with glLoadIdentity or by popping .

Answer 2

we have no idea how to precisely find a new location of the end of an arm in space to be able to add a new point to a line strip.

You do this by performing the matrix math and transformations yourself.

(from comment)

To do this we are suppose to multiply the matrices and get some information out of glGetFloatv

Please don't do this. Especially not if you're supposed to build a pretransformed line strip geometry yourself. OpenGL is not a matrix math library and there's absolutely no benefit to use OpenGL's fixed function pipeline matrix functions. But it has a lot of drawbacks. Better use a real matrix math library.

Your robot arm technically consists of a number of connected segments where each segment is transformed by the composition of transformations of the segments upward in the transformation hierachy.

M_i = M_{i-1} · (R_i · T_i)

where R_i and T_i are the respective rotation and translation of each segment. So for each segment you need the individual transform matrix to retrieve the point of the line segment.

Since you'll place each segment's origin at the tip of the previous segment you'd transform the homogenous point (0,0,0,1) with the segment's transformation matrix, which has the nice property of being just the 4th column of the transformation matrix.

This leaves you with the task of creating the transformation matrix chain. Doing this with OpenGL is tedious. Use a real math library for this. If your tutor insists on you using the OpenGL fixed function pipeline please ask him to show you the reference for the functions in the specicifications of a current OpenGL version (OpenGL-3 and later); he won't find them because all the matrix math functions have been removed entirely from modern OpenGL.

For math libraries I can recommend GLM, Eigen (with the OpenGL extra module) and linmath.h (self advertisement). With each of these libraries building transformation hierachies is simple, because you can create copies of each intermediary matrix without much effort.