OpenGL，围绕ELEMENT中心向下平移y并在z上旋转（在Android上）

Question

I have an orthogonal perspective which I initialize like so:

gl.glViewport(0, 0, Constants.SCREEN_WIDTH, Constants.SCREEN_HEIGHT);   
gl.glMatrixMode(GL10.GL_PROJECTION);    
gl.glLoadIdentity();                    
gl.glOrthof(0,Constants.GAME_AREA_WIDTH, Constants.GAME_AREA_HEIGHT, 0, 1, 10);
gl.glMatrixMode(GL10.GL_MODELVIEW);     
gl.glLoadIdentity();

What I want to do here is have a square start off the top of the screen (at like (x,-100,z) and the that square should descend (on y) while at the same time roate (on z).

The square's upper-left is what I use as reference for the square's position.

Ok, now, I think I get how to roate it around itself. I translate the thing to (-squareSize/2, -squareSize/2,z), rotate it along z, then translate back. And indeed, if I only test this rotation it works ok:

    gl.glLoadIdentity();
    angle = angle + 3;
    if(angle>360) {
        angle = angle - 360;
    }
    gl.glTranslatef(xCurrent+size/2, yCurrent+size/2,0);
    gl.glRotatef(angle, 0, 0, 1);
    gl.glTranslatef(-(xCurrent+size/2), -(yCurrent+size/2),0);
//omitted: enable client state, draw elements, disable client state.

With just this, no matter where I place my square (even small negative values for x and y which only make it partially show on the screen), it will rotate around its center.

However I can't figure out how to add the downwards translation on y. If I do something like this:

    angle = angle + 3;
    if(angle>360) {
        angle = angle - 360;
    }
    gl.glTranslatef(xCurrent+size/2, yCurrent+size/2,0);
    gl.glRotatef(angle, 0, 0, 1);
    gl.glTranslatef(-(xCurrent+size/2), -(yCurrent+size/2),0);

    yCurrent = yCurrent + realSpeed;
    if(yCurrent>Constants.GAME_AREA_HEIGHT+size) {
        yCurrent=-size;
    }
    gl.glTranslatef(0f, yCurrent,0f);

it will only work ok if my square start at (0,0,z) - in which case it will move down and rotate around it's center.

If however I start it at any positive or negative non 0 value for either x or y, it will still move down, but do a weird spiral motion instead of rotating agains its center.

Answer 1

The OpenGL matrix stack post multiplies. Which effectively means that you should do the most local transformation last.

So what you probably want to do is to perform a glTranslatef to the tile's current position, then do the translate/rotate/untranslate sequence to effect your rotation.

Answer 2

Editor's Note: This answer was moved from a question edit, it is written by the Original Poster.

First off, what Tommy sais in the answer below is right, I should first code the translation to the new position, and THEN add the lines of code that do translate/rotate/translate.

Also, the values I asign to x and y when wanting to translate the center of the square to coordinates (0,0,z) are simply wrong, I misscalculated them. The basic idea here is this. Let's say a square has the following vertices:

private static float xLeft = -0.75f;
private static float xRight = +0.25f;
private static float yTop = 2f;
private static float yBottom = 1f;
protected static float vertices[] = { 
        //x      y        z
        xLeft,  yTop,    -5f,   //Top left      triangle1-1     triangle2-1
        xRight, yTop,    -5f,   //Top right     triangle1-2
        xLeft,  yBottom, -5f,   //Bottom left                   triangle2-3
        xRight, yBottom, -5f    //Bottom right  triangle1-3     triangle2-2
}; 

then the translation amounts needed to place this square's center at (0,0,z) are:

private float xCenterTranslation = (xRight+xLeft)/2f;
private float yCenterTranslation = (yTop+yBottom)/2f;

and the code for translating the square on the y axis while at the same time rotating it along its center is:

gl.glTranslatef(0, translationAmountLinearY, 0); //translate on y
//decrement Y translation for next rendering
translationAmountLinearY+=translationDeltaLinearY;

gl.glTranslatef(xCenterTranslation, yCenterTranslation, 0);//translate BACK from center
gl.glRotatef(rotationAmountZDegrees, 0, 0, 1);//rotate
gl.glTranslatef(-xCenterTranslation, -yCenterTranslation, 0);//translate to center
//increment z rotation for next rendering: 
rotationAmountZDegrees+=0.04f;