Android OpenGL ES 2.0：围绕特定点旋转对象

Question

I want to rotate an element around a specific point defined by me and dynamically changed.

I am orientating myself at the guidelines from the google developers site .

My first approach is this:

scratch = new float[16];
Matrix.setIdentityM(mRotationMatrix, 0);
Matrix.setRotateM(mRotationMatrix, 0, angle, 0, 0, 1f);
Matrix.multiplyMM(scratch, 0, mMVPMatrix, 0, mRotationMatrix, 0);
element.draw(scratch);

This rotates the object around the center of the screen.

What do I have to add/change to make the object rotate around some other point?

Answer 1

Add a translation operation.

Grafika's Sprite2d class provides an example:

/**
 * Re-computes mModelViewMatrix, based on the current values for rotation, scale, and
 * translation.
 */
private void recomputeMatrix() {
    float[] modelView = mModelViewMatrix;

    Matrix.setIdentityM(modelView, 0);
    Matrix.translateM(modelView, 0, mPosX, mPosY, 0.0f);
    if (mAngle != 0.0f) {
        Matrix.rotateM(modelView, 0, mAngle, 0.0f, 0.0f, 1.0f);
    }
    Matrix.scaleM(modelView, 0, mScaleX, mScaleY, 1.0f);
    mMatrixReady = true;
}

This positions the object, then rotates it around the center of the object.

Answer 2

You need to translate the matrix in the reverse direction of the point first, then rotate and then translate it back. Look at it as if the rotation is always rotating around the center of the world, and the translation moves the center of the world.

Something like this (untested):

scratch = new float[16];
Matrix.setIdentityM(mRotationMatrix, 0);
Matrix.translateM(mRotationMatrix, 0, -x, -y, -z);
Matrix.rotateM(mRotationMatrix, 0, angle, 0, 0, 1f);
Matrix.translateM(mRotationMatrix, 0, x, y, z);
Matrix.multiplyMM(scratch, 0, mMVPMatrix, 0, mRotationMatrix, 0);
element.draw(scratch);

The x , y and z values need to be calculated as the delta between the current position of the object in the world and the position of the point you want to rotate around. You need to do that calculation yourself, but that's pretty trivial.