Android OpenGL 3D picking

Question

I'm on Android OpenGL-ES 2.0 and after all the limitations that come with it, I can't figure out how to take 2D screen touches to the 3D points I have. I can't get the right results.

I'm trying to implement shooting a ray into the point cloud, which I can then compare distances of my points to the ray, finding the closest point.

public class OpenGLRenderer extends Activity implements GLSurfaceView.Renderer {
    public PointCloud ptCloud;
    MatrixGrabber mg = new MatrixGrabber();
...
    public void onDrawFrame(GL10 gl) {

        gl.glDisable(GL10.GL_COLOR_MATERIAL);
        gl.glDisable(GL10.GL_BLEND);
        gl.glDisable(GL10.GL_LIGHTING);

        //Background drawing
        if(customBackground)
            gl.glClearColor(backgroundRed, backgroundGreen, backgroundBlue, 1.0f);
        else
            gl.glClearColor(0.0f, 0.0f, 0.0f, 1.0f);

        if (PointCloud.doneParsing == true) {
            if (envDone == false)
                setupEnvironment();

            // Clears the screen and depth buffer.
            gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT);

            gl.glMatrixMode(GL10.GL_PROJECTION);
            gl.glLoadIdentity();
            GLU.gluPerspective(gl, 55.0f, (float) screenWidth / (float) screenHeight, 10.0f ,10000.0f);

            gl.glMatrixMode(GL10.GL_MODELVIEW);

            gl.glLoadIdentity();
            GLU.gluLookAt(gl, eyeX, eyeY, eyeZ, 
                              centerX, centerY, centerZ, 
                              upX, upY, upZ);

            if(pickPointTrigger)
                pickPoint(gl);


            gl.glPushMatrix();

            gl.glTranslatef(_xTranslate, _yTranslate, _zTranslate);
            gl.glTranslatef(centerX, centerY, centerZ);
            gl.glRotatef(_xAngle, 1f, 0f, 0f);
            gl.glRotatef(_yAngle, 0f, 1f, 0f);
            gl.glRotatef(_zAngle, 0f, 0f, 1f);
            gl.glTranslatef(-centerX, -centerY, -centerZ);

            ptCloud.draw(gl);

            gl.glPopMatrix();
        }
    }
}

Here is my picking function. I've set the location to the middle of the screen just for debugging purposes:

public void pickPoint(GL10 gl){

        mg.getCurrentState(gl);

        double mvmatrix[] = new double[16];
        double projmatrix[] = new double[16];
        int viewport[] = {0,0,screenWidth, screenHeight};

        for(int i=0 ; i<16; i++){
            mvmatrix[i] = mg.mModelView[i];
            projmatrix[i] = mg.mProjection[i];
        }

        mg.getCurrentState(gl);

        float realY = ((float) (screenHeight) - pickY);
        float nearCoords[] = { 0.0f, 0.0f, 0.0f, 0.0f };
        float farCoords[] = { 0.0f, 0.0f, 0.0f, 0.0f };


        GLU.gluUnProject(screenWidth/2, screenHeight/2, 0.0f, mg.mModelView, 0, mg.mProjection, 0,
                    viewport, 0, nearCoords, 0);
        GLU.gluUnProject(screenWidth/2, screenHeight/2, 1.0f, mg.mModelView, 0, mg.mProjection, 0,
                    viewport, 0, farCoords, 0);

        System.out.println("Near: " + nearCoords[0] + "," + nearCoords[1] + "," + nearCoords[2]);
        System.out.println("Far:  " + farCoords[0] + "," + farCoords[1] + "," + farCoords[2]);



      //Plot the points in the scene
        nearMarker.set(nearCoords);
        farMarker.set(farCoords);
        markerOn = true;

        double diffX = nearCoords[0] - farCoords[0];
        double diffY = nearCoords[1] - farCoords[1];
        double diffZ = nearCoords[2] - farCoords[2];

        double rayLength = Math.sqrt(Math.pow(diffX, 2) + Math.pow(diffY, 2) + Math.pow(diffZ, 2));
        System.out.println("rayLength: " + rayLength);

        pickPointTrigger = false;   
    }

Changing the persepctive zNear and Far doesn't have the expected results, how could the far point of a 1.0-1000.0 perspective be 11 units away?

GLU.gluPerspective(gl, 55.0f, (float) screenWidth / (float) screenHeight, 1.0f ,100.0f);
.....
07-18 11:23:50.430: INFO/System.out(31795): Near: 57.574852,-88.60514,37.272636
07-18 11:23:50.430: INFO/System.out(31795): Far:  0.57574844,0.098602295,0.2700405
07-18 11:23:50.430: INFO/System.out(31795): rayLength: 111.74275719790872

GLU.gluPerspective(gl, 55.0f, (float) width / (float) height, 10.0f , 1000.0f);
...
07-18 11:25:12.420: INFO/System.out(31847): Near: 5.7575016,-7.965394,3.6339219
07-18 11:25:12.420: INFO/System.out(31847): Far:  0.057574987,0.90500546,-0.06634784
07-18 11:25:12.420: INFO/System.out(31847): rayLength: 11.174307289026638

Looking for any suggestions or hopefully bugs you see in my code. Much appreciated. I'm Bountying as much as I can (this has been a problem for a while).

