Android中SensorManager.getRotationMatrix函數原理解釋

    SensorManager是Android中的一個類，其有一個函數getRotationMatrix，可以計算出旋轉矩陣，進而通過getOrientation求得設備的方向（航向角、俯仰角、橫滾角）。函數getRotationMatrix的源碼如下所示，源碼中雖然對該函數整體進行了解釋，但是對代碼中各個參數的計算沒有說明，如為什么加速度的數值要和磁力計的數值做差乘。在網上各種搜索后，找到一段老外對這個問題的英文解釋，很好的回答了上述問題。大意翻譯（包括自己的理解）如下：加速度數值和磁力計數值均是向量，手機水平放置時，加速度讀數實際上就是重力向量，方向是豎直朝下的；磁力計表示本地的磁場，不考慮環境影響及磁偏角的話，認為磁場方向是水平南北朝向的。因此，代碼中首先對加速度和磁力計數據做了一個差乘，得出一個水平東西方向的向量（差乘的定義）。經過這個運算，本來只有一個平面的向量，變成了三個三維立體平面的向量，從而可以用來計算設備的方向。源碼中后面又做了一次差乘，是用計算出的水平東西方向的向量和重力向量做的差乘，這次運算重新得出一個水平南北方向的向量，最后旋轉矩陣中用這三個向量（兩個計算出的水平向量、一個重力向量）構成。   

1、SensorManager.getRotationMatrix

    public static boolean getRotationMatrix(float[] R, float[] I,
            float[] gravity, float[] geomagnetic) {
        // TODO: move this to native code for efficiency
        float Ax = gravity[0];
        float Ay = gravity[1];
        float Az = gravity[2];
        final float Ex = geomagnetic[0];
        final float Ey = geomagnetic[1];
        final float Ez = geomagnetic[2];
        float Hx = Ey*Az - Ez*Ay;
        float Hy = Ez*Ax - Ex*Az;
        float Hz = Ex*Ay - Ey*Ax;
        final float normH = (float)Math.sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
        if (normH < 0.1f) {
            // device is close to free fall (or in space?), or close to
            // magnetic north pole. Typical values are  > 100.
            return false;
        }
        final float invH = 1.0f / normH;
        Hx *= invH;
        Hy *= invH;
        Hz *= invH;
        final float invA = 1.0f / (float)Math.sqrt(Ax*Ax + Ay*Ay + Az*Az);
        Ax *= invA;
        Ay *= invA;
        Az *= invA;
        final float Mx = Ay*Hz - Az*Hy;
        final float My = Az*Hx - Ax*Hz;
        final float Mz = Ax*Hy - Ay*Hx;
        if (R != null) {
            if (R.length == 9) {
                R[0] = Hx;     R[1] = Hy;     R[2] = Hz;
                R[3] = Mx;     R[4] = My;     R[5] = Mz;
                R[6] = Ax;     R[7] = Ay;     R[8] = Az;
            } else if (R.length == 16) {
                R[0]  = Hx;    R[1]  = Hy;    R[2]  = Hz;   R[3]  = 0;
                R[4]  = Mx;    R[5]  = My;    R[6]  = Mz;   R[7]  = 0;
                R[8]  = Ax;    R[9]  = Ay;    R[10] = Az;   R[11] = 0;
                R[12] = 0;     R[13] = 0;     R[14] = 0;    R[15] = 1;
            }
        }
        if (I != null) {
            // compute the inclination matrix by projecting the geomagnetic
            // vector onto the Z (gravity) and X (horizontal component
            // of geomagnetic vector) axes.
            final float invE = 1.0f / (float)Math.sqrt(Ex*Ex + Ey*Ey + Ez*Ez);
            final float c = (Ex*Mx + Ey*My + Ez*Mz) * invE;
            final float s = (Ex*Ax + Ey*Ay + Ez*Az) * invE;
            if (I.length == 9) {
                I[0] = 1;     I[1] = 0;     I[2] = 0;
                I[3] = 0;     I[4] = c;     I[5] = s;
                I[6] = 0;     I[7] =-s;     I[8] = c;
            } else if (I.length == 16) {
                I[0] = 1;     I[1] = 0;     I[2] = 0;
                I[4] = 0;     I[5] = c;     I[6] = s;
                I[8] = 0;     I[9] =-s;     I[10]= c;
                I[3] = I[7] = I[11] = I[12] = I[13] = I[14] = 0;
                I[15] = 1;
            }
        }
        return true;
    }
    

2、英文原文解釋

If I understand your problem correctly you want your phone to know its 3D orientation. You need at least two vectors to do that. The xyz accelerometer produces a gravity vector that goes straight down. An xyz magnetometer can provide a second vector that is horizontally towards magnetic north and vertically downward in the northen hemisphere. The cross-product of these two vectors will be horizontal the magnetic east-west directions and the cross-product between the east-west vector and the gravity vector will be horizontal in the magnetic north-south directions. Formulas exist for converting magnetic to geographical north although I don't know them offhand. An xyz accelerometer by itself produces just the gravity vector, which could allow you to use your cell phone as an electronic bi-directional level (lateral and axial to the orientation of the accelerometer).

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