Android中SensorManager.getRotationMatrix函數原理解釋

標籤：

    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求得裝置的方向（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瞭解釋，但是對代碼中各個參數的計算沒有說明，如為什麼加速度的數值要和磁力計的數值做差乘。在網上各種搜尋後，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資料做了一個差乘，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，從而可以用來計算裝置的方向。源碼中後面又做了一次差乘，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，最後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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Android中SensorManager.getRotationMatrix函數原理解釋