Answer 1

I'm working on this, too - it's a very irritating irritating problem. I have two potential leads: 1. Somehow, the resulting z depend on where the camera is, and not how you'd expect. When the camera z is at 0, the resulting z is -1, no matter what winZ is. Up until now I've mainly been looking at the resulting z, so I don't have any exact figures on the other coordinates, but I messed around with my code and your code, just now, and I've discovered that the reported ray-length increases the farther the camera gets from (0,0,0). At (0,0,0), the ray-length is reported to be 0. An hour or so ago, I gathered a bunch of points (cameraZ, winZ, resultZ) and plugged them into Mathematica. The result seems to indicate a hyperbolic sort of thing; with one of the variables fixed, the other causes the resulting z to vary linearly, with the rate of change depending on the fixed variable.

My second lead is from http://www.gamedev.net/topic/420427-gluunproject-question/; swordfish quotes a formula:

WinZ = (1.0f/fNear-1.0f/fDistance)/(1.0f/fNear-1.0f/fFar)

Now, this doesn't seem to match up with the data I collected, but it's probably worth a look. I think I'm going to see if I can figure out how the math of this thing works and figure out what's wrong. Let me know if you figure anything out. Oh, also, here's the formula fitted to the data I collected:

-0.11072114015496763- 10.000231721597817 x - 0.0003149873867479971x^2 - 0.8633277851535017 y + 9.990256062051143x y + 8.767260632968973*^-9 y^2

Wolfram Alpha plots it like so: http://www.wolframalpha.com/input/?i=Plot3D[-0.11072114015496763%60+-+10.000231721597817%60+x+-++++0.0003149873867479971%60+x^2+-+0.8633277851535017%60+y+%2B++++9.990256062051143%60+x+y+%2B+8.767260632968973%60*^-9+y^2+%2C+{x%2C+-15%2C++++15}%2C+{y%2C+0%2C+1}]

---

AHA! Success! As near as I can tell, gluUnProject is just plain broken. Or, nobody understands how to use it at all. Anyway, I made a function that properly undoes the gluProject function, which appears to really be what they use to draw to the screen in some fashion! Code is as follows:

public float[] unproject(float rx, float ry, float rz) {//TODO Factor in projection matrix
    float[] modelInv = new float[16];
    if (!android.opengl.Matrix.invertM(modelInv, 0, mg.mModelView, 0))
        throw new IllegalArgumentException("ModelView is not invertible.");
    float[] projInv = new float[16];
    if (!android.opengl.Matrix.invertM(projInv, 0, mg.mProjection, 0))
        throw new IllegalArgumentException("Projection is not invertible.");
    float[] combo = new float[16];
    android.opengl.Matrix.multiplyMM(combo, 0, modelInv, 0, projInv, 0);
    float[] result = new float[4];
    float vx = viewport[0];
    float vy = viewport[1];
    float vw = viewport[2];
    float vh = viewport[3];
    float[] rhsVec = {((2*(rx-vx))/vw)-1,((2*(ry-vy))/vh)-1,2*rz-1,1};
    android.opengl.Matrix.multiplyMV(result, 0, combo, 0, rhsVec, 0);
    float d = 1 / result[3];
    float[] endResult = {result[0] * d, result[1] * d, result[2] * d};
    return endResult;
}

public float distanceToDepth(float distance) {
    return ((1/fNear) - (1/distance))/((1/fNear) - (1/fFar));
}

It currently assumes the following global variables: mg - a MatrixGrabber with current matrices viewport - a float[4] with the viewport ({x, y, width, height})

The variables it takes are equivalent to the ones that gluUnProject was supposed to take. For example:

float[] xyz = {0, 0, 0};
xyz = unproject(mouseX, viewport[3] - mouseY, 1);

This will return the point under the mouse, on the far plane. I also added a function to convert between a specified distance from the camera and its 0-1...representation...thing. Like so:

unproject(mouseX, viewport[3] - mouseY, distanceToDepth(5));

This will return the point under the mouse 5 units from the camera. I tested this with the method given in the question - I checked the distance between the near plane and the far plane. With fNear of 0.1 and fFar of 100, the distance should be 99.9. I have consistently gotten about 99.8977, regardless of position or orientation of the camera, as far as I can tell. Haha, good to have that figured out. Let me know if you do/don't have any problems with it, or if you want me to rewrite it to take inputs instead of using global variables. Hopefully this helps a few people; I had been wondering about this for a few days before seriously trying to fix it.

---

Hey, so, having figured out how it's supposed to be, I've figured out what they missed in implementing gluUnProject. They forgot (intended not to and didn't tell anyone?) to divide by the fourth element of the resulting vector, which kinda normalizes the vector or something like that. gluProject sets it to 1 before applying matrices, so it needs to be 1 when you're done undoing them. Long story short, you can actually use gluUnProject, but you need to pass it a float[4], and then divide all the resulting coordinates by the 4th one, like so:

float[] xyzw = {0, 0, 0, 0};
android.opengl.GLU.gluUnProject(rx, ry, rz, mg.mModelView, 0, mg.mProjection, 0, this.viewport, 0, xyzw, 0);
xyzw[0] /= xyzw[3];
xyzw[1] /= xyzw[3];
xyzw[2] /= xyzw[3];
//xyzw[3] /= xyzw[3];
xyzw[3] = 1;
return xyzw;

xyzw should now contain the relevant space coordinates. This seems to work exactly the same as the one I cobbled together. It might be a little bit faster; I think they combined one of the steps.